*Article* **Reexamining Different Factors of the Resonance-Enhanced High-Order Harmonic Generation in Atomic and Nanoparticle Laser-Induced Tin Plasmas**

**Rashid A. Ganeev 1,2,3,4,\* and Hiroto Kuroda 1,5,6**


**Abstract:** We reexamine the resonance enhancement of a single harmonic emission during the propagation of ultrafast pulses through atomic and nanoparticle tin-containing laser-induced plasma (LIP). We compare the single atomic Sn and Sn nanoparticle plasmas to demonstrate a distinction in the enhancement factor of the single harmonic in the case of fixed and tunable near-infrared pulses. The analysis of the dynamics of Sn LIP shows the range of optimal delays between heating and driving pulses (130–180 ns), at which the maximal harmonic yield can be achieved. The enhancements of the 17th and 18th harmonics of 806 nm pulses were analyzed in the case of single-color and two-color pumps of LIP, showing up to a 12-fold enhancement of even harmonics in the two-color pump case. We show the enhancement of a single harmonic in the vicinity of the 4d105s25p2P3/2→4d95s25p2 transitions of Sn II ions and demonstrate how this process depends on the constituency of the plasma components at different conditions of target ablation. The application of tunable (1280–1440 nm) radiation allows for demonstrating the variations of single harmonic enhancement using a two-color pump of Sn-containing LIP.

**Keywords:** high-order harmonic generation; nanoparticles; tin plasma; resonance enhancement of harmonics

#### **1. Introduction**

Resonance-related effects play an important role in different fields of laser physics and optics. The interest in these effects is related to the possibility of improving various processes during light–matter interactions. One example of the application of the resonance effects in nonlinear optics is the enhancement of high-order harmonic yield during the interaction of strong laser pulses with gases and laser-induced plasmas (LIPs). The studies of this process during the high-order harmonic generation (HHG) of ultrafast laser pulses have been the topic of different publications over the last two decades [1–18]. The HHG model describing the enhancement of the harmonic coinciding with the transition between the ground and the autoionizing states of ions has been developed in [10]. The third (recombination) step of the three-step scenario of HHG was partitioned into two steps: the capture of a laser-accelerated electron onto an autoionizing state of the parent ion, followed by the radiative relaxation of this state to the ground state with the emission of the harmonic photon. Probably, this scenario of resonance HHG could be applied to ionized large particles as well.

HHG in LIPs has actively been studied using different ablated media (bulk metals, organic materials, multiparticle-contained powders, etc. [19–41]). It was mentioned

**Citation:** Ganeev, R.A.; Kuroda, H. Reexamining Different Factors of the Resonance-Enhanced High-Order Harmonic Generation in Atomic and Nanoparticle Laser-Induced Tin Plasmas. *Appl. Sci.* **2021**, *11*, 2193. https://doi.org/10.3390/ app11052193

Academic Editor: Alessandro Belardini

Received: 6 February 2021 Accepted: 26 February 2021 Published: 3 March 2021

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in previous studies that the enhancement of the resonance harmonics compared with the neighboring ones—in the case, of the nanoparticle-containing plasmas—was notably smaller than in the case of the monomer-containing plasmas [33]. Additionally, different issues require further consideration, once one considers the resonance processes as the suitable method for a single harmonic enhancement. Particularly, tin-containing plasmas, which have earlier been examined as a suitable medium for the demonstration of this effect [42,43], allow for analyzing different processes in various constituents of LIPs. Additionally, the availability of tunable laser sources would allow for determining the influence of the detuning out of resonances on the enhancement factor of a single harmonic.

In this paper, we reexamine the single harmonic resonance enhancement during the propagation of the ultrafast pulses through tin-containing LIP. We demonstrate the enhancement of the 17th and 18th harmonics of 806 nm pulses in the case of different (single-color and two-color) pumps and compare the single atomic Sn and Sn nanoparticle LIPs to demonstrate a distinction in the enhancement factor of a single harmonic in the case of tunable near-infrared (NIR) pulses. The application of tunable (1280–1440 nm) radiation allows for demonstrating the variations of single harmonic enhancement using a two-color pump of Sn-containing plasma.

#### **2. Materials and Methods**

Bulk tin (Sn) and Sn nanoparticles (NPs; 70 nm, Sigma-Aldrich, St. Louis, MO, USA), glued onto a glass substrate, were ablated by different laser pulses to form LIP, with further HHG during the propagation of femtosecond laser pulses. The part of uncompressed radiation from a Ti: sapphire laser (central wavelength of 806 nm, pulse duration of 370 ps, pulse energy of 10 mJ, and a pulse repetition rate of 10 Hz) was used as a heating pulse (HP) for the target ablation (Figure 1). We also used a Nd: YAG laser for target ablation, using 1064 nm, 10 ns pulses.

**Figure 1.** Experimental scheme. DP: driving pulse; HP: heating pulse; T: target; P: laser-induced plasma; H: harmonic emission; XUVS: extreme ultraviolet spectrometer.

The focused compressed (64 fs) driving pulses (DP) were propagated through the LIP at a distance of 0.2 mm above the target surface. Apart from the single-color pump (SCP; 806 nm) of plasmas, we used the two-color pump (TCP; 806 nm and 403 nm) to generate odd and even harmonics. A 0.2 mm-thick beta-barium borate (BBO; type I) crystal was inserted into the vacuum chamber in the path of the focused 806 nm driving pulses to generate a second harmonic (λ = 403 nm, 3% conversion efficiency).

We also used an optical parametric amplifier (OPA), pumped by the above-described laser, to apply the tunable NIR DP for HHG in the LIP. The signal pulses from the OPA were used as the DP (0.8 mJ, 70 fs, 1280 nm). The intensity of the focused NIR DP inside the LIP was 2 × <sup>10</sup><sup>14</sup> W cm−2. Most of the experiments using the OPA were carried out using the TCP of the LIP. We used the second harmonic (H2) of the signal pulses to apply the TCP scheme (NIR and H2) for HHG in the plasma.

The harmonic radiation was analyzed using an extreme ultraviolet (XUV) spectrometer containing a gold-coated spherical mirror and a 1200 grooves/mm flat-field grating with variable line spacing. The spectrum was recorded on a micro-channel plate (MCP) detector with a phosphor screen, which was imaged onto a charge-coupled device (CCD) camera. The movement of the MCP along the focusing plane of the flat-field grating allowed for the observation of harmonics in different regions of the XUV spectrometer.

#### **3. Results**

#### *3.1. 806 nm Pump*

The upper panel of Figure 2 shows the raw image of the spectral distribution of plasma emission during ablation of the tin bulk target, using a 370 ps HP at a fluence of F = 3.2 J cm<sup>−</sup>2. This spectrum was collected without the propagation of a 64 fs DP through the plasma plume and is shown for the demonstration of various emission lines from highly-ionized tin LIP. The application of such plasma for HHG has two drawbacks: the first disadvantage is associated with strong incoherent radiation in the range of harmonic generation, which can entirely overlap later radiation, and the second disadvantage is related to a deterioration of the optimal phase-matching conditions between driving and harmonic waves. The latter disadvantage leads to a reduction or entire disappearance of harmonic emissions due to a phase mismatch of the interacting waves. In addition, it also affects the conditions for the resonant amplification of harmonics. The propagation of femtosecond pulses through this plasma did not result in harmonic generation or allow for the observation of the weak lower-order harmonics.

**Figure 2.** Raw images of plasma (upper panel) and harmonic (bottom panel) emission spectra. Upper and bottom lines show the calibrated wavelength (in nm) and harmonic axes, respectively.

To achieve the efficient generation of harmonics, we used a twice smaller fluence of 370 ps pulses on the target surface (1.6 J cm−2) when no lines attributed to the ionic transitions in this spectral range were observed (bottom panel of Figure 2). The propagation of the DP through such LIP resulted in the generation of an XUV spectrum, comprising the harmonics of 806 nm radiation up to the 21st order (H21). One can see a strong emission attributed to the resonance-enhanced H17 (λ = 47.4 nm), which notably exceeded the nearby harmonics. These studies were performed at a 150 ns delay between the HP and the DP. One can see that the strong H17 almost coincides with the positions of some weak emission lines of the plasma (upper panel of Figure 2). This harmonic was 4 to 10 times stronger than the nearest harmonic orders.

The raw images of the harmonic spectra provide a better comparative view of the plasma and harmonic emissions. The bottom image of Figure 2 shows the common feature of the gradually decaying plateau-like harmonic distribution along the whole studied XUV spectrum except for the single-enhanced harmonic (H17). These raw images were taken at the saturation conditions of the CCD camera for better viewing of the peculiarities of the harmonic distribution. Notice that all line-outs of the harmonic spectra shown in the following figures were taken using the images collected at the unsaturated conditions of registration.

We used two methods to analyze the dynamics of tin plasma spreading out from the target surface. Apart from the plasma emission spectra, we first analyzed the images of the plasma at different moments from the beginning of ablation. Useful information about ablated species can be retrieved by recording the spatial dynamics of the spreading of the plasma plume using a gated intensified charge-coupled device (ICCD) camera, which was used for imaging of the spreading tin LIP within a time interval ranging from 0 to 2000 ns with a variable time gate. In this case, we used 1064 nm, 10 ns pulses as the HP. The used HP energy (EHP = 20 mJ) was higher than that used for the harmonic generation, for better visibility of the plasma plume, while the overall dynamics of the plasma formation and spreading were similar, thus allowing for the determination of the main regularities.

At the initial moments from ablation (i.e., up to 50 ns), the LIP was spatially limited inside the dense and very bright small volume. As it was shown by analysis of the timeresolved spectra of the ns-induced LIP in the visible region [44], a strong continuum emission can be seen at the early periods of plasma dynamics. Neutral emission peaks were not evident at early times in the case of the ns-induced plasma spectra and required longer delays to appear. Additionally, they showed lower intensities compared to the ionic emissions at the early stages. This is attributed to a higher population of the charged ions emitting in the visible region compared to the neutral atoms, though once these ion populations decreased due to recombination processes in the LIP, at later times the emissions from neutral species became a dominating factor. Images in the case of the time delays above 100 ns show a small, expanded laser plume up to a distance of 1.2 mm from the surface of the bulk tin. Due to high brightness, we suppressed emissions by placing neutral filters in front of the ICCD camera. At a period of 200 ns from the ablation, the fastest components of plasma expanded up to a distance up to 2.5 mm. However, their role in harmonic generation is questionable due to a small concentration of these fast components of LIP. We analyzed the images of plasma up to 2000 ns from the beginning of ablation, when a weak, low-dense cloud of plasmas was still seen in the images.

The second method of the plasma dynamics studies was based on the analysis of the variations of harmonic emissions at different delays between the HP and the DP using a two-laser (Ti: sapphire and Nd: YAG) configuration. In this case, HHG spectra from Sn plasma were recorded at different delays between a 10 ns HP and a 64 fs DP. The intensity dependencies of the 11th (H11) and 15th (H15) harmonics on the delay between the HP and the DP are shown in Figure 3A. For this plasma, the maximum delay up to which we were able to observe HHG emission was equal to ~500 ns, at which a very weak emission of the lowest recorded harmonic (H9) was still seen in the XUV spectrum. We observed the clearly determined maximal yields of both H11 and H15 at the same (~150 ns) delay from the beginning of ablation. This pattern can be explained by the presence of the same type of emitters within the whole period of observation, when a decrease of plasma density, due to its expansion, causes the decay of the harmonic yield. The velocity of these emitters, according to optimal delay, can be estimated at ~1.3 × <sup>10</sup><sup>3</sup> m/s, taking into account the 0.2 mm distance between the target and the axis of DP propagation. Notice that a similar range of the "optimal" delays (140–200 ns) between the HP and the DP corresponded to the observation of the maximal harmonic yield in the case of the ablated Sn NP LIP.

**Figure 3.** (**A**) Variations of the 11th (open triangles) and 15th (filled circles) harmonic yields at different delays between the heating and driving pulses. The fluence of heating pulses on the tin surface was 1.5 J cm<sup>−</sup>2. (**B**) Raw images of harmonics in the case of a two-color pump (TCP; 806 nm and 403 nm, upper panel) and a single-color pump (SCP; 806 nm, bottom panel) of tin plasma. Arrows show the maximally enhanced harmonics and their second-order (S.O.) diffractions from the flat-field grating in the case of the two types of pumps.

One can note that during the ablation of bulk Sn, the plasma may contain tin atoms and ions, as well as NPs synthesized during laser ablation. The appearance of Sn nanoparticles was commonly registered at the relatively high fluencies of HP (F ≈ 3 J cm−2). The transmission electron microscope (TEM) analysis of the debris deposited on the nearby glass substrates while using this fluence of either picosecond or nanosecond HP revealed the presence of sparsely distributed NPs with sizes ranging between 2 and 10 nm. Once again, we emphasize that this mode of plasma formation was unsuitable for generating harmonics in Sn LIP. The use of the fluence F = 1.5 J cm−2, at which the strongest yield of harmonics from this plasma was achieved, did not reveal the presence of NPs in the deposited debris. Thus, the harmonics, in this case, originated from the atoms and ions of tin.

In these experiments, the femtosecond pulses were delayed with respect to those from the Nd: YAG laser to propagate through the formed plasma at a maximal density of the ejected particles. The synchronization of the femtosecond and nanosecond lasers was accomplished using a digital delay generator, and the delay between the HP and the DP was varied in the range of 0 to 1000 ns. We were also able to analyze the plasma and harmonic dynamics at high delays, spanning from a few units to several hundred microseconds. However, apart from the delay region, in which strong harmonics were observed (100–300 ns, Figure 3A), no harmonics appeared in the microsecond-long delays, thus pointing out the absence of the influence of large mass species on the whole yield of harmonic emissions from the tin LIP.

The application of the TCP to this plasma led to the appearance of a rather stronger difference between the whole set of harmonics and one of them, which was attributed to the influence of a resonance-induced mechanism of the enhancement of a single harmonic in the vicinity of the strong transition of tin ions. In the case of the 0.2 mm-thick BBO, some temporal delay between 806 and 403 nm pulses in the LIP still allowed for the effective interaction, leading to the odd and even harmonics generation, since the trailing part of the second harmonic wave overlaps with the leading part of the 806 nm wave (Figure 3B). Another spectrum appeared in the case of the installation of 0.5 mm-thick BBO on the path of the DP. The harmonic distribution became notably heterogeneous due to an insufficient overlap between the 806 nm and 403 nm pulses, delayed from each other by 95 fs in the plasma area, resulting in the generation of 2(2n + 1) harmonics (H10, H14, H18, and H22), while other even harmonics, corresponding to 4(n + 1) orders (H12, H16, and H20), were almost suppressed.

The most important finding in these TCP studies was the appearance of an exceptionally strong 18th harmonic (upper panel of Figure 3B) notably exceeding the aboveanalyzed 17th harmonic achieved during the SCP of the Sn LIP. Moreover, second-order diffraction of this harmonic caused a stronger image of H9 (upper right arrow), leading to the impression that H9 became stronger in the case of the TCP compared with the SCP (bottom panel of Figure 3B). The prevalence of H18 over H17 could have been caused by a stronger involvement of the resonance processes in the enhancement of the former harmonic emission. The wavelength of this harmonic (H18, λ = 44.8 nm, E = 27.68 eV) was closer to some 4d105s25p2P3/2→4d95s25p2 ionic transitions of tin, possessing strong oscillator strengths (gf). In the meantime, the gf of one of those transitions [4d105s25p2P3/2→4d95s25p2 ( 1D)(2D5/2)], at the wavelength of 47.20 nm, has been calculated to be 1.52, and this value is five times larger than other transitions from the ground state of Sn II [45]. From this point of view, one can expect an almost perfect coincidence of an H17 (<sup>λ</sup> = 47.4 nm) and 4d105s25p2P3/2→4d95s25p2 ( 1D)(2D5/2) transition, and stronger enhancement compared with H18. However, our experiment showed the reverse case when H18 is much stronger than H17.

A few reasons could be responsible for this contradiction. The presence of an even stronger ionic transition of Sn II in the 44 nm range of the XUV spectrum can cause a larger enhancement of H18 with respect to H17. Additionally, the Stark shift of transitions can modify their influence on the harmonic yield. Another option could be the involvement of the Sn III ions [43]. Some of them lie in the vicinity of H18 and their oscillator strengths (gf~0.5) are high enough to cause the resonance enhancement of nearby harmonics. Finally, H18 belongs to the group of 2(2n + 1) even harmonics, which can demonstrate larger conversion efficiency compared with the odd harmonics arising from the 806 nm pump. Notice that the efficiency of harmonics produced by shorter wavelength sources becomes higher due to the strong wavelength-dependent harmonic yield (Iharm ∞ λ−5) (Iharm is the harmonic intensity and λ is the driving field wavelength [46]).

#### *3.2. Tunable NIR Pump*

One can distinguish the importance of tuning the wavelength of the driving pulses to determine the variations of harmonic yields in the case of resonance-related processes. Therefore, the application of OPA-based tunable sources offers large perspectives in these studies. Below, we apply the tunable NIR pulses from the OPA and their second harmonics for the analysis of resonance enhancement in Sn LIP, as well as in Sn NP LIP.

High-order harmonic generation in two media using TCP pulses was optimized by different means (i.e., the fluence of HP, the intensity of DP, the delay between the HP and the DP, the application of BBO crystals of different thickness, etc.). Particularly, relatively stronger ablation of the Sn NP target allowed for the observation of the enhancement of odd and two neighboring harmonics in the vicinity of a strong ionic transition of tin, contrary to the case of the weak ablation of this nanoparticle-containing target. Our TEM studies of Sn NP debris deposited on nearby glass slides showed the presence of the small NPs ranging from 4 to 14 nm. These NPs appeared in the TEM images at the optimal fluencies of HP (F = 1.4–1.7 J cm<sup>−</sup>2), when the maximal harmonic yield was achieved.

The harmonics in the case of the NIR pulses (1 mJ, 1300 nm) were significantly weaker than in the case of the 3 mJ, 806 nm pump, due to a higher intensity of DP in the latter case, and the Iharm ∞ λ−<sup>5</sup> rule. The comparison of these two pumps at similar energies of pulses (1 mJ) showed a four-fold decrease of harmonic yield from the plasma produced on the bulk Sn target in the case of 1320 nm pulses compared with the 806 nm pulses, which, to some extent, corresponds to the theoretical prediction of this ratio (11), taking into account a difference in the spatial distributions of two focused beams in the plasma area. Meanwhile, the harmonic cutoff in the case of the NIR pulses was larger than in the case of 806 nm pulses, in accordance with the expectations in the extension of this parameter for the longer-wavelength pump (Ecutoff ∞ λ2). The harmonic cutoffs in the case of the 806 nm and NIR pump (~1300 nm) pulses were in the range of 42 nm (E = 29.5 eV) and 38 nm (E = 32.6 eV), respectively, while the expected cutoff was calculated to be 76 eV. However, the very small conversion efficiency of higher-order harmonics in the case of NIR pulses did not allow for the observation of harmonics well below the 40 nm spectral region. Thus, the use of 1-mJ NIR pulses for plasma harmonic studies caused the generation of weak odd harmonics in the longer-wavelength range of the XUV spectrum. For this reason, we used the TCP (NIR and H2) of plasma, which proved to enhance the odd harmonic yield. The extension of the harmonic cutoff compared with the single-color pump, the ten-fold growth of the yield of odd harmonics, the comparable harmonic intensities for the odd and even orders along the whole range of generation in spite of using the 0.5 mm-long crystal, contrary to the case of the 806 nm pump, and the tuning of harmonics that allowed for the optimization of resonance-induced single harmonic generation were among the attractive features of these experiments.

The raw images of the harmonic spectra presented in Figure 4 were obtained using NIR pulses (λ = 1370 nm) and the second harmonic of this radiation (λ = 685 nm) during their propagation through the plasma produced on the bulk tin and tin NP targets. As in the case of the 806 nm pump of the Sn LIP, we observed the enhanced harmonic in the region of 47 nm (Figure 4, upper panel). At the used pump conditions, it was the 29th harmonic (H29) of 1370 nm radiation. The application of ablated tin nanoparticles as the media for harmonic generation at the fluence similar to the one used for the ignition of plasma in the case of the tin bulk target (F = 1.4 J cm<sup>−</sup>2) allowed for the increase of the conversion efficiency of a whole set of harmonics (Figure 4, middle panel). The harmonics were extended up to the 31st order. However, no variations from the featureless plateau-like pattern of the envelope of the gradually decaying harmonic distribution were achieved in this case, except for some insignificant differences in the intensities of H29 and neighboring orders. This difference in

the harmonic spectra produced from the plasmas ignited on the bulk Sn and Sn NP targets was attributed to an insufficient amount of ionized single-particle species in the latter case.

**Figure 4.** Raw images of harmonic spectra in the case of 1370 nm and 685 nm pumps of tin-containing plasmas. Upper panel: Plasma produced on the tin bulk target at the fluence F = 1.4 J cm<sup>−</sup>2. Middle panel: Plasma produced on the Sn nanoparticle (NP) target at the fluence F = 1.4 J cm−2. Bottom panel: Plasma produced on the Sn NP target at the fluence F = 2 J cm<sup>−</sup>2. "W.A." and "S.A." correspond to weak and strong ablation of the Sn-containing target.

Changing the ablation conditions of the Sn NP target can lead to the appearance of single-particle species and additional excited states of ions that can, to some extent, amplify the neighboring harmonics. Among different types of ablated substances, tin plasma can be considered as an interesting subject for study since it allows for the modification of the excitation of various autoionizing states, depending on the ablation conditions of the bulk target. The variations of target ablation conditions could allow for the analysis of the nonlinear response of such plasma by comparing the amplification of different harmonics, provided that they coincide or remain close to those autoionizing states responsible for harmonic enhancement. It is interesting to consider this process in the case of the ablation of the targets containing nanoparticles since the modification of their morphology or even the disintegration of NPs onto the small species and atoms can drastically change the distribution of harmonics in the region of interest, where strong ionic transitions can cause the enhancement of harmonics in the case of an atomic/ionic plasma medium.

The fluence of heating 370 ps pulses was increased up to F = 2 J cm−<sup>2</sup> to produce a sufficient amount of Sn ions in the plasma ignited on the NP-containing surface. These conditions of ablation proved to be non-optimal for the efficient generation of harmonics. In this case, we observed the worsening of the phase-matching conditions, leading to a decrease in the conversion efficiency of the lower-order harmonics (bottom panel of Figure 4). The appearance of a large number of free electrons at stronger ablation caused the phase mismatch between the harmonic and driving waves, due to the growing group of velocity dispersion in such LIPs. In the meantime, we achieved the enhancement of a single harmonic and a few following harmonic orders in the area of strong ionic transitions of tin. H29, in this case, was notably stronger than any nearby lower-order harmonic, down to H19. Probably, at these conditions of nanoparticle ablation, they disintegrated in smaller nanoparticles, clusters, and single-atomic species, which can be presented in an ionic state, thus allowing the resonance-related enhancement of harmonics.

To further analyze the observed process of the variation of harmonic distribution at different conditions of DP–LIP interactions, we performed the tuning of the driving NIR pulses in the case of two plasmas. The line-outs of Figure 5A demonstrate the harmonic spectra generated in the plasmas produced on the bulk tin and tin NP powder. The three upper panels show the HHG spectra in the plasma produced on the tin bulk target at optimal conditions of ablation when the maximal yield of harmonics was achieved. The upper panel was obtained in the case of the SCP (1355 nm) of the plasma produced on the bulk Sn. One can see the weakly enhanced harmonic (H29) lying far from the whole set of the observed lower-order harmonics. We also used the TCP (1355 nm and 678 nm) of plasma at a similar wavelength of NIR pulses. Again, as in the case of the SCP, H29 and two neighboring harmonics can be clearly distinguished in the 46–48 nm spectral range. The tuning of the NIR pulses towards the shorter wavelength region (1335 nm) caused the change in the maximally enhanced harmonic order in the case of the TCP (H28, 1335 nm

and 668 nm pumps, third panel) and allowed for the generation of a higher yield of this harmonic compared with the neighboring ones.

**Figure 5.** (**A**) Line-outs of harmonic spectra generated in the plasmas produced on the bulk tin and tin NP powder using tunable near-infrared (NIR) driving pulses. First panel from the top: SCP (1355 nm) of the plasma produced on the bulk Sn. Second panel: TCP (1355 nm and 678 nm) of the plasma produced on the bulk Sn. Third panel: TCP (1335 nm and 668 nm) of the plasma produced on the bulk Sn. Fourth panel: SCP (1320 nm) of the plasma produced on the tin NP powder. Fifth panel: SCP (1350 nm) of the plasma produced on the tin NP powder. Sixth panel: SCP (1370 nm) of the plasma produced on the tin NP powder. Seventh panel: TCP (1320 nm and 660 nm) of the plasma produced on the tin NP powder. (**B**) TEM images of deposited tin NPs during ablation of nanoparticle powder at an optimal fluence of HP. The black markers correspond to 200 nm (upper panel) and 20 nm (bottom panel).

Similar studies were performed in the case of Sn NP LIP. The application of nanoparticles was a part of our efforts to demonstrate the fact that the presence of tin in plasma does not necessarily guarantee the enhancement of a single harmonic. The decrease of oscillator strength of ionic transitions, as well as the detuning of transitions, can cause the difference in the nonlinear optical response of this medium. Meanwhile, the expectation in the application of NPs was related to the stronger effect of single harmonic enhancement, while our studies showed the reverse effect.

The distribution of the harmonic spectrum was notably changed as soon as we ablated the Sn NP target. One can assume similar conditions for the resonance enhancement of H29 in this aggregated structure. However, in the case of the SCP of Sn NP LIP, we did not observe this process. At the used fluence of heating pulses (1.5 J cm−2), we did not see a strengthening of this harmonic, which points out the insignificant amount of the ionic tin component during the disintegration of Sn NPs in these conditions of ablation, independently of the wavelength of NIR DP.

Specifically, the experimental observations were as follows. The fourth panel from the top of Figure 5A shows the harmonic line-out in the case of the SCP (1320 nm) of the plasma produced on the tin NP powder. Only a few harmonics up to H19 generated at these conditions in the studied spectral range (38–89 nm). The optimization of plasma formation and stronger NIR pulses tuned towards 1350 nm allowed for achieving the harmonics up to H33 (fifth panel). At these conditions, no enhancement of the harmonic lying close to the 47 nm region was achieved. The tunings of the DP (1370 nm) also did not result in the generation of enhanced harmonics in the 47 nm region (sixth panel). Finally, the seventh panel shows HHG using the TCP (1320 nm and 660 nm) of the plasma produced on the tin NP powder. Again, we did not see the specific feature of single harmonic enhancement in the above-mentioned XUV range, but rather observed the gradual decay of harmonic yield down to H32. An insignificantly larger yield of H28 shown in this panel may indicate the involvement of the resonance process in the generation of this harmonic (similar to the raw image shown in the middle panel of Figure 4 in the case of 1370 nm and 685 nm pumps). The appearance of all even harmonics, in the case of NIR pulses, using thicker (0.5 mm) BBO crystal, revealed a sufficient spatiotemporal overlap of tunable 1300–1370 nm radiation and its second harmonic emission in LIPs due to a lesser difference in the group velocity dispersion of these pulses in the NIR range.

At these conditions of Sn NP ablation, the analysis of debris from the ablated area showed the presence of notably smaller NPs compared with the original 70 nm species glued on the glass substrates. Figure 5B shows two TEM images with different magnification factors of the debris deposited on the nearby substrates, which allow for the determination of the presence of a broad range of the dimensions of nanoparticles (between a few units of nm up to 15 nm). Some smaller clusters yet resolved in these images, being in a plasma state, could be responsible for the resonance enhancement of a single harmonic.

The studies of harmonics using idler pulses (1600–2400 nm) were carried out as well. The harmonics were generated using the wavelengths of a pump close to the regenerative regime of the OPA (1600 nm), due to higher pulse energy. The experiments were carried out in the 1600–1900 nm range. The application of these longer wavelength pumps led to a notable decrease in harmonic generation efficiency due to the Iharm ∞ *λ*−<sup>5</sup> rule. Only the two-color pump configuration was suitable, in this case, to generate odd and even harmonics, while the application of the single-color pump led to a notably weaker harmonic emission. This observation, as well as the above-presented data, points out the attractiveness of the two-color pump over the single-color pump for harmonic generation in laser-induced plasmas, independently on the spectral range of emissions of the fundamental radiation.

#### **4. Discussion**

The most important feature of these studies was the availability in the analysis of the excited states influencing the harmonic distribution at different excitation conditions of the ablating target. We presented the results of the harmonic spectra modification using tunable driving two-color (NIR and H2) orthogonally polarized pulses, which led to the observation of the resonance enhancement of some harmonic orders caused by different states of plasmas. Studying resonance-induced enhancement of harmonics using tunable NIR and H2 pulses provides the opportunity to fine-tune this high-order nonlinear optical process for wavelength-dependent enhancement of the harmonic yield. This advantage underlines the attractiveness of the analysis of metals, semiconductors, multi-particle systems, and so forth, and, particularly, of the oscillator strengths of some ionic transitions using the plasma HHG technique. Thus, this approach could be considered as a new method of nonlinear spectroscopy.

The second field (403 nm or 685 nm) breaks the inversion symmetry, which allows for the observation of even harmonics generation forbidden in the case of the 806 nm and 1370 nm pumps. The interaction of a strong fundamental wave (806 nm or 1370 nm) and a weak second harmonic wave (403 nm or 685 nm) in the LIP becomes a sufficient factor to drastically change the spectral pattern of harmonic emissions. Notice that, in this case, the yields of even harmonics were comparable with those of odd ones, in spite of a ~30:1 ratio of the energies of two pumps. The demonstrated effect shows that aweak second field serves as a trigger for the notable change of this nonlinear optical process.

Most of our studies were performed at the fluence F = 1.6 J cm−2. As we mentioned during the description of the results shown in Figure 4, the growth of the fluence of the 370 ps heating pulses on the target containing Sn NPs allowed for achieving the conditions when the resonance-induced enhancement of the harmonic in the vicinity of strong ionic transitions of Sn becomes pronounced. The disintegration of large NPs into smaller ingredients (atoms/ions, clusters, and tiny NPs) at these conditions of ablation resulted in the involvement of those ionized species in the process of HHG, followed by the observation of the enhancement of some specific harmonic (either H28 or H29) of the used tunable NIR radiation. The significant suppression of the "resonant"-induced harmonic gain (either the 17th order of the 806 nm pump or 28th and 29th orders of the NIR pump) could have been caused by the shift of the above-discussed transition. However, our experiments using tunable NIR pulses at the fluence of the HP at F = 1.6 J cm−<sup>2</sup> did not reveal the resonance-related processes lead to the enhancement of the harmonic yield. This observation suggests that the tuning of the ionic transition should not be the main factor in leading to the cancellation of the resonance-related effect.

Another factor may be a decrease in the oscillator strength of this transition. The transitions of Sn II and Sn III can be either detuned or weakened once the original species become presented in the form of nanoparticles. The reduction mechanisms of harmonic amplification can be related to either the reduction of the oscillator strength of this transition or the detuning from the wavelength of "resonant" harmonics, or both.

The macroscopic dispersion properties of the plasma could be another key factor for the formation of the resonance-induced enhancement of a single harmonic in tin plasma, as was suggested in [43]. Recent studies of two-component plasmas allowed for analyzing this opportunity in the case of one of the components (Sn) allowing for the generation of enhanced harmonics and the other component (Pb) causing the modification of plasma dispersion properties [47]. The observation of the enhancement of the even (H18) harmonic and the odd (H17) harmonic, in the case of the TCP and SCP of two-component plasma, have demonstrated that the macroscopic properties of the plasma cannot be considered as the origin of the single harmonic enhancement. In other words, the co-existence of lead plasma does not destroy the resonance effect and single harmonic enhancement caused by tin, which suggests the diminished role of the macroscopic effect in the modification of the resonance-enhanced properties of harmonics in the latter component of plasma.

We did not analyze the size-dependent effect of the harmonic yield in the case of nanoparticle-containing plasmas. Meanwhile, the assumption of the influence of a strong local field in the case of smaller-sized nanoparticles, like quantum dots, can predict the growth of harmonic yields in the latter case compared with the large nanoparticles. This assumption can be supported by the vision of HHG as a three-step process, when only atoms on the surface of nanoparticles efficiently participate in harmonic generation, while inner atoms cannot be considered as the emitters of harmonics due to their strong absorbance of generated radiation. The most probable scenario in determining the optimal sizes of atomic aggregates for HHG is the demonstration of the attractiveness of the species with sizes of 1–5 nm, when the quantum confinement effect allows for the increase of the local field-related nonlinearity while limiting the negative effects attributed to the large (20–100 nm) nanoparticles. This assumption has recently been confirmed during the application of metal sulfide quantum dots for HHG [48,49].

There are a few studies of HHG in the plasmas produced on the nanoparticle-coated targets. The aim of those studies was to elevate the nanoparticle cloud by laser ablation (like in our experiments) and to analyze the nonlinear conversion of infrared pulses towards the extreme ultraviolet range. Meanwhile, the most intriguing method would be the propagation of strong laser pulses through nanoparticle-coated thin films. Interest in HHG in solids has been increased dramatically, though this process was demonstrated using the mid-infrared laser sources. The difficulties related to the absorption of generated harmonics in UV and XUV ranges during propagation through solids can be diminished while using the thin films containing nanoparticles.

The main difference of the present study compared to refs 42 and 43 is the analysis of resonance enhancement of the harmonics in the region of ~47 nm during the propagation of the femtosecond pulses through the tin plasma. The analysis, particularly, includes the application of the tunable source in the near-infrared range, which allowed for the tuning of the order of the harmonic being enhanced (from the 28th to the 29th order), which allowed for the identification of the spectral range where the highest enhancement of single harmonics was achieved. The important finding in the case of the two-color pump study was the appearance of the exceptionally strong 18th harmonic of 806 nm radiation notably exceeding the earlier analyzed 17th harmonic achieved during the singlecolor pump of Sn laser-induced plasma. Our present study shows that the closeness of the wavelength of the harmonic with the ionic transition possessing large oscillator strength (as in the case of the almost perfect coincidence of the H17 (λ = 47.4 nm) and 4d105s25p2P3/2→4d95s25p2 ( 1D)(2D5/2) transition (λ = 47.8 nm)) does not necessarily lead to the stronger enhancement compared with the neighbor harmonic (H18, in our case). Notice that the latter harmonic became available due to the interaction of the weak second field (403 nm) with the strong fundamental wave (806 nm).

This contradiction was considered in our paper and different scenarios were suggested, which can, to some extent, clarify the observation of the large enhancement of the higher-order harmonic (H18) compared with the one coinciding with the strong ionic transition. The decrease of the oscillator strength of this transition, in the case of nanoparticle and molecular states of tin, as well as the influence of the collective processes when the harmonic in the region of anomalous dispersion of the ionic transition becomes quasiphase-matched with the driving field, can be the reasons of the observed contradiction with the earlier accepted vision of the resonance-enhancement of a single harmonic in plasma. Thus, the meaning of the reexamination of the earlier reported resonance enhancement of a single harmonic is related to the approach differing from earlier suggested theories and assumptions of the necessity of perfect coincidence of the harmonic and transition wavelengths [9,10,28,33,38,42,43].

As it was underlined, the application of a near-infrared single-color pump did not result in efficient tunable odd harmonics generation to demonstrate the effect of the tunable single harmonic enhancement, due to the reasons described in our manuscript. Because of this, we used only a two-color pump (NIR and H2) to extend the harmonic emissions up to the spectral region where the enhancement of harmonics can be achieved.

The important novelty in this approach is the application of the tunable source of femtosecond pulses, allowing for the analysis of the most suitable conditions for single harmonic enhancement. The comparison of HHG in atomic and nanoparticle plasmas is another approach, allowing for the demonstration of the role of the morphology of harmonic emitters on the enhancement factor of a single harmonic.

#### **5. Conclusions**

In conclusion, we have compared the resonance-induced enhancement of single harmonic emissions during the propagation of ultrafast pulses through tin-containing laser-induced plasmas. The analysis of the dynamics of LIPs produced on a Sn bulk target and a Sn NP target has shown the range of the optimal delays between heating and driving pulses (130–180 ns), at which the maximal harmonic yield can be achieved. The similarity of this parameter for two plasmas allows us to suggest the mechanism of energy transfer during ablation, resulting in similar kinetic energy of each ingredient of ejected species.

The enhancement of the 17th and 18th harmonics of 806 nm pulses was analyzed in the case of single-color and two-color pumps of plasma, showing up to a 12-fold enhancement of even harmonics compared with the neighboring orders in the latter case. We have compared the single-atomic Sn and Sn nanoparticles-containing plasmas to demonstrate a distinction in the enhancement factor of the single harmonic in the case of tunable nearinfrared pulses. We have shown the enhancement of a single harmonic in the vicinity of the 4d105s25p2P3/2→4d95s25p2 transitions of Sn II ions and demonstrated how this process depends on the constituency of the plasma components at different conditions of the target ablation.

The application of tunable (1280–1440 nm) radiation from the optical parametric amplifier allowed us to demonstrate the variations of single harmonic enhancement using a tunable two-color pump of Sn-containing plasma. Our studies using tunable NIR pulses at the fluence of an HP of F = 1.6 J cm−<sup>2</sup> did not reveal that resonance-related processes lead to the enhancement of the harmonic yield, which suggests that the tuning of ionic transitions should not be the main factor leading to the cancellation of the resonance-related effect. Meanwhile, the presence of tiny NPs and clusters and single-particle species appeared in LIPs during the disintegration of large (70 nm) original aggregates of Sn atoms allows for the formation of conditions for the involvement of tin ions in the enhancement of single harmonics in the vicinity of ionic transitions possessing strong oscillator strength.

**Author Contributions:** Conceptualization, R.A.G., H.K.; methodology, R.A.G.; formal analysis, R.A.G., H.K.; investigation, R.A.G., H.K.; writing—original draft preparation, R.A.G.; writing—review and editing, R.A.G., H.K.; visualization, R.A.G.; supervision, H.K.; funding acquisition, R.A.G., H.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by JSPS KAKENHI (grant number 24760048), ERDF (grant number 1.1.1.5/19/A/003), State Assignment to Higher Educational Institutions of Russian Federation (grant number FZGU-2020-0035), grant and the Common Research Facility at the American University of Sharjah (grant number FRG AS1801).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data that support the findings of this study are available from the corresponding author upon reasonable request.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**Rashid A. Ganeev 1,2,3,4,\*, Vyacheslav V. Kim 1,2, Konda Srinivasa Rao <sup>1</sup> and Chunlei Guo <sup>5</sup>**


**Abstract:** We study high-order harmonics generation from plasmas generated from graphite, fullerenes, carbon nanotubes, carbon nanofibers, diamond nanoparticles, and graphene. Our approach utilizes a heating nanosecond laser pulse to produce plasmas that serve as the media for high harmonic generation from a subsequent driven femtosecond laser pulse. High harmonics are generated at different time delays following the plasma formation, which allows us to analyze the spreading of species with different masses. We analyze the harmonic yields from species of single carbon atom, 60 atoms (fullerene), 106 atoms (diamond nanoparticles), 10<sup>9</sup> atoms (CNTs and CNFs), and even much larger species of graphene sheets. The harmonic yields are analyzed in the range of 100 ns–1 ms delays. The harmonic yields were significantly higher within the 200 ns–0.5 μs range, but no harmonic is observed between 10 μs–1 ms. Our observations show that, at the optimal ablation of atoms and clusters, the laser-induced plasmas produced on the surfaces of different carbon-contained species spread out from targets with the comparable velocities.

**Keywords:** high-order harmonic generation; nanoparticles; carbon plasma

#### **1. Introduction**

High-order harmonic generation (HHG) in extreme ultraviolet (XUV) range, which occurs when an intense laser pulse interacts with laser-induced plasma (LIP) formed by another laser pulse on the surfaces of bulk targets, is a rich field for a variety of material studies [1–15]. The high-order nonlinear optical properties of various inorganic nanoparticles (Ag, Au, Pd, Pt, Ru, BaTiO3, and SrTiO3) appearing in LIP were reviewed in [16].

The heating pulses (HP) are usually generated by splitting the amplified laser pulse beam (with pulse duration of a few hundred ps) before temporal compression in a chirpedpulse amplification laser system. The time delay between the picosecond HP and the femtosecond driving pulses (DP) for HHG is commonly created by the path length difference between the two optical paths, so the delays are usually restricted by ~100 ns during most of the previous HHG experiments. Correspondingly, the distance between the focus spot and target surface due to above limitations usually does not exceed 200 μm, thus involving particles with minimum velocities distribution at around 103 m/s. The presence of clusters consisting of hundreds to thousands of atoms in LIP requires the ability to control delay between HP and DP in a much more comprehensive range, which is difficult while using the optically driven delay between two pulses from the same laser.

One way to overcome this problem is applying a second source, in particular, nanosecond pulses from the Nd: YAG laser. An analysis of the application of longer (nanosecond)

**Citation:** Ganeev, R.A.; Kim, V.V.; Rao, K.S.; Guo, C. Probing Laser Plasma Dynamics Using High-Order Harmonics Generation in Carbon-Containing Nanomaterials. *Appl. Sci.* **2021**, *11*, 2143. https:// doi.org/10.3390/app11052143

Academic Editor: Gennady M. Mikheev

Received: 6 February 2021 Accepted: 24 February 2021 Published: 28 February 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

pulses for target ablation during HHG in LIP compared to picosecond pulses, has previously been reported in [17]. Nanosecond laser ablation has been widely used to synthesize various metal and oxide nanoparticles (NPs). However, numerous factors such as the duration of the laser pulse, fluence, and characteristics of irradiated targets affect the properties of synthesized NPs. The pulse duration is one of the most important parameters when considering the in-situ synthesis of NPs in LIP.

In this work, we apply the two-laser scheme to investigate HHG in carbon-based nanostructured plasmas. The nanosecond laser is used for LIP formation and the femtosecond laser is used for harmonics generation in plasma. The synchronization of the two laser sources may resolve, to some extent, the puzzle related to the enhancement of harmonics in the multi-atomic species produced during ablation of bulk materials or targets that initially contain NPs. The analysis of plasma components can be achieved by controlling the HP-DP delay in a wide range spanning between 0 and a few tens of microseconds, which should be sufficient for studying the fast and slow components of LIPs. Such an approach has already been used in reported studies to analyze the harmonics' delay dependencies from different ZnO-contained targets, resonance-enhanced harmonics in mixed LIPs, and HHG during propagation of femtosecond pulses through different ablated species [18–20].

#### **2. Materials and Methods**

Femtosecond pulses (50 fs, 806 nm, 2 mJ) from Ti:sapphire laser were focused inside the plasma plume to generate harmonics (Figure 1). The intensity of the driving pulses in the plasma area was maintained to be ~2 × <sup>10</sup><sup>14</sup> W cm−2. The beamwaist diameter of the femtosecond driving pulses in the focal plane of the 400 mm focal length spherical lens was measured to be 90 μm and the calculated Rayleigh length was 6 mm, which is notably larger than the sizes of target ablation.

**Figure 1.** Experimental setup of delayed excitation of nanosecond laser produced plasma for generation of high-order harmonics in carbon nanostructures contained plumes. DP: driving pulse; HP: heating pulse; LIP: laser-induced plasma; T: target; H: harmonic emission; XUVS: extreme ultraviolet spectrometer; CCD: charge-coupled device camera.

For the laser plasma formation, the 5 ns heating laser pulses (*λ* = 1064 nm, 5 mJ, 10 Hz) from Nd:YAG laser were used. The HP were focused by a 300 mm focal length spherical lens on the target surface at the spot with diameter 0.3 mm providing intensity of a few units of 10<sup>9</sup> W cm−<sup>2</sup> and fluence up to ~7 J cm−2. The lens used for focusing of heating pulses was approached to the target in such a way that the spot size on the target surface (0.3 mm) was notably larger that the beamwaist diameter in the focal plane (60 μm). The variable defocusing was adjusted to keep the "optimal" fluence of heating radiation for each of used samples, which allowed us to achieve the maximal harmonic yield.

The femtosecond pulses were delayed with regard to those from Nd:YAG laser using the digital delay generator to propagate through the formed plasma at maximal density of the ejected particles. The delay between pulses was tuned using the delay generator. The variable electronic delay range was equal to 0–106 ns. We analyzed plasma and harmonic dynamics from several nanoseconds to several hundred microsecond delays. The harmonics and plasma emission were detected using a flat field grazing-incidence XUV spectrometer.

The pressed carbon-contained nanostructured targets were glued on microscopic glass slides fixed on a digitally controlled XYZ stage inside the target chamber. The powdered nanoparticles were placed in the press machine and pressed to form the 5 mm thick tablets of 10 mm diameter. We used the laser ablation fluence varied between 1 and 7 J cm−<sup>2</sup> depending on target properties. In each case, the conditions of ablation were chosen to achieve the maximal harmonic yield. The optimization of ablation conditions for each sample assumed a determination of the fluence. The plasma plume allowed the generation of harmonics at a specific delay between heating and driving pulses. The targets were moved around during HHG experiments to provide fresh surface for ablation. Using motorized rotating targets notably improved the stability of HHG from LIPs, particularly, in the case of powdered targets, and significantly minimized the modification of the target surface that could cause degradation of harmonic yield. The periodic change of the ablation zone allowed cooling down the heated area and maintained stable plasma formation. Six materials were used as the targets: bulk graphite (bulk C), C60 powder, multi-walled carbon nanotube (MW CNT) powder (15 nm diameter; the length of tubes was varied in the range of 500 nm–20 μm), carbon nanofibers (CNF, 100–200 nm diameter and a few tens micrometers length), diamond nanoparticles (DN, size 3–8 nm) and graphene (GR) wrapped sheets (sizes of sheets ~20 nm). All samples were purchased from Sigma-Aldrich (St. Louis, MO, USA).

#### **3. Results**

The first set of our measurements was aimed at the analysis of plasma emission from the ablated species. The plasma emission spectra in the 30–100 nm wavelength range for the six targets are presented in Figure 2.

**Figure 2.** Spectral emission from different carbon-containing plasmas in the case of nanosecond laser ablation. The positions of harmonics (H9–H23) from 806 nm laser source are shown in red.

Plasma emission was recorded at heating pulse parameters (pulse energy and fluence) larger than the optimal ablation characteristics for harmonics generation. The fluence of heating pulses during these studies was equal to 15 J cm<sup>−</sup>2. We did not average the plasma spectra from these samples but instead used a single shot collection. The emission lines were determined using the NIST database [21]. The positions of the 806 nm radiation harmonics from the bulk carbon starting from 9th (H9) to 23rd (H23) orders are shown as the red curves. The harmonic profiles shown in this figure were included for demonstration of the closeness with some ionic transitions.

For the bulk C plasma produced by HP with the energy of EHP = 3 mJ, we can see the presence of intense CI and CII lines corresponding to the transitions in neutral and singly charged ions of carbon in the spectral region between 55 and 100 nm, as well as the presence of CIII lines below 55 nm. The density of free electrons in bulk C plasma was estimated to be ~5 × 1016 cm−3, which is similar to the estimates at the same laser parameters presented in [22]. The particle density was estimated in [23] to be in the range ~1018 –1019 cm−<sup>3</sup> for comparable laser fluencies. The contribution of continuum emission decreased the contrast of emission lines.

In the case of the targets comprising nanostructured materials, the shift of emission to larger presence of the lines attributed to CII and CIII transitions was observed, except for CNF and DN. A pattern similar to the above-described spectrum was observed in the case of CNF (EHP = 3 mJ) and GR (EHP = 3 mJ). However, contrary to bulk C plasma, the continuum emission was localized in the shorter wavelength region below 65 nm. In the case of C60 (EHP = 2 mJ) and MW CNT (EHP = 2 mJ), the relative intensities of CIII lines significantly increased, while additional strong CIV transitions appeared in the plasma spectra. A similar pattern was observed in the case of all nanostructure-containing plasmas, except CNF. In the case of C60, this behavior confirms the earlier reported observations that, under similar experimental conditions, the plasma from fullerenes reaches much higher ionization states than in the case of bulk graphite ablation [24]. This statement is valid for all nanostructured materials, while at the same time, we observed a decrease in the relative intensity of CI (85.9 nm) line corresponding to the transition in neutral carbon.

In DN (EHP = 4 mJ) case, the plasma spectrum contained less emission lines and a smaller continuum despite the stronger excitation of the target. The different applied HP energies for different samples are explained by the different optimal conditions for plasma formation suitable for HHG. The term "optimal conditions" refers here to the maximal harmonic yield from each ablated sample, which depends on the fluence of HP on the target surface at similar geometry of the focusing conditions. Additionally, the pressed tablets were destroyed at higher fluencies of HP due to their fragility. For example, the harmonic yield from GR and DN LIPs was more than twice as small as from other targets due to weaker ablation at which the pressed tablets remain intact. Correspondingly, we could not increase the HP fluence on those fragile surfaces.

As shown below, the ablation corresponded to the formation of low-ionized plasma using suitable fluence of HPs provided the conditions for efficient HHG. It is important to note that higher densities of free electrons cause the phase mismatch between the driving and harmonics waves for overheated and strongly ionized plasmas, which plays a destructive role in HHG. The moderate fluencies of nanosecond pulses also increased the lifetime of the targets and provided better survival of the original nanostructures being ablated and spread in the plasma plume without their destruction. It was demonstrated that, in the case of laser ablation of C60, MW CNT, CNF, and DN [25] at the experimental conditions similar to ours, the transmission electron microscopy analysis of deposited debris has shown that laser-produced plumes contained the original nanostructures.

Figure 3 shows the harmonic spectra in different plasmas at variable delays between heating and driving pulses in the 100–600 ns range. The dependences of the harmonic yield on the delay are plotted in Figure 4a.

**Figure 3.** High-order harmonic generation (HHG) spectra generated from the plasmas produced on the bulk C and C60 (left column), CNT and CNF (middle column), GR and DN (right column) at the HP-DP delays ranging from 100 ns to 600 ns. The contribution to HHG spectra from different components of ablated plume spreading with almost similar velocities is shown.

The left column of Figure 3 compares the harmonics generated from 9th to 25th order from bulk C (blue curve) and C60 (red curve). The maximal harmonic yields for both samples were observed at ~200 ns delay from the beginning of the ablation. Meanwhile, the delay dependence for C60 (Figure 4a, red line with empty squares) demonstrates higher integrated harmonics signal, as well as it is extended up to longer delays (~1 *μ*s). In the case of bulk C (Figure 4a, black line with filled squares) we observed a pronounced single maximum at 200 ns, which can be interpreted as the moment of arriving of the largest amount of elemental emitters to the interaction area with DP. The estimation for the velocity of the main part of emitters shows that it equals 1.2 × <sup>10</sup><sup>3</sup> m/s, which is close to our HHG-based measurements in the case of DP propagation at 0.2 mm distance from the target surface (~(1–2) × <sup>10</sup><sup>3</sup> m/s). The delay dependence in the case of C60 (Figure 4a) demonstrates a weak decay between 200 and 600 ns, which can be interpreted as a gradual passing of C60 and its different fragments through the interaction area at the velocities slightly varying from 1 × <sup>10</sup><sup>3</sup> m/s. As one can see (left column of Figure 3), in the case of harmonic spectrum from C60 their yield gradually increased and maintained almost equal for the 9th to 17th orders in the range of 200 to 500 ns delays.

Figure 4b shows the saturated images of harmonics collected by CCD camera from the phosphorous screen of the microchannel plate of XUV spectrometer at the optimal delays of each studied sample. The images are shown in log scale and normalized to 1. The purpose of such presentation of harmonics distribution is to define the maximal order of generated harmonics, i.e., harmonic cutoff, and better view the difference in harmonic intensities from various species. In this figure, an emission is observable on the right side of 9H in the first five spectra, which is a second-order diffraction related with strong emission from 17th order. One can also see the weak second-order diffraction related to the 19H (see third panel from the top in the case of MW CNT), which is seen on the left side of 9H. Similar pattern is seen in some panels of Figure 3 showing the lineouts of the harmonic spectra.

**Figure 4.** Panel (**a**): dependences of the integrated yield comprising 9th to 25th harmonics on the delay between nanosecond heating pulse (HP) and femtosecond driving pulse (DP). Panel (**b**): raw images of the harmonics at the optimal delay for each plasma sample. Images are normalized and logarithmically scaled. For bulk C, the maximal yield of harmonics is shown at a a delay equal to 200 ns. The optimal delays for C60, MW CNT, CNF, Gr, and DN were 200, 400, 300, 300, and 500 ns, respectively.

For bulk C and C60 we notice a difference in the harmonic cutoffs. From all six samples, ablated bulk C allowed the generation of the highest cutoff at similar conditions of experiments (25th order; we also observed very weak 27th harmonic, however, its signal was close to the sensitivity limit of our detection system). Harmonics generating in C60 LIP showed the smallest cutoff position (21th order).

#### **4. Discussion**

Table 1 comprises the optimal conditions of ablation for different targets. Note that earlier studies have demonstrated that neither pulse energy nor pulse intensity can be considered as the definitive parameters responsible for the optimization of plasma formation to produce maximal yield of harmonics. The most important parameter here is the fluence, or energy density, of the heating pulses on the target surface. In this table, we include the optimal fluencies for each studied sample.



It was demonstrated in [23,25,26] by time-of-flight mass spectroscopy (TOFMS) that LIPs from the graphite surface contain, along with neutral carbon atoms and its ions, different C*<sup>n</sup>* clusters and their ions. The number of carbon atoms in such clusters varies from *n* = 2 up to *n* = 20, and for strong excitation *n* could even reach 100.

Earlier, in the case of C60 ablation at conditions similar to ours, TOFMS demonstrated the presence of preferably C26<sup>+</sup> fragments and smaller amount of C60<sup>+</sup> ions, alongside the neutral nanoparticles, in LIP [25]. In order to provide a qualitative explanation of the obtained HHG results we use the semiclassical model of HHG in isotropic medium [27]. According to this model, the HHG cutoff is defined by the expression *Nc* ≈ (*Ip* + 3.2*Up*)/*ω*, where *Ip* is the ionization potential of elemental emitter, *ω* is the laser field frequency, *Up* = *Il*/(4*ω*2) is the pondermotive potential, and *Il* is the laser field intensity. The ionization potential of carbon atom is *Ip* (Bulk C) = 11.26 eV [28], while the ionization potential for small-sized carbon molecules varies from *Ip* (C2) = 11.35 eV, *Ip* (C3) = 11.5 eV to *Ip* (C9) = 9.4 eV [26] with the tendency to decrease toward bigger molecules. For C60, the ionization potential is correspondingly lower compared to smaller-sized molecules (*Ip* (C60) = 7.6 eV [29]). The application of our experimental parameters in expression for harmonic cutoff gives *Nc* (bulk C) = 31 and *Nc* (C60) = 29. Note that in the present work the 25th and 21st harmonics cutoffs from those species were observed. Thus, we attribute the observed peculiarities of HHG spectra in pair "bulk C–C60" to the presence of mostly C60 and its large fragments in the plasma plume, which was indirectly confirmed by our plasma emission spectra (Figure 2, C60 panel), where the relative intensity of the CI transition line is lower than that of CIII and CIV lines. Larger harmonics cutoff in bulk C targets can be attributed to the presence of mostly neutral and small-sized carbon molecules in LIP. The presence of highly charged ions does not provide sufficient contribution to the extension of HHG cutoff, since the HHG conversion efficiency quickly reduces with increasing ionization potential.

Returning to the model [27], harmonics generation is described as a process where the first step is the formation of the electron wave packet by tunneling ionization and the second step includes a classical mechanics description of released electron in laser field. The first step can be described by the Ammosov–Delone–Krainov (ADK) expression for ionization rates Γ*ion* for different ionization potentials [30] and defines in two-step model the efficiency of conversion. While estimating ADK rates we assumed the laser intensity to be equal to what we measured in the focal plane of the focused driving beam (2 × 1014 W cm<sup>−</sup>2). Direct comparison of ionization rates by ADK formula gives <sup>Γ</sup>*ion*[*Ip*(C) = 11.26 eV]/Γ*ion*[*Ip*(C+) = 24.38 eV]~105 higher rate for tunnel ionization in the cases of the neutral and single charged carbon atom. By applying the same approach to evaluate the difference in ionization rates of fullerenes and carbon, one can define the following ratio Γ*ion*[*Ip*(C60) = 7.6 eV]/Γ*ion*[*Ip*(C) = 11.26 eV] ≈ 5.

Thus, C60 molecules can be considered more efficient high harmonics emitters than ordinary carbon atoms or small-sized carbon molecules. Their presence in LIP leads to a stronger enhancement of the low-order part of HHG spectrum comprising the harmonics between 9th and 17th orders. We can conclude that, despite the lower density of C60 nanoparticles in plasma compared to C atoms and ions originated from graphite ablation, higher HHG efficiency allows the observation of harmonics even at notably larger delays (>1000 ns) compared with the latter species (Figure 4a). Higher cutoff position in the case of ablated graphite is attributed to the presence of neutral carbon and small-sized Cn (where *n* < 20) molecules. Note that the role of different small carbon clusters synthesized during ablation of graphite was analyzed in the studies related to HHG in carbon LIP [20].

The middle column of Figure 3 represents HHG spectra obtained from, to some extent, morphologically similar species: multiwalled carbon nanotubes (blue solid lines) and carbon nanofibers (red solid lines). MW CNT plasma dynamics showed the 400 ns optimal delay from the beginning of ablation corresponding to maximal harmonic yield. Simultaneously, the delay dependence (Figure 4a, blue line with solid circles) had the plateau-like structure between 200 and 400 ns. The harmonic yield in this time scale was equal or slightly higher than in the case of C60 plasma. The enhanced harmonics from 9th to 17th orders were observed between 100 and 400 ns delays (Figure 3, middle column). At the same time, the cutoff (25th harmonic) at the optimal delay (400 ns) was slightly higher compared to C60 plasma (Figure 4b).

We can assume that the enhanced low-order harmonics were attributed to the presence of small fragments of CNTs in LIP. At the same time, higher cutoff can be attributed to the coherent contribution to HHG from the carbon neutral atoms and small-sized carbon molecules. Notice that the ionization potential of single-walled CNT is in the range of 5–6 eV [31]. The HHG spectrum in the case of short (100 ns) delay indicates that small-sized components of such plasma can gain, to some extent, larger velocities, thus causing the enhanced harmonic spectra with larger cutoff order. This is what we see in the case of bulk C and MW CNT. At the same time, the large-sized components of LIP responsible for enhancing the lower orders of spectra are expected to appear at larger delays. Summarizing the analysis of HHG in MW CNT, one can conclude that, at the used parameters of HP, MW CNT plasma also contains small carbon particles alongside the fragments of nanotubes.

Meanwhile, the HHG spectrum from CNF was surprisingly similar to C60. CNF plasma showed optimum delay at 300 ns (Figure 4a, green line with empty circles) and similar to C60 cutoff (21st order, Figure 4b). We assume that plasma from CNF ablation was less fragmented compared to MW CNT despite the higher HP energy used there (3 mJ vs. 2 mJ).

Earlier reported TOFMS spectra have demonstrated the similarities between the MW CNT and CNF, with the presence of small carbon C*n* fragments (with *n* varied up to 20) and no ions higher than low-sized carbon clusters in the mass spectra up to 5000 mass/charge units [25]. Additionally, the emission from ablated MW CNT and C60 targets showed almost similar spectra (Figure 2), with strong relative lines for CIII and CIV transitions. We can suppose that, in the case of MW CNT, the fragmentation process induces the appearance of small-sized carbon molecules and clusters inducing the larger cutoff, since at short delay (100 ns, Figure 4a) the integrated harmonic signal from MW CNT plasma exceeds that from bulk C LIP. Plasma spectra for CNF demonstrate the most contradictive result, with strong relative CI transition line, which indirectly points out to the presence of large number of neutral carbon atoms, but without extending the HHG cutoff.

TOFMS is a natural and obvious way to precisely determine the mass-to-charge state of the ablation plume. Notice that the main goal of present research was to study highorder harmonics generation from the plasmas generated on the graphite, fullerenes, carbon nanotubes, carbon nanofibers, diamond nanoparticles, and graphene targets. Meantime, the joint application of HHG and TOFMS facilities in a single set of experiments is hardly to be achieved. Earlier studies, which combined the data revealed from above facilities, were performed separately, which did not allow for a conclusive argument for the similarity of the plasma formation conditions in these two sets of experiments. Meanwhile, we demonstrate that the HHG approach allows for analyzing the dynamics of plasma spreading out from ablated surface thus revealing some interesting peculiarities hardly obtainable in the case of TOFMS approach. Our present research, as well as earlier reported studies of harmonic generation in laser-induced plasmas, enabled a demonstration of the attractive features of the high-order nonlinear spectroscopy of these species.

The HHG spectra generated in the plasmas produced on the graphene sheets and diamond nanoparticles are shown on the right column of Figure 3. The harmonic yields from GR and DN was multiplied by a factor of 2 to make them more visible and, in order to compare with other spectra. Both plasmas allowed the generation of weaker harmonics compared to the other four samples. The delay dynamics in the case of GR (Figure 4a, solid pink line with filled rhombuses) indicated the presence of large fragments in LIP, with maximal harmonic yield observed at 300 ns delay. The delay dynamics curve is more flattened with respect to the above-discussed materials, with comparable integrated harmonic yield in the range of 100 ns to 700 ns. We attribute this pattern of delay dynamics to the wide distribution of GR's pieces possessing different velocities centered at ~1 × <sup>10</sup><sup>3</sup> m/s. The harmonic spectrum changed at optimum delay (Figure 4b) and showed the cutoff at 23rd order, and the enhanced 11th and 13th harmonics (Figure 3, left column, black line). We attribute this increase in harmonic yield to the arrival of large-sized fragments of graphene to the interaction area.

Among all studied materials, DNs have the largest crystal lattice energy. This characteristic can explain, to some extent, the better survival of DNs in the plasmas produced by the heating pulses. This may also explain why DNs showed relatively extended optimum delay (500 ns; Figure 4a, dark yellow line with empty rhombuses). With the increasing of the delay, the 11th to 15th harmonics also enhanced (Figure 3, right column, red solid lines), while up to 500 ns delay the harmonic spectral shape and cutoff located at 25th order remained the same (Figure 4b). The observed peculiarities of HHG spectra from GR and DN plasmas can be explained by the presence of the small-sized carbon molecules and clusters having uniform distribution of velocities. The latter assumption can explain the flattened delay curves with the same HHG cutoffs (23rd and 25th orders).

The cutoff positions for all studied samples were, to some extent, close to each other except for graphene (Figure 3). Though the ionization potentials were almost similar, the studied plasmas were distinguished from each other by the harmonic yield rather than by cutoff energy.

Below, we address the importance of considering the above delay-dependent experiments for understanding the dynamics of plasma propagation. The signature, indicating the presence of specific emitters, is the increase in the output of harmonics at certain specific delays from the beginning of ablation. We can assume that the same average kinetic energy E = mv2/2 could characterize all plasma components containing the same basic atom, in our case carbon. Accordingly, the same average arrival time could be expected for carbon clusters of different sizes. The duration for cluster propagation from the target surface to the optical axis of the femtosecond pulse propagation corresponds to the optimal delay between HP and DP. Our results show that small carbon clusters enter the area of interaction with the femtosecond beam much earlier than expected, assuming only kinetic consideration when it is assumed that the components reach thermodynamic equilibrium during expansion. Alternatively, we can suppose that all carbon clusters acquire the same kinetic energy from the very beginning and propagate from the surface at speed approximately similar to that of a single carbon ablated from bulk material. The arrival times of particles consisting of a single carbon atom, 60 atoms (fullerene), 106 atoms (diamond nanoparticles), 109 atoms (CNT and CNF), and even much larger species, such as parts of graphene sheets, were comparable to each other (200-400 ns). Thus, the role of the cluster's atomic weight in HHG becomes questionable if only a simple kinetic energy mechanism is considered. In other words, from the very beginning, all the atoms in the clusters acquire the same kinetic energy and propagate from the surface at speed approximately equal to that of a single carbon atom.

When we use the term "heating" for the laser ablation, we do not merely suppose the thermal evaporation of the target. It is not a simple thermal evaporation induced plasma formation. This process depends on the level of target excitation that is used for laser ablation. The creation of nonlinear medium above the target surface is not based on the simple heating of the target surface and steady-state processes of melting, evaporation, and spreading of the particles with the velocities defined from the thermodynamic relations. This relation refers to cw heating. In this case the velocity of the C60 molecule at 1000 K is in the range of 1.5 × <sup>10</sup><sup>2</sup> m s<sup>−</sup>1. Correspondingly, during the first few hundred nanoseconds (~200 ns corresponding to our observation of maximal yield of harmonics) the fullerene molecules will move only 30 μm above the surface. Notice that femtosecond driving pulse propagates at the distance of ~0.2 mm above the target's surface. If one assumes that plasma creation by laser pulses is defined by this slow process, then no harmonics at all should be observed in such experimental configuration for any of our targets, be it C60, CNT, CNF, graphene, or DN. In the meantime, laser ablation of any of the above targets creates a very efficient plasma medium, which generates extreme high harmonics when the femtosecond pulse propagates 200 μm above the target surface.

This contradiction is explained by another model of creation of the cloud of particles, namely, plasma explosion during ablation of the targets. The dynamics of plasma front propagation during laser ablation is studied by few groups (for example [32] and references therein). The dynamics of plasma formation and spreading can be analyzed by either the time resolved ICCD images or shadowgram technique. A numerical analysis of the generation of such plasmas for the case of single-pulse interaction with the target surface was described in [33]. Previously, the dynamics of the spatial characteristics of laser plasmas generated from B and Mo targets, measured using the shadowgraphs of the plasma, was reported in [34]. For Mo, the plasma front spreads with the velocity of ~6 × <sup>10</sup><sup>3</sup> m s−1. For example, the plasma front reaches 200 μm distance from the target after hundred nanoseconds rather than a few thousand ns, as we can estimate if we assume the steadystate expansion of the plasma particle cloud. Obviously, the formation of "optimal" plasma is not restricted by appearance of the plasma front in the area of femtosecond pulse. We

must wait until the density of the particles becomes sufficient for efficient HHG, while the free-electron concentration remains below the level when the impeding processes prevail over the harmonic generation. In our case the velocity of the "optimal" part of carbon nanostructures contained plasma cloud was measured to be 1 × 103 m s<sup>−</sup>1.

The appearance of continuum points out the strong heating of target surface. The strong incoherent emission of plasma also decreases the overall "quality" of generated XUV radiation when the former emission becomes stronger than coherent emission of harmonics. That is why the determination of "optimal" plasma for HHG [35] includes various factors playing an important role in amendment and suppression of harmonic yield. Briefly, moderate (1017 cm−3) plasma density, a small ionization rate, and correspondingly small electron density (a few units of 10<sup>16</sup> cm<sup>−</sup>3) helped achieve the best conversion efficiencies towards the harmonics in the plateau range (10−<sup>5</sup> and higher), which was almost two orders of magnitude higher than in the case of "overheated" targets. The application of "optimal" plasma immediately allowed for the demonstration of such unique properties of HHG in ablated debris like the resonance-induced enhancement of single and group of harmonics, the resonance-induced suppression of some harmonics, the quasi-phase matching of the groups of harmonics in different ranges of XUV, the efficient application of clusters, quantum dots and relatively large nanoparticles for harmonics generation, the application of extended plasmas at the conditions when the coherence length for some harmonics does not exceed the sizes of laser-induced torches, etc. These advanced features of HHG in optimally prepared plasmas cannot be reproduced in the plasmas formed during strong ablation of target surfaces. Moreover, most of above advantages could not be repeated in the gas media commonly used of HHG.

The continuum shown in the emission spectra was produced during the strong excitation of our targets. The motivation to show plasma emission spectra at these conditions is: (a) to demonstrate the similarity in emission lines of different nanostructured materials caused by the presence of carbon in each of these species and (b) to show the closeness of harmonic and plasma emission lines, which does not lead to the resonance-induced enhancement of those harmonics. Moreover, our spectral measurements were carried out at the conditions when we could not distinguish the emission from the target surface and emission from nearby (~0.2 mm above the ablated surface) plasma.

At the moderate ablation conditions (i.e., at the fluence of 2 to 7 J cm−<sup>2</sup> on the target surface) the nanostructures are not affected by the temperature of surrounding material (~900 K) but rather safely elevate from the surface. The survival of carbon nanostructures at these conditions of ablation and their presence at the moment of propagating the driving femtosecond pulses through such plasma formations was confirmed by the SEM analysis of the debris deposited on the nearby surfaces.

To summarize, we considered two models: the model of plasma spreading and the model of harmonics generation in the plasmas comprising of the same element (carbon, in our case) either in a single atomic mode or complex morphology state. The first model allowed us to confirm the similarity in the velocities of single-atomic and multi-atomic debris, which corroborates with our observations of the maximal yield of harmonics at approximately same delay between the heating and driving pulses for each of these species. The second model offers the consideration of C and C*<sup>n</sup>* (*n* refers to the number of atoms in cluster) particles as the harmonic emitters from the point of view of their ionization potentials and harmonic yield. An approximate similarity in the ionization potentials led to similarity, to some extent, of the cutoff harmonics, while a larger number of atoms in nanostructures allowed for increasing the cross section of recombination of the accelerated electron with the parent particle. The latter peculiarity distinguished the harmonic yields from the single-atomic plasma produced from ablated graphite and the multi-atomic plasma produced from other studied carbon-contained species (fullerenes, multiwalled nanotubes, nanofibers, diamond nanoparticles, and graphene). Thus, by combining the analysis of delay dependences of the integrated harmonic signals and HHG spectra in the 30–100 nm wavelength range, the roles played by the carbon monomers, small-sized

carbon molecules, and large nanoparticles in the former process were revealed. A search of new approaches in this direction allows for demonstrating the advantages of high-order nonlinear spectroscopy of ablated nanostructured solids.

#### **5. Conclusions**

In conclusion, we presented studies on the high-order harmonics generation in the plasmas generated from six carbon-contained materials (graphite, fullerenes, multiwalled nanotubes, nanofibers, diamond nanoparticles, and graphene). The contribution of different components in laser ablated plume from carbon nanostructure-containing targets in the range of 100 ns to 1 μs delays between HP and DP was analyzed. We have shown the difference of delay dependence curves between bulk graphite and other samples containing nanoparticles while recognizing the similarity of the optimal values of delays for different species at which highest harmonic yield was achieved. By combining the analysis of delay dependences of integrated harmonics signals and of HHG spectra in the 30–100 nm wavelength range, the role of carbon monomers, small-sized carbon molecules, and large nanoparticles in the former process were revealed. We demonstrated that the presence of nanoparticles and its fragments leads to an enhanced harmonics signal in the wavelength range of 50–95 nm (i.e., harmonics from 9th to 17th orders), especially in C60, CNF and MW CNT. It was also shown that different carbon-containing species demonstrate sufficiently variable patterns of HHG spectra at comparable heating pulse energy. The important role of utilizing two digitally controlled laser sources for obtaining extensive delays between heating and driving pulses was underlined.

The presented studies allow for a better understanding of the plasma spreading dynamics in the harmonics generation from ablated species comprising similar basic element (carbon). The approximately similar average arrival times were observed for carbon clusters of different sizes. The arrival times for the particles comprising single carbon atom, 60 atoms (fullerene), 10<sup>6</sup> atoms (diamond nanoparticles), 10<sup>9</sup> atoms (CNTs and CNFs), and even much larger species like parts of graphene sheets, were comparable (200–400 ns). We analyzed the HHG yield in the range of 10 μs–1 ms delays and did not observe any harmonics. Our observations showed that, at the optimal ablation of atoms and clusters, the laser-induced plasmas produced on the surfaces of different carbon-contained species spread out from targets with the comparable velocities.

**Author Contributions:** Conceptualization, R.A.G., C.G.; methodology, R.A.G., V.V.K.; formal analysis, V.V.K., K.S.R.; investigation, V.V.K., K.S.R.; writing—original draft preparation, V.V.K., R.A.G.; writing—review and editing, R.A.G., C.G.; visualization, V.V.K.; supervision, C.G.; funding acquisition, R.A.G., C.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Jilin Provincial Science & Technology Development Project (20200802001GH), K. C. Wong Education Foundation (JTD-2018–08), ERDF project (1.1.1.5/19/A/003), State Assignment to Higher Educational Institutions of Russian Federation (FZGU-2020-0035).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data that support the findings of this study are available from the corresponding author upon reasonable request.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**Anton Maydykovskiy 1,†, Marina Temiryazeva 2,†, Alexey Temiryazev 2,† and Tatiana Murzina 1,\*,†**


**Abstract:** The structure of magnetic domains is an exciting research object that shows an enormous variety of delightful patterns. Epitaxial garnet is one of the most studied magnetic dielectrics with well-recognized bulk domains, while the magnetic composition at the surface is less investigated. Here we apply the nonlinear optical microscopy technique for the visualization of the interface magnetic domains of 10 μm thick (*LuBi*)3*Fe*5*O*<sup>12</sup> film and prove that it is qualitatively similar for both garnet/air and garnet/substrate interfaces. As an efficient extension of the second harmonic generation microscopy, we suggest and demonstrate the possibilities of the third harmonic generation one, which provides higher resolution of the method.

**Keywords:** magnetic force microscopy; garnet films; magnetic domain structure; optical second harmonic generation

#### **1. Introduction**

Magnetic domains are of high interest to researchers due to both the bright underlying physics that governs their organization, and because of an important role played by domains in a lot of applications of magnetic nano- and microstructures [1]. One of the most studied and attractive objects here are the crystalline ferrimagnetic iron garnet films that combine strong magnetooptical (MO) activity with high transparency in the red and infrared spectral ranges, pronounced mechanical properties, and the ability to control the parameters of the MO spectra by modification of their chemical composition [2–5]. It is generally recognized that garnets are widely used as optical disks [6], resonators [7], and in microwave devices [8]. Moreover, they are known as an efficient platform for spintronic and magnonic devices due to their exciting ability for the transport and processing of spin waves [9–11].

The most important properties of garnets are determined to a large extent by their domain organization, which is governed by many parameters such as the crystallographic symmetry, type and concentration of dopants, magnetic and crystalline anisotropy, demagnetization fields, etc. [1,2,12,13]. As the properties of the surface and bulk magnetic domains are interconnected, their study is an interesting research task. Furthermore, the development of efficient experimental methods for the visualization of magnetic domains in the surface and bulk areas of garnet films seems also to be quite important.

The best-known approaches here are the polarization-sensitive magnetooptical microscopy typically performed in the Faraday or Voigt geometries [14,15], X-ray diffraction techniques, first of all the surface-sensitive Lorentz microscopy [16,17], and magnetic force microscopy (MFM) [18,19]. In the case of yttrium iron garnet films with perpendicular magnetic anisotropy, the Lorentz microscopy allows to study the magnetic domains at the nanoscale. It also revealed an important role played by the demagnetization field in the formation if domains and domain walls dynamics [20]. These studies involved the

**Citation:** Maydykovskiy, A.; Temiryazeva, M.; Temiryazev, A.; Murzina, T. Nonlinear Optical Microscopy of Interface Layers of Epitaxial Garnet Films. *Appl. Sci.* **2023**, *13*, 8828. https://doi.org/ 10.3390/app13158828

Academic Editor: Andrés Márquez

Received: 18 June 2023 Revised: 27 July 2023 Accepted: 27 July 2023 Published: 31 July 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

high spatial resolution of the Lorentz microscopy technique (that is below 100 nm), and the temporal resolution of this surface sensitive probe can be made less than 1 ps [21]. This allows the study of spin relaxation dynamics and the domain wall's motion under the application of the external magnetic field. The magnetic force microscopy technique allows the visualization of complicated fractal-like and closure domains at the surface of epitaxial garnet films that are absent in bulky materials; it was recognized that the shape of the surface domains depend on the films' thickness and composition [22].

A special place is occupied by the optical second harmonic generation (SHG) [23], which has been shown to provide giant values of magnetooptical effects in the SHG response predicted prior to their experimental observation [24,25]. It is also known for its high surface sensitivity if being applied to materials with intrinsic inversion symmetry [26–30]. In the case of iron garnet films, the application of the SHG technique is beneficial due to (i) symmetry forbiddance of the even-order nonlinear optical effects (including SHG) in the bulk of centrosymmetric materials such as yttrium iron garnet crystals (in the electric dipole approximation), which provides high SHG sensitivity to the properties of the interface regions with inevitably broken inversion symmetry [23,31,32], (ii) absence of the SHG contribution from the substrates, which is typically centrosymmetric gallium-gadolinium garnet (GGG) of a few hundreds of microns in thickness and which can also reveal weak MO responses, (iii) the large value of the MO effects in the SHG response and (iv) larger (as compared to the linear MO microscopy) SHG spatial resolution originating from the nonlinear nature of the effect, and (v) the ability to use a multiple-color pump and probe experimental schemes. As an example, magnetic domains were visualized via the SHG microscopy in [33] in the scheme of the magnetooptical Faraday effect in iron garnet films of different crystallographic orientations, which provided additional information on the domain's magnetization distribution as compared to a linear magnetooptical probe. Symmetry analysis of the magnetic nonlinear optical response at the SHG wavelength was discussed in detail in [34,35]. It was underlined that high-rank tensors describing different components of the SHG process that are of the first and of second orders in magnetization **M**, as well as induced by gradients of **M**, can be used for a thorough characterization of the residual magnetic structure of garnets and other objects.

Third-order nonlinear optical spectroscopy is also a well recognized and powerful technique [36] that is widely applied to the studies of biological objects and tissues [37,38], resonant and local field effects in non-magnetic nanostructured objects [39] and metasurfaces [40,41]. One of substantial benefits of this probe is an intrinsic usage of the two-color scheme. In that case, no laser-induced damage is expected if a tissue is transparent to the intense laser radiation of the infrared spectral range, while a much less intense third harmonic of visible or UV radiation and which is specific to a concrete type of a tissue, enables label-free visualization of biological structures on the scales down to a cell size. At the same time, to the best of our knowledge, magnetization-induced third-order nonlinear optical effects, including third harmonic generation (THG), have not been applied to the studies of magnetic microstructures. This can be due in part to the low values of the magnetizationinduced effects in THG as compared to the case of SHG, as was demonstrated in [31] for the case of metallic magnetic nanostructures.

Recently it was shown that the SHG microscopy can distinguish stripe domains in the bulk of garnet films, as well as the closure domains at the outer garnet/air interface [42]. At the same time, the domain structure of the hidden interface of the ferrimagnetic film with the substrate remained unexplored. In this paper we apply magnetization-sensitive nonlinear optical microscopy to the study of magnetic ordering at the garnet/GGG interface and show that it reveals a complicated domain structure similar to that of the garnet/air one. Another finding is the extension of the magnetization-sensitive nonlinear optical microscopy method to the case of third harmonic generation, which shows higher resolution as compared to the case of the SHG probe.

#### **2. Experimental Procedure and Samples under Study**

Experiments were performed for 10 μm thick (*LuBi*)3*Fe*5*O*<sup>12</sup> epitaxial films grown by liquid phase epitaxy on a (111) facet of centrosymmetric GGG substrates. Figure 1a shows the transmission and optical density (OD) spectra of the studied samples, which reveal high absorption at the wavelengths below 600 nm that is typical for garnet films [2]. Namely, the absorption coefficient in the blue spectral range is about four orders of magnitude larger as compared to the wavelength in the near-IR spectral range, which is rather important for the nonlinear optical experiments.

**Figure 1.** (**a**) Optical density (OD) and transmission spectra of (*LuBi*)3*Fe*5*O*<sup>12</sup> film, high absorption region corresponding to the second and third harmonics wavelengths is in green, high transparency range is in red. (**b**) Optical transmission microscopy image of the film measured for the crossed orientations of the polarizer and the analyzer; and (**c**) MFM image of the (*LuBi*)3*Fe*5*O*<sup>12</sup> film.

Magnetic force microscopy (MFM) experiments of the garnet films were performed using the set-up described in detail in [42]. In brief, we used the atomic force microscope SmartSPM (AIST-NT, now produced by HORIBA Scientific) with a special magnetic tip composed of a multilayered [*Co*(2)/*Pt*(5)]<sup>10</sup> film, the thickness of the corresponding layers in Angstrom is denoted in brackets. Such a composition of the sensitive layer of the tip provided, first, the perpendicular magnetic anisotropy of the film and, second, its small magnetic moment. As a result, the magnetic structure of the studied sample was not disturbed during the MFM measurements.

MFM images of (*LuBi*)3*Fe*5*O*<sup>12</sup> films were obtained in a standard two-pass technique (the so called lift mode), when at the first step the topography of the studied sample is recorded followed by the registration of the magnetic response in the constant distance surface-probe mode at the second step. Our measurements have shown that the films are flat, the root mean square average of the profile height deviations from the mean value (RMS) being about 1 nm. It is worth noting that the MFM probe reveals the distribution of the magnetic stray field along the normal to the surface, while the field associated with the in-plane components of magnetization remain much less pronounced in the MFM profile.

For the nonlinear optical microscopy studies, we used the radiation of an optical parametric oscillator (OPO) system Topol 1050-C (Avesta) with the laser pulse duration of up to 180 fs, wavelength tunable in the spectral range from 740 nm up to 1800 nm, and the mean power of 100 mW. The pump radiation was focused by a Nikon Plan Apo 60× oil objective with the NA = 1.4 in a spot of about 0.7–0.8 μm in diameter, which provided the waist length of the laser beam of a few micrometers, depending on the wavelength of the laser radiation. Mitutoyo M Plan Apo 100x objective with the NA = 0.7 was used for gathering the transmitted radiation at the second or third harmonic's wavelengths, the nonlinear optical signal being detected by the Hamamatsu R4220 photomultiplier (PMT). In our experiments, the (*LuBi*)3*Fe*5*O*<sup>12</sup> film was fixed at the Ratis three-axes piezo scanner stage, providing the positioning accuracy of a few nanometers. Polarizations of the input and harmonics' radiation were controlled by the Glan–Taylor calcite polarizers and the necessary set of color filters placed in front of the PMT were used to block the pump beam passing through the garnet layer.

In accordance with the transmission spectrum of the (*LuBi*)3*Fe*5*O*<sup>12</sup> layer shown in Figure 1a, the studied garnet films are transparent for the fundamental laser radiation in the whole tuning range marked by red in Figure 1a, while second and third harmonics' wavelengths typically fall into the absorption band. This allows the study of the nonlinear and magnetic properties of the interfaces of garnet films with the surrounding media (air and GGG) using the SHG or THG microscopy technique. Besides the evidently high in-plane spatial resolution of the nonlinear optical probe provided by strong focusing of the pump radiation, the in-depth resolution is mostly determined by small escape lengths at harmonics' frequences at the wavelengths shorter than 600 nm. Importantly, the in-depth resolution of the nonlinear microscopy techniques exceeds that of the linear optical one due to the nonlinear dependence of the response on the pump intensity; the higher the order of the nonlinearity, the stronger the spatial localization of the nonlinear optical response at the second or third harmonics' wavelengths.

#### **3. Experimental Results**

Figure 1b shows the optical transmission image of the studied (*LuBi*)3*Fe*5*O*<sup>12</sup> film in the absence of the external magnetic field for the crossed polarizations of the incident and transmitted beams. Dark and light regions on the Figure correspond to stripe domains in the bulk of the garnet film with the period of the domain structure of about 4.4 μm; the contrast in the image appears as the result of the opposite in sign Faraday rotation in the adjacent domains with residual magnetization oriented predominantly along the normal to the garnet layer.

A magnetic force microscopy image of the (outer) (*LuBi*)3*Fe*5*O*12/air interface measured over the 20 μm × 20 μm surface area is shown in Figure 1c. Besides the periodic magnetic structure associated with the aforementioned stripe domains, it reveals a zigzaglike pattern with the period of approximately 1.6 μm associated with the block blind domains. It is worth noting that the high contrast of the MFM signal from the adjacent domains indicate the predominant perpendicular magnetic anisotropy of the film.

Similar conclusions were made based on the studies of the second harmonic generation microscopy of the (*LuBi*)3*Fe*5*O*12/air interface, as the pump laser beam at the wavelength of 850 nm was incident on the sample from the substrate side (see Figure 2a). In that case, the SHG response at the wavelength of 425 nm is formed by the surface layer of 2–3 μm in thickness (determined by the escape length of the radiation at the SHG wavelength), which allows the study of the surface domain structure of garnet film at this hidden interface.

Figure 2b,d show the SHG intensity patterns for the parallel (panel *b*) and orthogonal (panel *d*) polarizations of the fundamental and SHG beams. In both cases the pump beam was polarized along the stripe domains oriented in the vertical direction on the Figure; the scanning was performed over the surface area of 7 μm × 7 μm. One can see that in the first case, the SHG pattern reveals the stripe domains that appear as the bands with a strong difference in the SHG intensity, while for the crossed polarizations of the pump and SHG waves, a chessboard-like pattern of the SHG intensity is attained. Figure 2c shows the 3D distribution of the SHG intensity from the same surface region as in Figure 2d. It also demonstrates a strongly periodic modulation of the nonlinear optical response with the periods of about 4.2 μm in the horizontal direction and corresponds to the stripe magnetic domains, while the period of 1.6 μm appears along the vertical direction. These images confirm the existence of zigzag-shape closure domains with a predominant in-plane orientation of magnetization, which stems from the symmetry analysis discussed in [42]. Importantly, the stripe domains' alignment and relevant SHG patterns are independent on the crystallographic orientation of the film and follow the direction of the external magnetic field used for their magnetization, which was removed prior to the MFM or nonlinear optical studies.

**Figure 2.** (**a**) Scheme of the light beams propagation in the nonlinear optical microscopy measurements of the (*LuBi*)3*Fe*5*O*12/air interface; (**b**,**d**) SHG intensity patterns of the (*LuBi*)3*Fe*5*O*<sup>12</sup> film, the polarization plane of the fundamental radiation is oriented in the vertical direction on the figure, the polarization of the generated SHG is vertical (**b**) and horizontal (**d**). (**c**) The 3D SHG intensity pattern corresponding to that shown in panel (**d**).

Similar SHG microscopy experiments were performed for the hidden (*LuBi*)3*Fe*5*O*<sup>12</sup> /GGG interface, which is inaccessible by the MFM technique (Figure 3). Really, in that case the MFM probe is separated from the garnet layer by a GGG substrate that is several hundreds of micrometers in thickness. In order to attend the (*LuBi*)3*Fe*5*O*12/GGG interface by the SHG microscopy probe, we reversed the experimental geometry so that the laser beam was incident on the sample from the film side, as shown schematically in Figure 3a. The effective thickness of the garnet layer participating in the SHG process was estimated by measuring the dependence of the SHG intensity on the coordinate along the normal to the film, *z*, which is shown in Figure 3b. One can see that the intensity of the SHG response reveals a maximum with the full width at half maximum (FWHM) of about ≈2.5 μm situated close to the interface. The coordinate of this SHG maximum *zmax* corresponds to the escape length of the SHG wavelength in the garnet films and thus determines the in-depth resolution of the SHG probe; its position was used as a reper when scanning along the *z*-direction.

Similarly, we switched to the studies of the third harmonic microscopy of the garnet films. Figure 4 shows the THG intensity patterns for the hidden (*LuBi*)3*Fe*5*O*12/GGG interface; the experimental scheme is sketched in Figure 4a. The fundamental wavelength in the spectral range of 1200–1600 nm was used, so that the detected THG at 400–530 nm wavelength corresponds to the high absorption of the garnet film. Figure 4b shows that the effective thickness of the layer contributing to the third harmonic generation is about 2 μm, which is less than for the case of the SHG scheme due to the higher-order nonlinearity of the process. Similarly, higher in-plane resolution of the THG probe is attained.

**Figure 3.** (**a**) Scheme of the light beam propagation in the SHG microscopy measurements of the (*LuBi*)3*Fe*5*O*12/GGG interface; (**b**) dependence of the SHG intensity on the coordinate within the garnet film, z = 0 corresponds to the garnet/GGG interface. (**c**,**d**) SHG intensity patterns of the (*LuBi*)3*Fe*5*O*12/GGG interface layer, the polarization plane of the fundamental radiation is oriented in the vertical direction on the figure, the polarization of the generated SHG is vertical (**c**) and horizontal (**d**).

Contrary to the SHG case, the THG intensity pattern for the parallel polarizations of the fundamental and harmonic's beams is constant within the experimental accuracy over the whole scanning range of 10 × 10 μm. This indicates that the relative value of the magnetization-induced components of the THG polarization are negligibly small as compared to the non-magnetic (crystallographic) ones. At the same time, if the detected THG polarization is close to the orthogonal position with respect to the polarization plane of the laser beam and forms the angle of 85◦ (Figure 4c) or 90◦ (Figure 4d) with it, pronounced THG patterns appear. One can see a zigzag-type dependence similar to that attained in the SHG response and very much similar to the MFM pattern shown in Figure 1c. For crossed-pump and the THG waves' polarizations, the domain structure demonstrates nearly triangular-like features places in a chess-like order above the stripe domains. If the analyzer is rotated by 5◦ from the crossed position, an even more detailed magnetic pattern is observed, indicating the spatial resolution of the THG probe of less than 0.5 μm.

**Figure 4.** (**a**) Scheme of the light propagation in the THG microscopy measurements; (**b**) the dependence of the averaged THG intensity of the coordinate *z* along the normal to the film. THG intensity patterns measured with the polarization plane of the fundamental radiation oriented in the vertical direction in the figure, the THG polarization is horizontal (**c**) and tilted to about 5◦ from the horizontal direction (**d**). Fundamental wavelength of 1500 nm was used in these measurements.

#### **4. Discussion**

For the case of noncentrosymmetric magnetic media, nonlinear polarization at the second or third harmonics' wavelengths is given by a vector sum of the two types of terms of the electric field at the corresponding wavelengths, the so called *even* and *odd* components with respect to magnetization: **P**2*ω*,3*<sup>ω</sup>* ∝ **E***even* <sup>2</sup>*ω*,3*<sup>ω</sup>* + **<sup>E</sup>***odd* <sup>2</sup>*ω*,3*ω*. In turn, these field components are determined by the effective *even* and *odd* components of the nonlinear susceptibilities *χeven* 2*ω*,3*ω*(*M*)=*χeven* <sup>2</sup>*ω*,3*ω*(− M) and *<sup>χ</sup>odd* 2*ω*,3*ω*(M)=−*χodd* <sup>2</sup>*ω*,3*ω*(−M), the latter changes its sign under the magnetization reversal. In this simplified description, we restrict ourselves linearly in **M** terms of the magnetization-induced nonlinear optical response at the SHG or THG wavelengths, as they are the strongest in the case of a magnetized sample or in a medium with spontaneous magnetic structure (i.e., in a domain-like one) [35]. Interference of these components of the harmonics' fields provides linear in magnetization modulation of the SHG (THG) intensity, which can be characterized by the corresponding magnetic contrast

*<sup>ρ</sup>*2*ω*,3*<sup>ω</sup>* <sup>∝</sup> *<sup>χ</sup>odd* 2*ω*,3*ω χeven* 2*ω*,3*ω* [25] and allows the visualization of the magnetic domains with different

orientation of the average magnetization. At this stage, magnetization-induced effects in the nonlinear optical response are qualitatively similar to their linear optical analogues, i.e., magnetooptical Kerr and Faraday effects, while the values of the SHG magnetic contrast *ρ*2*<sup>ω</sup>* is typically one to two orders of magnitude larger.

Evidently, the contrast in the nonlinear optical response from different types of magnetic domains required for their imaging appears only if both *odd* and *even* in **M** effective components of the nonlinear susceptibility exist. The sets of the nonzero components of the nonlinear susceptibility tensors are governed by the crystallographic and magnetic symmetry of a medium. As garnet belongs to the centrosymmetric cubic (*m*3*m*-symmetric) class, the bulky SHG is suppressed by symmetry arguments and thus the second harmonic (in the electric dipole approximation) should be generated by the interfaces with broken inversion symmetry. At the same time, the bulk SHG effect was registered in substituted garnets with the structure distorted by the presence of large ions such as bismuth or induced by the lattice mismatch at the garnet/GGG interface [43], which seems to be our case. Meanwhile, third harmonic generation is allowed in the bulk of the materials of any symmetry class, including garnets.

If taking into consideration the transparency of garnet films at the fundamental wavelength, transmission coefficients at the second and third harmonic's wavelengths and localization of the pump beam in the laser beam waist, the intensity of the SHG (THG) transmitted through the garnet film can be expressed as

$$I\_{m\omega}(\pm M, z, r) = \int\_{V} T\_{m\omega}(z) (\chi\_{m\omega}^{\varepsilon \text{rev}} \pm \chi\_{m\omega}^{\text{odd}}(\pm M))^2 L(z, r)^m dz dr \tag{1}$$

where *m* = 2, 3 corresponds to the number of harmonic (second or third), *L*(*z*,*r*) is the dependence of the fundamental field intensity on the transversal radius-vector **r** and on the coordinate along the direction of the beam propagation, *z*. Integration over *z* can be restricted by the waist length according to the expression *<sup>L</sup>*(*z*,*r*) = *<sup>I</sup>*0/(<sup>1</sup> + ( *<sup>z</sup> zR* )2), where *zR* is the Rayleigh length of the focusing objective and *d* is the film's thickness, *I*<sup>0</sup> is the input intensity of the fundamental laser beam, *Tmω*(*z*) ∝ exp[−*αmω*(*d* − *z*)] are the intensity transmission functions at the SHG and THG wavelengths, and the integral is taken over the excited volume *V* of the (*LuBi*)3*Fe*5*O*<sup>12</sup> film. Here we assume that the effective nonlinear susceptibilities *χm<sup>ω</sup>* are uniformly distributed in the garnet film and the nonlinear contribution of the GGG substrate is negligibly small, as stems from our experiments. Thus the SHG or THG intensity maxima of the *Imω*(*z*) dependencies (see Figures 3b and 4b) are attained within the garnet film close to its exit boundary. It is worth noting that the resolution of the THG microscopy technique is higher as compared to the SHG one due to the third-order dependence of its intensity on *L*(*z*,*r*), while it is quadratic for the SHG case.

The analysis of the SHG and THG intensity patterns shown in Figures 3 and 4 is a complicated task, as the epitaxial garnet films are (111) symmetric and the tensors *χ*ˆ(2) and *χ*ˆ(3) contain many nonzero components, both crystallographic (*even*) and magnetizationinduced (*odd*) [35,44]. Still, based on the analysis of the SHG intensity patterns measured for the parallel (Figures 2b and 3c) and orthogonal (Figures 2d and 3d) combinations of

polarization of the fundamental and SHG beams, one can judge the orientation of the magnetization in domains similarly to those discussed recently in [42] for the garnet/air interface. Namely, the method reveals only the in-plane M components orthogonal to the polarization of the SHG wave, i.e., "vertical" in the first case and "horizontal" in the second. It means that the spontaneous magnetization of stripe domains of the garnet film is tilted with respect to the film's normal, which may be due to the (111) film's symmetry. Similar conclusion on the direction of the magnetization in such films has been proposed based on the analysis of the MFM image of the cleavage (end face) of the garnet film [42]. This provides a large (up to 60%) contrast in the second harmonic intensity generated by the neighbour stripe domains.

Shorter-period modulation of the SHG intensity in the direction along the stripe domains observed at the interfaces of the (*LuBi*)3*Fe*5*O*<sup>12</sup> layer with air (Figure 2) and with the GGG substrate (Figure 3) is associated with the nonlinear response of the block (closure) domains; the modulation is better seen for the crossed polarizations of the SHG and pump radiation (panels *d* in Figures 2 and 3). In that case, the maximum contrast of the SHG intensity is attained for the adjacent closure domains placed along the horizontal line in Figures 2d or 3d, which correspond to the opposite signs of the "vertical" **M** component. If taking into account the analogous analysis of the SHG intensity pattern for the parallel polarizations of the SHG and pump beams, we have to conclude that the in-plane magnetization of the closure domains forms a nonzero angle with the magnetic stripes. This is probably the reason for the formation of the zigzag-shape patterns attained both in the MFM measurements (see Figure 1c) and in the THG response (Figure 4).

Based on the results of the experiments described in this paper, we may conclude that the organization of magnetic domains at the hidden (*LuBi*)3*Fe*5*O*12/GGG interface is quite similar to that of the (*LuBi*)3*Fe*5*O*12/air interface; even the periods of stripe and block domains nearly coincide. This shows that a discontinuity of the garnet crystalline structure plays the most important role in the formation of the closure surface magnetic domains, while the influence of the surrounding media, namely crystalline gallium gadolinium garnet or air in our case, is less important.

#### **5. Conclusions**

Summing up, we performed experimental studies of the magnetic domain structure of 10 μm thick *Bi*, *Lu*-substituted epitaxial garnet films by a combination of magnetic force microscopy and nonlinear optical microscopy techniques based on the effects of the second and third harmonics generation. In the latter case, strong localization of the pump radiation of a pulsed femtosecond laser source along with the nonlinear power dependence of the registered harmonics' signal allowed to the visualization of the magnetic stripe domains in the bulk of the garnet film through a pronounced contrast in the average second and third harmonics' intensity in adjacent domains. Based on the symmetry analysis of the nonlinear optical response, we conclude that magnetization of this type of domain is tilted with respect to the film's normal as well as to the stripe domains .

Moreover, we applied the nonlinear optical technique to approach and investigate the magnetic organization of the buried interface of the (*LuBi*)3*Fe*5*O*<sup>12</sup> epitaxial layer with the gallium gadolinium garnet substrate, which is inaccessible for the MFM studies. We found that a zigzag-shape interface domain appear above the bulk stripe ones, similarly to the upper (*LuBi*)3*Fe*5*O*12/air interface studied quite recently. This confirms that the main role is played here by the discontinuity of the garnet crystalline structure for the magnetic domains' organization, while the type of neighbour medium is less important.

We also present the first experimental demonstration of the efficiency of the the third harmonic generation microscopy for the study of magnetic domains in garnet films. In spite of relatively small linear values in magnetization contribution to the third harmonic response, the THG microscopy for the nearly crossed polarizations of the fundamental and THG beams allows the visualization of the surface magnetic closure domains at the hidden garnet/GGG interface and provides even higher spatial resolution of the magnetic structure as compared to magnetization-induced second harmonic generation.

**Author Contributions:** Conceptualization, A.T., A.M. and T.M.; methodology, M.T. and A.M.; software, A.T. and A.M.; validation, M.T., T.M. and A.M.; formal analysis, A.T. and A.M.; investigation, M.T., A.M. and A.T.; resources, A.M.; data curation, M.T. and A.M.; writing—original draft preparation, T.M. and A.T.; writing—review and editing, A.T. and A.M.; visualization, A.T.; supervision, T.M.; project administration, A.T. and M.T.; funding acquisition, T.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Russian Science Foundation, Grant 19-72-20103-P. MFM studies were supported by Russian Science Foundation, Grant 19-19-00607-P.

**Institutional Review Board Statement:** Not applicable.

**Data Availability Statement:** The data presented in this paper are available upon request.

**Acknowledgments:** The authors acknowledge useful discussions with M. Logunov.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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## *Article* **Femtosecond Optical Nonlinearity of Nanodiamond Suspensions**

**Gennady M. Mikheev 1,\*, Viatcheslav V. Vanyukov 2, Tatyana N. Mogileva 1, Konstantin G. Mikheev 1, Alexander N. Aleksandrovich 1, Nicholas A. Nunn 3,4 and Olga A. Shenderova <sup>3</sup>**


**Abstract:** High pressure-high temperature (HP-HT) nanodiamonds and detonation nanodiamonds have unique optical properties and are promising materials for various applications in photonics. In this work, for the first time, comparative studies of the nonlinear optical properties of aqueous suspensions of HP-HT and detonation nanodiamonds under femtosecond laser excitation are performed. Using the z-scan technique, it was found that for the same laser pulse parameters HP-HT nanodiamonds exhibited optical limiting due to two-photon absorption while detonation nanodiamonds exhibited saturable absorption accompanied by short-term optical bleaching, revealing the different electronic-gap structures of the two types of nanodiamonds. The saturable absorption properties of detonation nanodiamonds are characterized by determining the saturable and non-saturable absorption coefficients, the saturation intensity, and the ratio of saturable to non-saturable losses. The nonlinear absorption in HP-HT nanodiamonds is described with the nonlinear absorption coefficient that decreases with decreasing concentration of nanoparticles linearly. The results obtained show the possibility of using aqueous suspensions of nanodiamonds for saturable absorption and optical limiting applications.

**Keywords:** nanodiamonds; nonlinear optics; nonlinear refraction; nonlinear absorption; two-photon absorption; saturable absorption; optical limiting

#### **1. Introduction**

From the invention of lasers to the present time, the intensive study of the nonlinear optical properties of various materials has continued. The rapid development of nanotechnology in recent years has led to a wide variety of nanomaterials, including nanocarbons, which have nonlinear optical properties and that are of great interest for various applications. To date, there are a large number of works devoted to the study of the nonlinear optical properties of carbon nanotubes, graphene, and various composites based on them. These works are aimed at investigating, e.g., optical limiting (a nonlinear decrease of the transmitted light intensity) [1] and saturable absorption (a nonlinear increase of the transmitted light intensity) [2] to develop and create optical limiters of nanosecond laser pulses [3–13] and passive laser shutters for generating picosecond and femtosecond laser pulses [14–24], respectively. Nanodiamond, being another form of nanocarbon material, is also attractive due to its unique properties [25–33]. Among the various methods for producing nanodiamonds [27,34], the most prevalent are the detonation synthesis method [35] and the method of grinding diamonds synthesized at high pressure and high temperature (HP-HT) [36].

**Citation:** Mikheev, G.M.; Vanyukov, V.V.; Mogileva, T.N.; Mikheev, K.G.; Aleksandrovich, A.N.; Nunn, N.A.; Shenderova, O.A. Femtosecond Optical Nonlinearity of Nanodiamond Suspensions. *Appl. Sci.* **2021**, *11*, 5455. https://doi.org/ 10.3390/app11125455

Academic Editor: Alessandro Belardini

Received: 14 May 2021 Accepted: 10 June 2021 Published: 11 June 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

The nonlinear optical properties of detonation nanodiamonds and various complexes based on them have been extensively studied. Similar to carbon nanotubes and graphene, detonation nanodiamonds have been studied for the development and creation of nonlinear optical filters operating in a wide wavelength range to protect the eyes and sensitive optical components from the damaging effect of powerful laser pulses of nanosecond duration. It was found that in addition to nonlinear absorption, the nonlinear scattering of light has a significant effect on the nonlinear decrease in the optical transmittance with increasing incident light fluence in the nanosecond time domain [37–41]. Nonlinear absorption and nonlinear scattering have been found, depending on the nanodiamond particles size and concentration in suspensions [42–44]. It was also found that the functionalization of detonation nanodiamonds with other nanoparticles and complexes suitable for this purpose leads to a further decrease in the nonlinear transmittance coefficient [41,45–48]. It has been also shown that aqueous suspensions of detonation nanodiamonds exhibit a saturable absorption (a short-term increase in the transmittance) under nanosecond [49] and femtosecond [50] excitations. Despite the number of studies of nonlinear optical properties of detonation nanodiamonds, to the best of our knowledge, there is only one work on the nonlinear optical properties of HP-HT nanodiamonds. In that work, the observation of optical limiting in an aqueous suspension of HP-HT nanodiamonds under excitation by nanosecond laser pulses at a wavelength of 532 nm was reported [51]. This is of interest for further investigation of the nonlinear optical properties of HP-HT nanodiamonds by exploring the femtosecond time domain and to compare the nonlinear optical response of those with the detonation nanodiamonds under the same experimental conditions.

In this work, we show that aqueous suspensions of HP-HT nanodiamonds exhibit nonlinear optical properties in the femtosecond time domain. Moreover, we show that aqueous suspensions of detonation and HP-HT nanodiamonds with an average size of ~10 nm possess different nonlinear optical properties under femtosecond laser excitation. Specifically, suspensions of HP-HT nanodiamonds exhibit optical limiting originating from the two-photon absorption, while suspensions of detonation nanodiamonds demonstrate optical self-bleaching due to saturable absorption.

#### **2. Materials and Methods**

HP-HT nanodiamonds were obtained from Van Moppes, Geneva, Switzerland. The HP-HT nanodiamond particles are monocrystals with a substitutional nitrogen content of ~100 ppm. The purification of nanodiamonds from carbon was carried out by processing in the air at a temperature of 500 ◦C for two hours, followed by treatment in hydrochloric acid at a temperature of 70 ◦C for two hours. The nanoparticles were dispersed in deionized water at 1.65 wt% concentration and the suspensions were stored in plastic vessels.

Detonation nanodiamonds were synthesized by an explosion of an oxygen-deficient explosive mixture of trinitrotoluene and hexogen at a weight ratio of 1:1 in a closed steel chamber. The resulting detonation soot contains the nanodiamond particles (more than 30%), the other allotropic states of carbon, and various metallic impurities. Purification of the diamond soot in the mixture at the high temperature reduces the amount of impurities down to 1 wt%. These detonation nanodiamonds received from a vendor were additionally purified at Adamas Nanotechnologies with HCl, reducing the metal content to 0.4 wt%. Detonation synthesis leads to the formation of nanodiamonds with a primary particle size of about 5 nm. The natural agglomeration of nanodiamonds leads to the formation of solid particles of much larger sizes. To obtain nanoparticles with a given average size the purified nanodiamonds were suspended in deionized water by sonication and processed in a planetary mill for 4 h using zirconia beads. Additional sp2-carbon from milling was removed by treatment at 400 ◦C in the air for 3 h. After this high-temperature treatment, the resulting product was resuspended in deionized water at 1% *w*/*v* by sonication. Centrifugation at 25,000× *g* forces was used to extract nanodiamond particles with an average diameter of ~10 nm. The nitrogen content in the detonation nanodiamonds is ~10,000 ppm.

The major differences in HP-HT and detonation nanodiamonds are in the size of the primary particles, the presence of aggregates consisting of few primary particles in detonation nanodiamonds and nitrogen content. While treatments to reduce sp2-carbon content were performed, residual sp2-carbon is still present in both types of nanodiamond particles, with a higher content expected in detonation nanodiamonds due to the smaller size of primary particles.

For surface and particle size analysis, small droplets of fabricated suspensions of HP-HT and detonation nanodiamonds were placed on a flat glass surface and dried to form a uniform film. The topography images of the nanodiamond films were acquired with an NTEGRA Probe Nanolaboratory atomic-force microscope (AFM) in semicontact mode. The particle size distribution was attained by processing the atomic-force microscope images with Image Analysis 3.5.0 software (NT-MDT Spectrum Instruments, Zelenograd, Russia) based on the combination of the correlation analysis and the method of sections at a certain relative height. The AFM images and the particle size distribution of the nanodiamond films are shown in Figure 1. The performed measurements reveal that more than 75% of the HP-HT and detonation nanodiamonds have sizes in the ranges of 9–20 and 6–13 nm, respectively.

**Figure 1.** Atomic force microscopy images of (**a**) HP-HT and (**c**) detonation nanodiamond films. The image processing reveals the HP-HT and detonation nanodiamond particle size distributions shown in figures (**b**) and (**d**), correspondingly.

Raman spectra of the attained nanodiamond films were recorded using Horiba LabRam HR800 Raman spectrometer (Lille, France) with a 632.8 nm laser. A 100× objective with the attenuation of the incident radiation (neutral filter D1) was used to provide an intensity (less than about 5 kW/cm2) below the graphitization of nanodiamond material at 632.8 nm [29,52]. The measured Raman spectra of detonation and HP-HT nanodiamond films show pronounced peaks with frequency shifts of 1329 and 1330 cm−1, respectively (see Figure 2a). Taking into account the known dependences of the Raman shifts of carbon nanomaterials on the excitation wavelength [53] and the nanoparticle size [54], one can attribute these peaks to nanodiamonds (sp3-form of carbon). The decomposition of the spectra presented in Figure 2a shows that the full width at half maximum (FWHM) of diamond lines of HP-HT and detonation nanodiamonds are 8 and 22 cm<sup>−</sup>1, respectively. It is noteworthy that along with the specified peaks, the Raman spectra exhibit broad luminescence bands caused by defects of various natures contained in HP-HT and detonation nanodiamonds [29,55].

**Figure 2.** (**a**) Raman spectra of HP-HT and detonation nanodiamonds film and (**b**) X-ray diffraction patterns of HP-HT and detonation nanodiamond powders. The X-ray diffraction pattern of diamond (Powder Diffraction File 00-006-0675) is presented for a reference.

For the X-ray diffraction studies, nanodiamond powders were obtained by drying the suspensions at room temperature and subsequent mechanical grinding. When obtaining diffraction patterns, the studied powders were placed on a glass substrate. The diffraction pattern of the substrate without powder was recorded separately. To obtain the diffraction pattern of the studied powder, the corresponding subtraction of the substrate response from the experimental data was performed.

The crystalline structure of the nanodiamonds was studied using Bruker D2 PHASER X-ray diffractometer with a copper-based X-ray tube generating radiation at a wavelength of 0.1541 nm (Kα<sup>1</sup> line). The diffraction patterns of the detonation and HP-HT nanodiamonds powders (see Figure 2b) contain three solitary peaks in the range of 2θ variation from 25◦ to 100◦. These peaks are observed at 2θ angles of 43.9◦, 75.3◦, and 91.5◦. They correspond to X-ray diffraction on the (111), (220), (311) planes of diamond crystallites with interplanar spacings of d111 = 0.2060 nm, d220 = 0.1261 nm, and d311 = 0.1075 nm, respectively, where the subscripts at d denote crystallographic planes. Note that according to the reference data of diamond (see Figure 2b), the intensities of the diffraction lines of monochromatic radiation on the (111), (220), (311) planes are equal to 100, 25, and 16 arb. units, respectively (see Powder Diffraction File (PDF) 00-006-0675). Figure 2b shows that for both diffraction patterns, the ratio between peak amplitudes at angles 2θ equal to 43.9◦, 75.3◦, and 91.5◦ is the same. Processing the measured X-ray diffraction pattern using TOPAS 4.2 software revealed that the mean crystallite sizes (LVol-IB) of the HP-HT and detonation nanodiamond particles are 8.6 and 2.7 nm, respectively. Thus, the

measurements on an X-ray diffractometer show that all the samples under study consist of diamond material.

For the optical measurements, suspensions of both types of nanodiamonds were prepared at three concentrations. Figure 3 shows the optical densities of aqueous suspensions of HP-HT and detonation nanodiamonds at three different concentrations measured in a 1 mm thick optical quartz cell. The measurements were performed using a PerkinElmer Lambda 650 (Shelton, WA, USA) two-beam spectrophotometer relative to the same 1 mmthick quartz cell filled with distilled water. It can be seen that for the suspensions of both types of nanodiamonds, the optical density decreases monotonically with an increase of light wavelength which is the characteristic of nanodiamonds [29,32,49,56,57]. For the suspensions of HP-HT nanodiamonds, the increase in optical density with decreasing wavelength is more pronounced than for the suspensions of detonation nanodiamonds. This can be explained by stronger light scattering in the suspension of HP-HT nanodiamonds caused by the following reasons: (i) the slightly larger average nanoparticle size of the HP-HT nanodiamond suspension compared to the average nanoparticle size of the detonation nanodiamond suspension; (ii) the larger "effective" refractive index of HP-HT nanodiamonds compared to the "effective" refractive index of detonation nanodiamonds due to the difference in their crystal structures. For both types of nanodiamonds the optical density measured at different wavelengths is proportional to the concentration (see insets in Figure 3a,b).

**Figure 3.** The optical density of the (**a**) HP-HT and (**b**) detonation nanodiamond suspensions in 1 mm thick quartz cell. Insets show the corresponding optical density as a function of concentration measured at three different wavelengths of 400, 532, and 795 nm.

Studies of the nonlinear optical properties of nanodiamond suspensions were carried out using the z-scan technique [58] with femtosecond linearly polarized laser pump (wavelength 795 nm, pulse duration 120 fs, and the repetition rate of 1 kHz). In the experiments, simultaneous measurements of transmittance in the closed- and open-aperture configurations were performed (Figure 4). The laser radiation was focused on a cell with a focal length of 75 mm. The cell had 1 mm-thick quartz walls with a 1 mm opening distance. The laser beam waist radius was w0 = 12.9 μm, which corresponds to the Rayleigh length of z0 = 0.65 mm (z0=πw0 2/λ, where λ is the wavelength). The scanning of the cell was performed along the optical z-axis of the focused laser beam using computer numerical control with a step of 0.1 mm with multiple averaging of the pulse energies Eoa and Eca recorded using "open-aperture" and "closed-aperture" photodetectors, respectively (see Figure 4).

**Figure 4.** Sketch of the z-scan experimental setup.

In the experiments, the dependences of the nonlinear transmittance coefficients Toa(z) = Eoa(z)/Ein (with an open-aperture) and Tca(z) = Eca(z)/Ein (with a closed-aperture) were measured during scanning of the cell along the z-axis, where Ein is the incident laser pulse energy measured using a reference photodetector. This made it possible to determine the dependences of the normalized nonlinear transmittance coefficients Toa,n(z) = Toa(z)/Toa(z = ∞) and Tca,n(z) = Tca(z)/Tca(z =∞) with open- and closed-apertures respectively, where Toa(z = ∞) and Tca(z = ∞) are the optical transmittance coefficients at open- and closedapertures, respectively, obtained far from the beam waist, i.e., far from z = 0. The energy of laser pulses incident on the cell was varied using a polarizer and a half-wave plate. To visualize nonlinear refraction in the experiments, the ratio of nonlinear transmittance obtained in a closed- aperture to the data obtained in an open-aperture tnr(z) = Tca,n (z)/Toa,n (z) was determined [59].

#### **3. Results**

The dependences Toa,n(z) and tnr(z) obtained for a cell filled with distilled water (a,b) and an empty cell (c,d) at Ein = 200 nJ are presented in Figure 5a–d. The dependence Toa,n(z) obtained for a cell with distilled water shows a small dip in the vicinity of z/z0 = 0 indicating a weak nonlinear absorption. At the same time, the experimental data Toa,n(z) obtained for an empty cell (Figure 5c) shows no corresponding dip. This means that the observed weak nonlinear absorption for a cell with distilled water occurs because of distilled water and not because of the cell. The nonlinear absorption in distilled water originates from multi-photon absorption [60]. Comparison of the closed/open-aperture data for a cell filled with water (Figure 5b) and an empty cell (Figure 5d) shows that the observed nonlinear refraction leading to self-focusing of the femtosecond laser beam occurs mainly in the quartz walls of the optical cell. The observed cluster of dots at the vicinity of z/z0 = 0 in Figure 5d arises from the quartz walls-air-quartz walls boundary and not affecting on the amplitude of the normalized transmittance. Closed/open-aperture measurements were also performed for both the studied types of nanodiamonds with the results shown in Figure 5e,f). Adding the nanoparticles to water has no noticeable impact on the nonlinear refraction of the suspensions as one can observe by comparing Figure 5b,d–f) indicating weak nonlinear refraction in both suspensions for given concentrations.

**Figure 5.** The normalized transmittance of the quartz cell with (**a**) distilled water and (**c**) an empty cell obtained in the openaperture z-scan. The ratio of the nonlinear transmittance obtained in the closed to the data obtained in the open-aperture z-scan for the quartz cell (**b**) with distilled water, (**e**) with HP-HT nanodiamond suspension, (**f**) with detonation nanodiamond suspension, and (**d**) an empty cell. The measurements were performed at the incident laser pulse energy of 200 nJ.

The results of the open-aperture normalized transmittance measurements for aqueous suspensions of HP-HT nanodiamonds are shown in Figure 6. The measurements were performed at the same incident pulse energy of Ein = 200 nJ. In order to reveal the dependence of the nonlinear optical properties, i.e., nonlinear absorption on the nanoparticle concentration C, we performed the measurements for the C ranging from 0.1 to 1 wt%. It is shown that the higher the concentration, the stronger the nonlinear absorption, the lower the transmittance at z/z0. Even at a low concentration of 0.08 wt%, the nonlinear transmittance exhibits a visible dip. It is noteworthy that the dependencies shown in Figure 6 are symmetric relative to z/z0 = 0 indicating prominent optical limiting properties of femtosecond laser pulses.

**Figure 6.** (**a**–**e**) Normalized transmittance of suspensions of HP-HT nanodiamonds with different concentrations recorded in the open-aperture z-scan. Dots correspond to the experimental data while solid lines represent the result of the fitting with Equation (2). Figure (**f**) represents the dependence of the calculated two-photon absorption coefficient β as a function of concentration C.

One can assume that the mechanism of optical limiting in suspensions of HP-HT nanodiamonds is two-photon absorption, in which the absorption coefficient *αTPA* of the medium depends on the radiation intensity I according to the equation [61]

$$
\mathfrak{a}\_{TPA}(I) = \mathfrak{a} + \beta I,\tag{1}
$$

where α and β are the coefficients of linear and nonlinear absorption, respectively. This can be verified by approximating the experimental data presented in Figure 6 with the wellknown equation (see [61]) derived to describe two-photon absorption for the open-aperture z-scan for a Gaussian laser beam and temporally Gaussian pulse:

$$T\_{\text{ou,tr}} = 1 + \sum\_{m=1}^{\infty} \left[ -q(z, t=0) \right]^m / \left( m+1 \right)^{3/2} \,, \tag{2}$$

where *q*0(*z*, *t* = 0) = *βI*0(*t* = 0)*Leff* /(1 + *z*2/*z*<sup>2</sup> <sup>0</sup>), *Leff* <sup>=</sup> <sup>1</sup> <sup>−</sup> *<sup>e</sup>*−*αL* /*α* , *α* = −*lnT*0/*L*, *I*<sup>0</sup> (*t* = 0) = *Ein*/[*πw*<sup>2</sup> <sup>0</sup>Δ*t* <sup>√</sup>*<sup>π</sup>* 2 √ *ln*2 ] (see [58]), *I*0(*t*) is the on-axis irradiance at focus (i.e., z = 0), Δt is the pulse duration (FWHM) of a Gaussian laser pulse, T0 is the linear transmittance of the studied sample with thickness L. Equation (2) with the first four terms from an infinite series of elements is in good agreement with the experimental z-scan data shown in Figure 6. The values of β found as a result of the approximation of the experimental data, depending on the concentration of nanoparticles C, are shown in Figure 6f and can be expressed as β(m/W) = (5.7 + 22.1 × C(wt%)) × <sup>10</sup>−15. It follows from the approximation, that the defined <sup>β</sup> does not vanish when the concentration of nanoparticles in suspension is tending to zero confirming the earlier obtained z-scan data for a cell filled with distilled water (see Figure 5a). Based on the above, one can conclude that the two-photon absorption well describes the mechanism of the nonlinear behavior in aqueous suspensions of HP-HT nanodiamonds.

The results of the normalized transmittance recorded in the open-aperture z-scan for a fixed concentration of aqueous suspension of detonation nanodiamonds are shown in Figure 7. We have not presented the measurements for the various concentrations as for HP-HT nanodiamonds because those have been already reported [49]. Instead, measurements of the normalized transmittance with variation of the incident laser pulse energy have been performed. In contrast to HP-HT nanodiamonds, suspensions of detonation nanodiamonds exhibit an increase in the nonlinear transmittance with increasing incident light intensity. In the range of incident laser pulse energies, the experimental curves of Toa,n(z) presented in Figure 7 are symmetrical relative to the focal point z/z0 = 0. This suggests that the observed phenomenon is not associated with laser-induced irreversible bleaching [62,63], but originates from the saturable absorption which has been extensively studied in graphene, carbon nanotubes [15,23,24,64,65] and has also been reported in detonation nanodiamonds with larger particle sizes under femtosecond excitation [50]. Similar to graphene and carbon nanotubes the observed saturable absorption in detonation nanodiamonds is characterized by a short-term decrease of its absorption coefficient during the passing of a light pulse of high intensity and caused by the electronic transition between two energy levels.

**Figure 7.** (**a**–**d**) Normalized transmittance of suspensions of detonation nanodiamonds obtained in the open-aperture z-scan for a fixed concentration of 1.25 wt% for various incident laser pulse energies ranging from 106 to 360 nJ. Dots represent the experimental data while solid lines represent the result of the fitting with Equation (5).

In accordance with [65,66], the absorption coefficient at saturable absorption is given by:

$$
\mathfrak{a}\_{SA}(I) = \mathfrak{a}\_{ns} + \mathfrak{a}\_0 / \left(1 + I / I\_{\rm sat}\right) \tag{3}
$$

where *αns* is the linear absorption coefficient due to the presence of light losses in the medium that are not associated with saturable absorption, *α*<sup>0</sup> is the coefficient characterizing the absorption in a two-level energy system, where the population moves under the action of resonant laser pumping, leading to equalization of the level populations at high intensities (saturation of absorption) [67], *Isat* is the saturation intensity, i.e., the intensity at which *α*<sup>0</sup> is halved. It should be noted that the linear absorption coefficient *αSA*(*I* = 0) = *αns* + *α*0, and at *I Isat αSA*(*I* → ∞) = *αns*, is true, i.e., even at very high pump intensities, complete bleaching of the medium does not occur. The coefficients *α*<sup>0</sup> and *αns* are commonly referred to as saturable and nonsaturable absorptions, respectively.

As was established above, the observed multiphoton absorption in pure distilled water is weak and therefore one can neglect its effect on the saturable absorption. In order to find the dependence of nonlinear transmittance on the incident intensity of a suspension of nanoparticles exhibiting saturable absorption the following differential equation should be solved:

$$dI/dzt = -\mathfrak{a}\_{SA}I\_{\prime} \tag{4}$$

which is describing the propagation of the light pulse in a nonlinear medium [61] with the absorption coefficient presented in the form (3). For this case, the exact solution of Equation (4) yields to [49]:

$$T\_{\rm ox,n} = \left[\frac{I\_{\rm out}/I\_{\rm sat} + 1 + \alpha\_0/\alpha\_{\rm ns}}{I\_{\rm in}/I\_{\rm sat} + 1 + \alpha\_0/\alpha\_{\rm ns}}\right]^{-\alpha\_0/\alpha\_{\rm ns}},\tag{5}$$

where *Iout* and *Iin* are the output and incident radiation intensities. Saturable absorption leads to a slight increase in the intensity at the output of the cell (see Figure 7), therefore, the following expression is valid *Iout* = *T*<sup>0</sup> × *Iin*. For a Gaussian beam during z-scan, the relation *Iin* = *I*0/(1 + *z*/*z*0)<sup>2</sup> is satisfied. Taking all this into account, one can arrive at the following equation describing the dependence of the normalized transmittance on the sample position:

$$T\_{\rm out,n} = \left\{ \frac{T\_0 \times A + (1+B) \times \left(1 + \left(z/z\_0\right)^2\right)}{A + \left(1+B\right) \times \left(1 + \left(z/z\_0\right)^2\right)} \right\}^{-B},\tag{6}$$

where *A* = *I*0/*Isat* and *B* = *α*0/*αns*.

Equation (6) makes it possible to approximate the experimental dependences shown in Figure 7 with two parameters *A* and *B*. Considering that *lnT*<sup>0</sup> = −(*αns* + *α*0) × *L*, where *T*<sup>0</sup> is the linear transmittance of the suspension, we arrive at the *Isat* = 110 GW/cm2 , *αns* = 2.0 cm−<sup>1</sup> and *α*<sup>0</sup> = 0.36 cm<sup>−</sup>1. It is seen from Figure 7 that Equation (6) with the defined parameters approximates the experimental data well. It should be noted that the obtained values of *αns* and *α*<sup>0</sup> are defined for the nanoparticle concentration of C = 1.25 wt% and depend linearly on concentration [49], i.e., *<sup>α</sup>*(cm<sup>−</sup>1) = 1.6 × C (wt%), *<sup>α</sup>*<sup>0</sup> (cm<sup>−</sup>1) = 0.24 × C (wt%). This means that for both the HP-HT and detonation nanodiamonds, the nonlinear absorption coefficients, i.e., two-photon absorption β and saturable absorption *α*<sup>0</sup> coefficients, linearly depend on the nanoparticles concentration. The obtained *αns* and *α*<sup>0</sup> are similar to those obtained for the single-digit detonation nanodiamonds [49]. The attained saturation intensity *Isat* which is concentration independent [49] is the same order as for the aqueous suspensions of detonation nanodiamonds with an average particle size of 50 nm under the femtosecond pulse excitation [50] but 11 × <sup>10</sup><sup>3</sup> times higher than that for the single-digit detonation nanodiamonds under the nanosecond pulse excitation [49]. A similar difference in saturation intensities in nanosecond and femtosecond time domains has been observed in a graphene polymer composite [68].

Another important parameter characterizing the saturable absorption properties and the applicability of the materials for the passive mode-locking is the ratio of the saturable to non-saturable losses [65]:

$$R = \left\{ \exp\left(-a\_{\text{ns}}L\right) - \exp\left[-\left(a\_{\text{ns}} + a\_0\right)L\right] \right\} / \left[1 - \exp\left(-a\_{\text{ns}}L\right)\right] \tag{7}$$

which should be as high as possible. Since the products *αnsL* and *α*0*L* are small, we arrive at *R* = *α*0/*αns* = 0.18 which is lower than for graphene and single-walled carbon nanotubes (*R* ≈ 1) used for passive mode-locking and Q-switching [65].

It should be added that in our experiments, despite the nonlinear absorption, the nonlinear refraction in the nanodiamond suspension due to heat absorption does not manifest itself. This is explained by the fact that the nonlinear absorption observed in the experiments is weak. For example, in the HP-HT nanodiamond suspension at a nanoparticle concentration of C = 1.65 wt% at a laser pulse energy of 200 nJ, the nonlinear absorption is only about 3% (see Figure 6a), and in the suspension of detonation nanodiamonds at the concentration of nanoparticles C = 1.25 wt% at the energy of laser pulses 360 nJ the nonlinear absorption does not exceed 4%.

#### **4. Discussion**

Comparing the obtained results of the nonlinear optical properties of HP-HT and detonation nanodiamond suspensions in the femtosecond time domain one can conclude that they have similar nonlinear refraction but different nonlinear absorption properties. The nonlinear refraction is weak for both types of nanodiamonds and has no impact on the nonlinear refraction of the aqueous suspension with a nanoparticle concentration of about 1 wt%. Under the same experimental conditions, two-photon absorption occurs in suspensions of HP-HT nanodiamonds leading to a decrease in the transmittance, while saturable absorption appears in an aqueous suspension of detonation nanodiamonds leading to self-bleaching indicating that the electronic structures of HP-HT and detonation nanodiamonds differ from each other significantly. It is well known that the energy of the bandgap Eg of a pure bulk diamond is 5.4 eV and as a result there is no optical absorption in such material. The photon energy of the femtosecond laser we used is 1.56 eV, which is about 3.5 times less than Eg. This means that one-photon or two-photon absorptions, as well as saturable absorption at a wavelength of 795 nm in pure bulk diamond, are impossible. However, as can be seen from Figure 3, aqueous suspensions of HP-HT and detonation nanodiamonds are semitransparent in the optical range and their optical densities increase monotonically with decreasing wavelength. In accordance with [56], this is caused by light scattering (the cross-section of which decreases with an increase in the wavelength of incident radiation) and optical absorption that occurs in detonation nanodiamonds in the energy range of 1–2 eV. In a recent paper [69], it was shown that the characteristic extinction spectrum (see Figure 3) of detonation nanodiamonds with a size less than 100 nm is mainly determined by absorption rather than a scattering of light. The saturable absorption we observed in a suspension of detonation nanodiamonds at a photon energy of 1.56 eV is in agreement with these studies. The absence of saturable absorption in a suspension of HP-HT nanodiamonds indicates that there are no energy transitions that effectively absorb radiation at a wavelength of 795 nm. On the other hand, the observation of nonlinear absorption described by two-photon absorption shows that the suspensions of HP-HT nanodiamonds have an absorption band with transition energy of about 3.1 eV, which agrees with the optical density spectrum shown in Figure 3. The significant difference in the femtosecond nonlinear behavior of two types of nanodiamonds may be caused by their different structure.

Indeed, as established above, the average crystallite sizes of HP-HT and detonation nanodiamonds are 8.6 and 2.7 nm, respectively. Taking into account the sizes of the nanoparticles studied (see Figure 1), this means that HP-HT nanodiamonds are predominantly composed of one or two single crystallites, while detonation nanodiamond particles are conglomerates predominantly composed of two to five single crystallites. The difference in the structures of nanoparticles of the two types of nanodiamonds is also indicated by the difference in their Raman spectra presented in Figure 2a. The diamond Raman lines of the HP-HT and detonation nanodiamond spectra with frequency shifts of 1330 and 1329 cm−1, respectively, differ from each other in line width and shape. The FWHM of the diamond line of detonation nanodiamonds is approximately 2.8 times greater than the corresponding value found for HP-HT nanodiamonds. In addition, the diamond line of detonation nanodiamonds is asymmetric with a more pronounced broadening towards lower wavenumbers. All these findings are in agreement with the literature data, and, according to Refs. [34] and [70], indicate a greater number of defects present in detonation nanodiamonds. Overall, monocrystalline HP-HT nanodiamonds have a uniform structure with a concentration of lattice defects (such as dislocations or twinning) lower than in detonation nanodiamonds containing a diamond core and various lattice defects, transient sp3/sp2 layer, and sp2 surface shell that may carry various surface functional groups [70]. The sp2-carbon content in detonation nanodiamonds is expected to be higher than in HP-HT nanodiamond due to the smaller size of primary particles. It should be noted that along with the presence of the sp2-carbon [71], the appearance of energy transitions lower than Eg in nanodiamond can be caused by the presence of diamond-like shells [72], the

dimer chains on the surface of diamond nanoparticles [56], as well as the numerous defects, vacancies, and impurities (see, for example, [29,73–75]). Independently of the origin of the two-photon absorption observed in an aqueous suspension of HP-HT nanodiamonds, it can be used for the optical limiting to protect sensitive optical components and eyes from the damaging effect of high-power femtosecond laser radiation with a wavelength of about 800 nm.

#### **5. Conclusions**

The nonlinear absorption of suspensions of HP-HT and detonation nanodiamonds at a wavelength of 795 nm of femtosecond excitation differ from each other significantly. At the same parameters of femtosecond laser pumping and experimental conditions, saturable absorption occurred in an aqueous suspension of detonation nanodiamonds accompanied by short-term nonlinear bleaching, while in an aqueous suspension of HP-HT nanodiamonds, two-photon absorption appeared, leading to optical limiting. The nonlinear absorption coefficient of the aqueous suspension of HP-HT nanodiamonds decreased linearly with the decreasing nanoparticle concentration. The important parameters characterizing the saturable absorption of detonation nanodiamonds in an aqueous suspension were determined. The results obtained show that the energy structures of HP-HT and detonation nanodiamonds differ from each other significantly. Aqueous suspensions of HP-HT nanodiamonds can be used for the optical limiting of high-power femtosecond laser pulses while suspensions of detonation nanodiamonds possess properties of the saturable absorber and can be employed for shortening the duration and to remove the pedestal ("tail") of the laser pulses.

**Author Contributions:** Conceptualization, G.M.M. and V.V.V.; methodology, G.M.M., V.V.V. and K.G.M.; software, V.V.V.; validation, G.M.M. and O.A.S.; formal analysis, V.V.V.; investigation, G.M.M., V.V.V., K.G.M., T.N.M. and A.N.A.; resources, N.A.N. and O.A.S.; data curation, T.N.M.; writing—original draft preparation, G.M.M. and V.V.V.; writing—review and editing, G.M.M., V.V.V., N.A.N. and O.A.S.; visualization, T.N.M.; supervision, G.M.M. and O.A.S.; project administration, G.M.M.; funding acquisition, G.M.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Ministry of Education and Science of the Russian Federation, state registration number AAAA-A19-119021890083-0, by the Academy of Finland grants no. 298298 and 323053, Flagship Programme "Photonics Research and Innovation (PREIN)" decision no. 320165.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Acknowledgments:** The authors wish to thank S.G. Bystrov for his help in experiments. This study was performed using equipment of the Shared Use Center "Center of Physical and Physicochemical Methods of Analysis and Study of the Properties and Surface Characteristics of Nanostructures, Materials, and Products" UdmFRC UB RAS.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Article* **Carbon Dots with Up-Conversion Luminescence as pH Nanosensor**

**Kirill Laptinskiy 1,2, Maria Khmeleva 1, Alexey Vervald 1, Sergey Burikov 1,2 and Tatiana Dolenko 1,2,\***


**Abstract:** In this study, the up-conversion luminescence for aqueous suspensions of carbon dots with polyfunctional and carboxylated surfaces synthesized by a hydrothermal method was investigated. The obtained quadratic dependence of the luminescence intensity on the power of the exciting radiation indicates that the up-conversion luminescence of these carbon dots is caused by twophoton absorption. The optimal wavelength of the exciting radiation was determined for the studied samples. The dependences of the signal for the up-conversion luminescence of carbon dots on the pH value of the suspension were obtained. It was shown that these carbon dots can be used as the nanosensor of pH of liquid media in a wide range of pH values. The advantage of this nanosensor is that the excitation of the up-conversion luminescence of carbon dots does not entail excitation of autoluminescence of the biological medium. It expands the possibilities of using this sensor in biomedical applications.

**Keywords:** carbon dots; up-conversion luminescence; two-photon absorption; nonlinear spectroscopy

#### **1. Introduction**

In recent years, there has been a rapidly growing interest in the nonlinear optical properties of carbon nanoparticles [1–3]. This interest has been caused, among other things, by the wide prospects for the use of carbon dots (CDs) and nanodiamonds as medical nanoagent photoluminescent markers for the rapid and sensitive detection of analyte, drug carriers, adsorbents, etc. [4–8]. Together with the photostability and a high quantum yield of luminescence, solubility in water, biocompatibility, and the possibility of surface modification, the recently discovered property of various carbon dots to luminesce in the anti-Stokes region significantly expands the prospects for the use of such CDs in biomedicine. Upon excitation of the up-conversion luminescence (UCL) of nanoparticles, the autofluorescence of biological tissue is not excited, while UCL itself falls into the spectral region of the biological "transparency window", which ensures deep penetration of radiation in tissue.

The first report on the observation of UCL of carbon dots, upon the excitation of CDs obtained by laser ablation by pulsed laser radiation with a wavelength of 800 nm, was made by L. Cao et al. [9] in 2007. The CDs' UCL spectrum was a broad band with a maximum near 470 nm. The authors found a quadratic dependence of the UCL intensity of the CDs on the excitation power and explained the observed UCL as a result of two-photon absorption.

From 2007 to 2013, numerous publications appeared, including those in high-ranking journals, in which the authors reported on the observation of CDs' UCL when excited by a conventional xenon lamp of a spectrofluorimeter [10–12]. However, the authors of [13,14] showed that the supposed CD UCL signals observed on the spectrofluorimeter are artifacts such as interference from leaking second-order diffraction of the excitation light when broad-band light sources and diffraction gratings are used for excitation wavelength

**Citation:** Laptinskiy, K.; Khmeleva, M.; Vervald, A.; Burikov, S.; Dolenko, T. Carbon Dots with Up-Conversion Luminescence as pH Nanosensor. *Appl. Sci.* **2022**, *12*, 12006. https:// doi.org/10.3390/app122312006

Academic Editor: Gennady M. Mikheev

Received: 31 October 2022 Accepted: 21 November 2022 Published: 24 November 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

selection. According to [9,14,15], the main criterion for a "real" CD UCL is the quadratic dependence of the UCL intensity on the excitation radiation intensity.

The results of active studies on CDs' UCL over the past 5 years have shown that the properties of UCL of CDs of different synthesis differ significantly [9,14,16–18]. This is explained by the existence of various mechanisms for the formation of UCL [19], including UCL of CDs: two-photon absorption through real and virtual levels [9,14,15,20], multiphoton absorption [21], thermal activation [22], and the state of surface traps [20,23]. In the vast majority of publications, two-photon absorption is considered to be the main one.

However, the dependences of the CDs' UCL intensity on the power of the exciting radiation are not always quadratic. For example, for CDs doped with nitrogen by the photochemical method, these dependences resembled those for lanthanoid-based upconversion nanoparticles and was linear in the double-log coordinates with the slope 0.69 [18], while for thermally-activated CDs, this dependence was found to be linear in standard linear coordinates (as well as in the double-log coordinates with the slope 1) [22].

The observed dependences of the CDs' UCL intensity on the excitation wavelength also differ. For CDs synthesized by different methods or doped with different atoms, these dependences have one [21], two [18,24], or three [25] maxima with different positions. For other CDs, such as CDs simultaneously doped with S and Se [16] and for CDs synthesized by the Hummers method [17], excitation wavelength-independent NIR emission was observed.

Thus, the accumulated results of UCL studies of various CDs at this stage are characterized by many contradictions and uncertainty. The next step is to search for correlations and systematize all the data obtained. It should also be noted that CDs' UCL with different surface functionalization has not yet been studied, although it is well known that the surface properties of nanoparticles significantly affect their properties, primarily colloidal and optical [26,27].

Despite the contradictions in the results of studying the properties of CDs' UCL, there are many examples of successful application of CDs with UCL in various fields. The main application of CDs with UCL is the optical visualization of nanoparticles in cancer cells and biological tissues [9,28], in a multiphoton confocal microscope [18], for photothermal therapy of cancerous tumors [12]. It was shown that CDs' UCL could be detected in tissue from a depth up to 1800 μm [21], which is an important result from the point of view of CDs applicability in biological imaging. The authors of [22] suggested using CDs with UCL for thermosensing. Due to the fact that some substances quench UCL upon interaction with CDs, it was proposed to use CDs with UCL as nanosensors for hypochlorite [29], hydrogen sulfide [30], and Cu2+ ions [31]. CDs with UCL can be used as a laser amplification medium in low-threshold diode-pumped lasers [32].

While pH nanosensors on the basis of CDs' Stokes luminescence have been actively developed [8,33,34], there are almost no publications devoted to the CDs' UCL dependence on pH. At the time of writing, we managed to find only one paper, in which such dependence was shown: intensity of UCL (emission with the maximum around 640 nm upon the excitation at 690 nm with pulse laser) for the studied CDs was shown to significantly change in cells upon their incubation at buffers with different pH (from 4 to 8), at tumor/normal muscle mice tissue (pH 6.5–6.8 against pH 7.4), and in zebrafish injected with CDs in buffers of different pH (from 4 to 8). Unfortunately, while this publication presents a dependence on the Stokes luminescence spectra for CDs on pH in wide region 0.5–9 (excitation at 573 nm), the same was not the case for their UCL [35]. The advantage of this nanosensor, based on UCL is that excitation of up-conversion luminescence does not lead to autoluminescence of the biological medium.

This article presents the results of studying the dependence of the intensity of UCL on the wavelength and on the power of the exciting radiation for different functionalized CDs synthesized by the hydrothermal method. The features of CDs' UCL with a functionalized surface were studied for the first time. The possibility of using CDs with UCL as a pH nanosensor is shown. For the first time, the accuracy of determining the pH of an aqueous solution and biological tissue using the CDs' UCL spectra was estimated.

#### **2. Materials, Their Characterization, and Research Methods**

#### *2.1. Synthesis of Carbon Dots and Functionalization of Their Surface*

The objects of study were CDs obtained by the hydrothermal method from citric acid and ethylenediamine. The concentrations of precursors in the initial aqueous solution were 0.15 M for citric acid and 3 M for ethylenediamine (i.e., the ratio of precursors was 1:20, respectively). This solution was placed in a 15 mL polytetrafluoroethylene (PTFE) tube, which was placed in an autoclave. The autoclave with a mixture of precursors was placed in a Sputnik muffle furnace (Russia). The heating temperature was 190 ◦C, the heat treatment time was 2 h. Next, the autoclave was removed from the oven and cooled at room temperature for 7 h. To remove large particles, the synthesized CDs were passed through a syringe membrane filter with a pore diameter of 0.22 μm.

In this way, CDs with a polyfunctional surface (CD-poly) were synthesized, which were then functionalized with hydroxyl (CD-OH) and carboxyl (CD-COOH) groups. To functionalize CDs with hydroxyl groups (CD-OH), the dried residue of the solution after synthesis was mixed with 1 g of sodium nitride and 3 mL of hydrochloric acid to remove amide groups. To obtain the carboxylated surface of CDs (CD-COOH), 10 mL of water and 4.2 mL of NaOH solution with a concentration of 0.5 M were added to the dried residue.

#### *2.2. Electron Microscopy of Obtained Carbon Dots*

Studies of the CDs' structure were carried out by scanning transmission electron microscopy using a high-angle annular dark field detector (HAADF STEM) on a Tecnai Osiris microscope (Thermo Fisher Scientific, USA) at an accelerating voltage of 200 kV. The results are shown in Figure 1a. Elemental analysis was carried out using a special SuperX EDS system, which includes four Bruker silicon detectors, the design of which makes it possible to obtain the distribution of chemical elements in a few minutes. The diagram of elemental analysis is presented in Figure 1b.

**Figure 1.** STEM image of the synthesized nanoparticles (**a**) and their elemental analysis (**b**).

As can be seen from the presented image, the synthesized nanoparticles are about 7 nm in size. The lattice fringes are clearly visible (Figure 1, inset, red lines) with the lattice parameter around 0.189 nm that corresponds to the (102) lattice fringes of graphite.

#### *2.3. Preparation and Characterization of Aqueous Solutions of Carbon Dots*

Deionized water (Millipore Simplicity UV water purification system) was used to prepare aqueous solutions of CDs. Aqueous solutions of CD-poly, CD-COOH, and CD-OH were prepared with a nanoparticle concentration of 0.1 mg/mL (obtained from gravimetric analysis).

To change the pH in the range from 2 to 12, either an aqueous solution of HCl (Sigma Aldrich, concentration 1 M, pH = 0) or an aqueous solution of NaOH (Dia-M, concentration 1.8 M, pH = 14) was added to the solution. Measurements for the pH value of aqueous solutions of CDs were carried out using the ionometric converter Akvilon I-500 equipped with an InLab Nano pH electrode (Mettler Toledo). All measurements were carried out at a fixed temperature of 22 ◦C.

Zeta potentials and sizes of nanoparticles in aqueous solutions were measured using dynamic light scattering on a Malvern Zetasizer NanoZS instrument. According to the data obtained, the sizes of the studied CDs were 182 ± 21, 105 ± 12, and 176 ± 23 nm for CD-poly, CD-COOH, and CD-OH, respectively. The corresponding zeta potentials were −39.7 ± 4.3, −29.1 ± 4.5, and −17.2 ± 1.3 mV. The obtained values of the zeta potentials indicate the colloidal stability of aqueous solutions of all CDs.

#### *2.4. IR Absorption Spectroscopy of Carbon Dots*

Analysis of the structure and functional surface groups of CDs was carried out using FTIR spectroscopy on a Bruker Invenio R IR spectrometer equipped with an ATR attachment based on a diamond crystal. The spectral resolution was 4 cm–1. The obtained IR absorption spectra for the studied CDs are shown in Figure 2.

**Figure 2.** IR absorption spectra of water and powders of synthesized CDs.

The IR absorption spectra of three CD samples contain a similar set of bands that differ in relative absorption intensity. In the region of 3000–3700 cm<sup>−</sup>1, there is a wide band caused by stretching vibrations of the surface hydroxyl and amino groups and OH groups of water molecules adsorbed on the surface of the samples. The relative intensity of this band for CD-poly and CD-COOH is significantly lower than for CD-OH. In the region of 2800–3000 cm−<sup>1</sup> there are bands of stretching vibrations of CHx groups. In the region of 2055 cm<sup>−</sup>1, there is a band that presumably belongs to overtones/combinations of various vibrations in CDs [36].

The band at 1745 cm−<sup>1</sup> in the spectrum of CD-COOH corresponds to the stretching vibrations of C=O bonds of surface carboxyl groups. The weak relative intensity of this band is due to the fact that the COOH groups belong exclusively to the surface of this CD, while most other vibrational bands are due to the vibrations of the groups that are also in the CD's core. This situation is typical for CDs with a size of about 100 nm and does not manifest itself, for example, for nanodiamonds with a carboxylated surface: in them, the diamond core is not active, and the relative intensity of the vibration bands of all surface groups is much higher [37].

In the region of 1640 cm<sup>−</sup>1, there is a band of bending vibrations of OH bonds. In the spectra of CD-COOH and CD-OH, it manifests itself as a "shoulder" of a wide intense band with a maximum in the region of 1570 cm–1, which is due to stretching vibrations of C=C bonds [36]. In the region of 1580–1650 cm<sup>−</sup>1, the band of bending vibrations of NH groups overlaps with it.

In the IR spectrum of the CD-poly, intense narrow bands are observed with maxima in the regions of 1600 and 1505 cm–1, which, according to the authors of [36,38], are due to skeletal vibrations of the polycyclic aromatic elements of CDs. The absence of such bands in the spectra of CD-COOH and CD-OH indicates that the functionalization of these CDs occurred primarily due to the rupture and subsequent addition of radicals to such aromatic rings.

The band with a maximum in the region of 1390 cm−<sup>1</sup> corresponds to stretching vibrations of C–O bonds in –COOH groups [39]. The band with a maximum in the region of 1335 cm−<sup>1</sup> is also due to C–O vibrations, but particularly in the C–O–C groups [40]. The set of bands in the range of 950–1180 cm–1 is mainly due to stretching vibrations of C–O and bending vibrations of C–H bonds in various environments [36].

An analysis of the IR spectra showed that the CD-poly contains a large number of polycyclic aromatic elements and various functional groups, such as C–O–C, C=C, N–H, OH. As a result of the functionalization of the CD-poly, on the surfaces of CD-COOH and CD-OH during the destruction of aromatic rings, a large number of oxygen-containing groups were formed, and the relative intensity of the bands due to vibrations of the C–O–C, C–O, and OH groups bonds increased. Additionally, in the spectra of CD-COOH bands corresponding to vibrations of carboxyl groups appeared. Thus, the results of IR absorption spectroscopy allow us to conclude that the functionalization of CD-COOH and CD-OH was successful (Figure 2).

#### *2.5. Spectrophotometry of Aqueous Solutions of CDs*

The optical extinction spectra of aqueous solutions of CD-poly, CD-COOH, and CD-OH were obtained on a Shimadzu UV-1800 spectrophotometer in the wavelength range of 190–1100 nm with a resolution of 1 nm. The informative part of the obtained spectra is shown in Figure 3.

**Figure 3.** Optical extinction spectra of aqueous solutions for the studied CDs. pH = 7.

As can be seen from the presented data, the extinction spectra of aqueous solutions of CDs have a number of features. In all optical extinction spectra for the studied aqueous solutions, an intense peak is observed in the short-wavelength region, the right shoulder of the band of which extends up to ~250–300 nm. According to the literature data [41], the peak of CDs in this region is due to π–π\* transitions in aromatic sp2 carbons. In the extinction spectra of CDs with polyfunctional and carboxylated surfaces, a peak is observed in the region of 275 nm, corresponding to n–π\* transitions of C=O [42] bonds and corresponding to n–π\* transitions of C=O, C–N, or C–OH bonds in sp3-hybridized domains associated with carboxyl (–COOH) or amine (–NH2) groups on the CDs' surface [43]. In the optical extinction spectra of CD-OH, these peaks are absent.

#### *2.6. Photoluminescence Spectroscopy*

The up-conversion luminescence of the CDs was studied on the experimental setup shown in Figure 4. A pulsed nanosecond Nd:YAG laser (model LQ629-100, Solar Laser Systems, Belarus) was used as a pump source. The third harmonic (355 nm, pulse duration 10 ns, pulse repetition rate 100 Hz) of the Nd:YAG laser was used to pump an LP603 parametric light generator (Solar Laser Systems, Belarus), whose radiation was the source of excitation of the CDs' UCL. This laser system allows the pump wavelength to be changed in the range from 532 to 1070 nm. The radiation of the parametric light generator passed through a KS-11 light filter, which did not transmit the third harmonic of the initial laser radiation, and was directed through a rotating mirror to a mechanical optical shutter, which was used to record and then subtract the background signal from the CDs' UCL spectra. The probing of the sample in the cuvette was carried out through the bottom of the cuvette. The resulting radiation of the sample at an angle of 90◦ was collected with a lens system to a recording system consisting of a monochromator (MBP80) with a focal length of 500 mm, equipped with a grating of 150 lines/mm, and a CCD camera (Horiba-Jobin Yvon, Synapse BIUV). Light filters SZS-22 and SZS-23 at the entrance of monochromator did not transmit the signal from the pump and isolated the luminescent signal in the spectral range of registration from 418 to 773 nm. The spectral resolution of the experimental setup was 2 nm. The power of the excitation radiation at the sample was recorded using an Ophir Nova 2 power meter equipped with a PE50-DIF-C pyroelectric sensor.

**Figure 4.** Scheme of the experimental setup for the study of CDs' UCL: 1—pulsed nanosecond Nd:YAG laser; 2—parametric light generator; 3—light filter KS-11; 4—rotatory mirror; 5—power meter; 6—mechanical shutter; 7—rotatory mirror and lens; 8—cuvette with the solution of nanoparticles; 9—optical system of two lenses; 10—light filters SZS-22 and SZS-23; 11—registration system consisting of a monochromator and a CCD camera.

#### **3. Results and Discussion**

#### *3.1. Dependence of the UCL Intensities of Aqueous Solutions of CDs on the Wavelength of the Exciting Radiation*

To study the UCL of CDs, the UCL spectra of CDs' aqueous solutions at pH 11.7 (initial pH for studied aqueous solutions) were obtained under excitation by laser radiation with different wavelengths in the range from 670 to 840 nm with excitation radiation power of 50 mW (Figure 5). From them, the dependences of the integral intensities of these spectra on the wavelength of the exciting radiation were calculated (Figure 6). For CD-OH, no photoluminescence signal was observed in the specified spectral range, what corresponds to the absence of the intense absorption bands in the optical absorption spectra of this sample in the range from 250 to 500 nm. Additionally, it is worth noting that the synthesized CDs were characterized by stable UCL, both in terms of reproducibility of the up-conversion luminescence of CD aqueous suspension obtained in different synthesis batches under the same synthesis conditions (see Figure S1) and in terms of the UCL stability of aqueous suspensions of CDs for 10 days (see Figure S2).

**Figure 5.** UCL spectra of aqueous solutions of CD-poly and CD-COOH upon excitation by laser radiation at wavelengths of 680, 720, and 800 nm (pH = 11.7).

**Figure 6.** Dependences of the integrated UCL intensities of aqueous solutions of CD-poly and CD-COOH on the wavelength of the exciting radiation (pH = 11.7).

The processing of the spectra consisted in averaging 4 consecutively recorded spectra and normalizing their intensity to the power of the exciting radiation and to the time of accumulation of the spectra. The spectra were smoothed by a third-order polynomial using the Savitsky–Golay method.

It can be seen from the obtained results that the maxima of the dependences of the UCL integral intensity on the wavelength of the exciting radiation for the two types of CDs are close and are in the region of 720 nm (Figure 6). Therefore, this excitation wavelength can be considered optimal for both types of CDs, and it was used for the excitation of the CDs' UCL in following measurements. The proximity of the excitation wavelengths that provide the maximum integrated intensity of UCL of CD-COOH and CD-OH is explained by the same adsorption features of these CDs' solutions related to their functional groups (Figure 3). Nevertheless, it should be noted that, upon excitation of UCL by radiation at a wavelength of 720 nm, the UCL intensity of an aqueous solution of CD-COOH is approximately 1.7 times higher than that of an aqueous solution of CD-poly at pH = 11.7. Thus, the presence/absence of CDs' UCL and its characteristics depend on the functionalization of the nanoparticle surface.

#### *3.2. Dependence of the UCL Intensity of Aqueous Solutions of CDs on the Power of the Exciting Radiation*

As discussed earlier, according to some photophysical models, the UCL of CDs is due to a two-photon absorption process. In this case, the CDs' UCL integrated intensity should depend quadratically on the power of the exciting radiation.

To check this, the UCL spectra of aqueous solutions of CD-poly and CD-COOH were obtained for different values of the excitation radiation power, which varied in the range from 12 mW (5.1·104 <sup>J</sup>·cm−2·s−1) to 83 mW (3.5·10<sup>5</sup> <sup>J</sup>·cm−2·s−1). The dependences of the UCL integrated intensity of CD-poly and CD-COOH in water on the value of the pump power are shown in Figure 7. They are well approximated by a quadratic function.

**Figure 7.** Dependences of the UCL integrated intensity of aqueous solutions of CD-poly and CD-COOH (pH = 11.7) on the power of exciting radiation and approximation of experimental data by quadratic dependences.

The obtained quadratic dependences for the intensity of UCL in aqueous solutions of CDs on the power of the exciting radiation prove the fact that the UCL of studied CDs is due to two-photon absorption. In following processing of the spectral data, the intensity of the CDs' UCL will be normalized to the square of the power of the exciting radiation.

From Sections 3.1 and 3.2 it can be concluded that the mechanisms for nonlinear (photoluminescence in the result of two-photon absorption) optical properties of CDs, as with linear ones (classic photoluminescence in the Stokes region [34,44]), depend on the type and composition of surface functional groups.

#### *3.3. Dependence of the UCL Intensity of Aqueous Solutions of CDs on pH*

The UCL spectra for aqueous solutions of CD-poly and CD-COOH with pH from 2 to 12 were obtained. From them, the dependences of the integrated intensity and position of the maxima of UCL spectra of CDs on the pH of aqueous solutions were calculated (Figure 8). As can be seen, these spectral parameters depend significantly on pH. Moreover, for CDs with polyfunctional and carboxylated surfaces, these dependences differ significantly. The UCL intensity of an aqueous solution of CD-COOH monotonically increases as the pH of the solution increases from 2 to 12, while the UCL intensity of CD-poly increases with the increase in pH from 2 to 5, and then decreases at pH > 5 (Figure 8a).

**Figure 8.** Dependence of the integral intensity (**a**) and the position of the maximum (**b**) of the UCL spectra of aqueous solutions of CD-COOH and CD-poly on pH. The vertical lines represent the pH limits of applying the linear fit to UCL intensity vs. pH.

The maximum of the UCL spectra of CD-COOH sharply shifts to the short-wavelength region by 20 nm with an increase in the pH value of the solution from 2 to 5, while at further increase in the pH its position practically does not change (Figure 8b). It should be noted that in the pH range from 2 to 5, deprotonation of carboxyl groups on the surface of nanoparticles in water occurs, which significantly affects the state of the electronic levels of surface states [37,44]. The maximum UCL spectra of CD-poly gradually shifts to the short wavelength region by 10 nm with an increase in the pH value of the solution from 2 to 10, and then sharply shifts by 8 nm to the long wavelength region with a further increase in the pH of the solution. It can be assumed that the course of the dependences obtained for CD-poly solutions is also to some extent affected by the processes of deprotonation in the COOH, OH, and NH surface groups in water [37,44].

#### *3.4. Carbon Dots with Up-Conversion Luminescence as a pH Nanosensor*

It follows from the obtained results that the dependences of the integrated intensity for UCL of CDs' aqueous solutions on the pH have linear sections: CD-COOH in the pH range from 2 to 9, CD-poly in the pH range from 5 to 9 (Figure 8a). This means that the studied CDs with UCL can serve as promising nanoagents for use as nanosensors of pH in liquid media, including at the cellular level.

Approximations of the linear regions for the dependences of the UCL integrated intensity of aqueous solutions of CDs on pH (Figure 8a) can be used as calibration curves for the determination of the pH of the CDs' aqueous environment. Using them, the pH of the environment can be measured from the UCL spectra of CD-poly with an accuracy of 0.13, and from the UCL spectra of CD-COOH with an accuracy of 0.21.

Approbation of the pH nanosensor based on the CDs' UCL was carried out for chicken egg white (Figure 9). For this, the UCL spectra of CDs added to four different egg whites (concentration of CDs was 0.1 mg/mL, the same as for aqueous solutions) were obtained, and the integrated intensity of the UCL of all spectra was determined. For each egg white, five UCL spectra of CD-poly and CD-COOH were obtained. Using the calibration curves of the linear sections of the dependences of the integral intensity of UCL on pH (Figure 8a), the pH values for each sample were determined, and averaged for five corresponding spectra. Parallel to it, the pH value at the probing point of the exciting laser radiation of each chicken egg white was measured using a pH electrode. All of the obtained pH values are presented in Table 1.

**Figure 9.** UCL of CDs in chicken egg white (lower half of the image) upon excitation at a wavelength of 720 nm.

**Table 1.** The pH values of the water and chicken egg white obtained using a pH electrode and from the spectra of CDs' UCL.


As can be seen from the presented results, the pH values of egg whites obtained by two independent methods are in good agreement. The error of the determination of pH for the CD-poly samples is smaller than for the CD-COOH samples, what was already observed for CDs' aqueous suspensions. In addition, the slope of the calibrations' straight line for CD-poly is greater in modulus than for CD-COOH (Figure 6), which also affects the accuracy of determining the pH of the medium. Thus, the functionalization of the CDs' surface with carboxyl groups did not give a benefit in pH measurement. However, it is known that it is the carboxylation of the surface of carbon nanoparticles that provides them with a high degree of biocompatibility, which is extremely important when using CDs in nanomedicine.

It should be noted that the accuracy of pH measurement according to the UCL spectra of CDs in aqueous solution is higher than that in chicken egg white. This is explained by the fact that the calibration dependences of the UCL intensity on pH obtained for an aqueous solution of CDs were used to determine the pH in the egg white. Nevertheless, the accuracy of determining the pH of both water and biological tissue from the UCL spectra of the nanosensor based on CDs (Table 1) satisfies the needs of biomedicine.

Thus, the pH nanosensor on the basis on CDs' up-conversion luminescence intensity was successfully approbated for the biological substances. Due to the fact that the anti-Stokes luminescence does not overlap with the autofluorescence of the biological medium, a good accuracy of pH determination was achieved. All pH nanosensors based on Stokes luminescence would be hindered by the biological autofluorescence, fully avoided for UCL-based probes.

#### **4. Conclusions**

In this work, the UCL for aqueous solutions of carbon dots with a polyfunctional surface and a surface functionalized with carboxyl groups was studied. It was found that UCL is absent in CDs functionalized with hydroxyl surface groups.

The obtained quadratic dependence of the CDs' UCL intensity on the power of the exciting radiation proves the fact that the UCL for the studied CDs is caused by two-photon absorption processes.

The differences in the UCL of CD-poly and CD-COOH aqueous solutions and its absence for CD-OH indicates that the mechanisms of nonlinear optical properties of CDs (photoluminescence in the result of two-photon absorption), such as linear ones (classic photoluminescence in the Stokes region), depend on the type and composition of surface functional groups.

It was found that the UCL for aqueous solutions of CD-poly and CD-COOH in water depends on the wavelength of the excitation radiation and on the pH value of the solution. The analysis of the obtained results showed that CDs' UCL is most effectively excited at a wavelength of 720 nm. It has been shown that the studied CD-COOH and CD-poly with up-conversion luminescence can be used as pH nanosensors in the linear response pH ranges from 2 to 9 and from 5 to 9, respectively. In these ranges, the estimated accuracy in the determination of the pH of the environment by UCL spectra for aqueous solutions of CDs was 0.13 for CD-poly and 0.21 for CD-COOH. Approbation of pH nanosensors in biological tissue—chicken egg white—was carried out, which demonstrated the prospects of using the proposed method of using CDs' UCL to determine the pH of biological media.

Obviously, CD-COOH are more promising for biomedical problems as pH nanosensors, since they have high biocompatibility and can measure pH in a larger range of its linear changes in biological tissue.

**Supplementary Materials:** The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/app122312006/s1, Figure S1: Reproducibility of up-conversion luminescence of CD aqueous suspension obtained in different synthesis batches under the same synthesis conditions, Figure S2: Demonstration of the up-conversion luminescence stability of aqueous suspension of CDs for 10 days.

**Author Contributions:** Conceptualization, T.D. and K.L.; methodology, S.B., M.K., and K.L.; software, A.V.; validation, M.K. and A.V.; formal analysis, A.V.; investigation, M.K. and K.L.; resources, T.D.; data curation, T.D. and K.L.; writing—original draft preparation, T.D. and K.L.; writing—review and editing, T.D.; visualization, M.K.; supervision, T.D.; project administration, T.D.; funding acquisition, T.D. All authors have read and agreed to the published version of the manuscript.

**Funding:** The study was carried out at the expense of a grant from the Russian Science Foundation No. 22-12-00138, https://rscf.ru/project/22-12-00138/ (accessed on 2 September 2022).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** We acknowledge the Interdisciplinary Scientific and Educational School of Lomonosov Moscow State University "Photonic and Quantum technologies. Digital medicine". Some of the experimental results used in this study were obtained using a FTIR spectrometer purchased under the Development Program of Moscow State University (Agreement No. 65, 4 October 2021).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**Kirill A. Kuznetsov 1, Daniil A. Safronenkov 1, Petr I. Kuznetsov <sup>2</sup> and Galiya Kh. Kitaeva 1,\***

<sup>1</sup> Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia;

kirill-spdc@yandex.ru (K.A.K.); safronenkov.da14@physics.msu.ru (D.A.S.)

<sup>2</sup> Kotelnikov IRE RAS (Fryazino branch), 141190 Fryazino, Russia; pik218@fireras.su

**\*** Correspondence: gkitaeva@physics.msu.ru

**Abstract:** In this study, the efficient generation of terahertz radiation by a dipole photoconductive antenna, based on a thin island film of a topological insulator, was experimentally demonstrated. The performance of the Bi1.9Sb0.1Te2Se antenna was shown to be no worse than those of a semiconductor photoconductive antenna, which is an order of magnitude thicker. The current–voltage characteristics were studied for the photo and dark currents in Bi1.9Sb0.1Te2Se. The possible mechanisms for generating terahertz waves were analyzed by comparing the characteristics of terahertz radiation of an electrically biased and unbiased topological insulator.

**Keywords:** topological insulator; photoconductive antenna; terahertz waves

#### **1. Introduction**

Currently, topological insulators (TIs) are considered to be promising new 2D materials for terahertz (THz) generators and detectors [1–3]. TIs are characterized by the presence of stable (topologically protected against backscattering), conducting surface states of an electronic gas. TIs can be used in the development of various interdisciplinary connections in many modern areas, including spintronics [4], laser physics [5], and quantum information [6].

Angle-resolved photoemission spectroscopy (ARPES) detects the presence of Dirac electrons with nondegenerate spins in many solids [7]. In addition to ARPES, there are other methods that are sensitive to edge electronic states. In [8], a new method was proposed for detecting the surface states of electrons based on the photo-electromagnetic effect (PEM), which is not sensitive to bulk conductivity. In [9], ultrafast manipulation of topologically enhanced surface transport was demonstrated using THz and mid-IR pulses in bismuth selenide. Correspondingly, the generation of THz radiation can also be sensitive to surface electron transfer. Hamh et al. demonstrated a circular anisotropy of the photon drag effect (PDE) in Bi2Se3, which proves optical coupling with topological surface states [10].

In a number of previous studies, the generation of THz radiation under the action of pulsed optical pumping was investigated in bismuth chalcogenides of double [11,12] and quaternary [13] chemical compositions. A comprehensive review of the photovoltaic effects in Bi2Te3 and Sb2Te3 was given in [14]. A number of conclusions were drawn regarding the prevailing mechanisms of the generation of THz radiation, due to the excitation of photocurrents in the epitaxial films of topological insulators in the absence of any external electric bias field. In [15], it was shown that the contribution to the photocurrent from the PDE is an order of magnitude greater than the contribution from the diffusion current, and two times higher than the contribution from the drift current.

Topological insulators of quaternary compositions Bi2−xSbxTe3−ySey are actively studied in connection with the possibility of smooth changes in their properties over a wide range. In [16], it was shown that there is a certain optimal curve (the "Ren's curve") in the composition-structure diagram y(x), where the properties of electronic surface states are

**Citation:** Kuznetsov, K.A.; Safronenkov, D.A.; Kuznetsov, P.I.; Kitaeva, G.K.. Terahertz Photoconductive Antenna Based on a Topological Insulator Nanofilm. *Appl. Sci.* **2021**, *11*, 5580. https://doi.org/ 10.3390/app11125580

Academic Editor: Gennady M. Mikheev

Received: 14 May 2021 Accepted: 15 June 2021 Published: 16 June 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

most pronounced. This is associated with a significant suppression of the bulk contribution to the conductivity, as the actions of acceptors and donors cancel each other, which leads to the predominance of surface electron transport. Bi2−xSbxTe3−ySey films with compositions located under the Ren's curve, as a rule, predominantly have p-type conductivity; while compositions located above this curve have conductivity of the n-type.

At present, research is continuing on the most efficient methods for generating and detecting terahertz radiation. Photoconductive semiconductor antennas are effective devices in the THz range for applications in spectroscopy, and various imaging and data transmission systems [17,18]. Due to the availability of components in the telecommunications industry, modern systems often use optical excitation at a wavelength of 1550 nm with femtosecond pulses of an erbium fiber laser [19,20]. Semiconductor structures, based on indium-gallium arsenide, were well studied as photoconductive materials for THz due to their suitable optical absorption wavelength of 1.5 μm. Recently, THz detectors fabricated from rhodium (Rh)-doped In0.53Ga0.47As showed a record peak dynamic range of 105 dB and a bandwidth up to 6.5 THz [21]. A significant improvement in the characteristics of these devices was achieved with the help of such nanotechnological tools as plasmonic contact gratings, arrays of optical nanoantennas, optical nanocavities [22,23], and non-standard orientation of the substrates [24,25].

Another important area is the development and optimization of couplers at the output surfaces of photoconductive antennas. The performance of planar terahertz antennas can be improved by using hemispherical dielectric lenses. However, this increases the weight and volume of the antenna. Artificially created composite metamaterials have recently attracted considerable attention from both the scientific and engineering communities due to their unconventional properties [26–30].

It is also of interest to use various other photoconductive materials for their application in antennas pumped by telecom wavelength lasers. Singh et al. [31] presented a significantly ultra-broadband (extending up to 70 THz) THz emission from an Au-implanted Ge emitter that was compatible with mode-locked fiber lasers operating at wavelengths of 1.1 and 1.55 μm.

The development of new photoconductive nanomaterials for THz PCAs still remains a relevant and urgent task. In our previous work [32], we demonstrated amplification of the THz radiation power by applying a weak external electric field to a TI. In this work, we study the generation of a photoconductive antenna under the application of a strong bias external field.

#### **2. Proposed System Design**

A TI sample of Bi1.9Sb0.1Te2Se (BSTS) was prepared with a composition near the Ren's curve at the composition-structure diagram. It was grown by metalorganic vapor-phase epitaxy (MOVPE) on a (0001) sapphire substrate with a 10-nm zinc telluride (ZnTe) buffer layer of orientation (111) at the atmospheric pressure of hydrogen in a horizontal quartz reactor. The sources of organometallic compounds of bismuth, antimony, zinc, tellurium, selenium, trimethyl bismuth, trimethyl antimony, diethyl zinc, diethyl tellurium, and diethyl selenium were used. The ZnTe buffer layer was grown in one technological cycle with a BSTS film at a temperature of 463 ◦C. To determine the elemental composition of the films, we used X-MaxN energy dispersive X-ray spectrometer with an electron microscope. A thin film of BSTS, 40 nm thick and of necessary composition, was selected for THz generation (Figure 1a).

A dipole antenna was fabricated by patterning Ti/Pd/Au metal electrodes (of corresponding thicknesses 50/120/200 nm) onto BSTS film. The gap between electrodes was 20 μm. Templates were preliminarily applied using the photolithography method. The fabricated TI-antenna had an impedance of 490 Ω. A hemispherical high-resistance silicon lens of 1 cm diameter was mounted on the surface of the Al2O3 substrate to collect the generated THz radiation (Figure 1c).

**Figure 1.** The (**a**) atomic force microscopy image of BSTS sample surface; (**b**) sketch of the In-GaAs/InAlAs heterostructure; and (**c**) sketch of the antenna emitter.

To analyse the generation efficiency, we compared the generated THz pulses from two photoconductive antennas with the same dipole structure, one fabricated on the BSTS film (TI PCA) and the other on a semiconductor multilayer heterostructure (semiconductor PCA). Another dipole photoconductive antenna, fabricated on a low-temperature grown In0.5Ga0.5As/In0.5Al0.5As superlattice, was used as a second antenna for reference. The parameters of similar spiral antenna were previously studied and reported in [33]. The multilayer heterostructure InGaAs/InAlAs for semiconductor PCA was grown on an InP (111) substrate (Figure 1b). Such structures are usually prepared by molecular beam epitaxy and exhibit a high conversion efficiency of optical radiation into the broadband THz radiation. The overall thickness of the InGaAs/InAlAs heterostructure was 2000 nm, and the total thickness of all InGaAs layers was 1200 nm. An impedance semiconductor PCA was 12.8 kΩ.

We measured the room temperature absorption coefficient at the pump wavelength. It was 4300 cm−<sup>1</sup> for our InGaAs layer lattice and 120,000 cm−<sup>1</sup> for the BSTS sample. In both cases, the thickness of the antenna material was less than the pump field penetration depth. Thus, the selected film thicknesses, 40 nm in the case of BSTS and 1200 nm of the total thickness of the InGaAs layers, provided almost uniform pumping illumination throughout the depth of the samples.

Figure 2a shows a photograph of the board. The electrodes were deposited on the samples of photoconductive films with five dipole gaps (Figure 2b). One of the five interelectrode gaps, located above the most homogeneous region in the case of the topological insulator nanofilm, was chosen. Then, by heating with hot air from a soldering station, the electrodes were soldered to the board. A photograph of electrodes under a microscope is shown in Figure 2c. A hemispherical high-resistivity silicon lens 1 cm in diameter was pressed onto the substrate from above.

**Figure 2.** A (**a**) photo of the circuit board assembly; (**b**) sketch of the electrodes, with the gray circle representing the projection of the silicon lens onto the plane of the electrodes; and (**c**) image of the inter-electrode gap under a microscope. The gap width is 20 μm.

The measurements of THz generation characteristics were conducted on an experimental setup schematically presented in Figure 3. An Er3+fiber laser was used as a source for optical pulsed pumping at a wavelength of 1560 nm, pulse repetition rate of 70 MHz, and pulse duration of 100 fs. Eighty percent of the radiation power (approximately 100 mW in the average intensity) was directed onto the antenna under study, and the last 20% of the radiation was used to run a commercial (Menlo Systems) semiconductor heterostructure photoconductive antenna. The latter was used for the detection of the waveforms of emitted THz fields. The pump beam was focused on the TI PCA1 with a short-focus (5 mm) lens. The parabolic mirrors collected the THz radiation and focused it on the input silicon lens of the antenna-detector PCA2.

**Figure 3.** Schematics of the terahertz time-domain spectroscopy setup.

The photocurrents from the PCAs' were measured by a micro-ammeter and by a lock-in-amplifier at different bias voltages and laser pump powers. Sufficiently high photocurrents were measured simultaneously by using a current-sensitive input of the lock-in-amplifier. After the calibration of the lock-in-amplifier output data in microamperes, this sensitive device was used for measuring the lower photocurrents against a background of significant dark currents.

#### **3. Results**

A waveform of THz radiation, recorded from TI PCA at a bias voltage of 20 V, and its spectrum, obtained using fast Fourier transform, are shown by red curves in Figure 4a,b, respectively. The spectra in Figure 4b are "bumpy" due to re-reflection in the substrates and absorption by the water vapor. They extend up to 2 THz, which corresponds to the spectral range of the antenna-detector. The dynamic range of the obtained TI PCA radiation was approximately 60 dB.

**Figure 4.** The (**a**) time-domain waveforms of dipole antennas based on BSTS (red) and In-GaAs/InAlAs (blue); (**b**) fast Fourier transform spectra of BSTS (red) and InGaAs/InAlAs (blue) antennas; and (**c**) THz electric field amplitude versus bias voltage for BSTS antenna.

The blue curve in Figure 4a shows a waveform of THz radiation from a similar dipole semiconductor PCA biased at the same voltage U = 20 V (the curves were vertically shifted artificially). Though the thicknesses of active media differed by almost an order of magnitude (40 nm and 2000 nm), the amplitudes of the generated THz fields were comparable to each other. Even the peak-to-peak amplitude was 1.5 times more in case of thin TI PCA. Hence, we can conclude that, with the unit thickness of the medium, generation using BSTS is much more efficient than that using InGaAs/InAlAs. Figure 4c shows the dependence of the electric field amplitude on the bias voltage for TI PCA. The linear character of this dependence is clearly seen in the wide voltage range. At higher voltages, the THz signal was not recorded to avoid possible damage to the sample due to electrical breakdown.

As the generated photocurrents are responsible for the generation of THz radiation, it was interesting to measure them in the range of acting bias voltages of 0–20 V. First, the steady current-voltage characteristic was recorded, i.e., the dependence of the dark current on the voltage in the absence of incident optical pumping (Figure 5a). This characteristic was well approximated up to 13 V by a linear curve. However, at higher voltages some deviation from the linear fit was observed, which can be explained by a decrease in the resistance of the sample due to heating. We recorded the heating of the BSTS from room temperature to 50 ◦C by a thermocouple at a maximal bias voltage, Ub = 20 V. Figure 5b demonstrates the dependence of the average photocurrent on the bias voltage. It was also well described by a linear law over the entire range of Ub. For comparison, a similar dependence was shown for the semiconductor antenna, which lies well below the curve for the TI PCA. Figure 5c shows the obtained dependence of the TI PCA photocurrent on the pump power. It is linear; this is a typical situation for photoconductive antennas operating far from breakdown voltages and carrier screening effects.

**Figure 5.** The (**a**) I-V characteristic of TI PCA measured without pump radiation; (**b**) filled circles: voltage dependence of the time-averaged photo-excited current of TI PCA; open circles: the same dependence for InGaAs/InAlAs PCA; and (**c**) dependence of the time-averaged photo-excited current on the pump power for TI PCA.

Figure 6a demonstrates the phase change of the generated THz radiation by 180◦ when the polarity of the bias voltage Ub =15 V was reversed. If we summarize the two signals obtained at inverse voltages, we realise practically the same waveform as in the absence of an external voltage (Figure 6b). Similar results were observed at a higher voltage of 20 V.

**Figure 6.** The (**a**) THz pulses at opposite bias voltages; and (**b**) comparison of the unbiased THz pulse (blue) with the result of averaging of two waveforms from oppositely biased antennas (magenta).

#### **4. Discussion**

In general, a fairly large set of different mechanisms can be used to explain THz generation in TIs of double and quaternary compositions. The most instantaneous one is direct optical rectification of the laser pump field [11] due to nonlinear polarization.

$$\mathbf{P}(t) \sim \int\_{-\infty}^{t} \hat{\chi}^{(2)}(t - t', t - t'') : \mathbf{E}(t') \mathbf{E}^\*(t'') dt' dt'' + c.c. \tag{1}$$

Here, **E**(*t*) stands for the laser pump field and *χ*ˆ(2) describes the second-order nonlinearoptical susceptibility. Due to the centrosymmetric structure of TI volume, the components of *χ*ˆ(2) tensor are non-zero only at its surface and, thus, this effect is related specifically to surface excitations. However, its contribution was much smaller [34] than the THz field generated by transient currents of photo-induced charge carriers. The current-induced THz field depends on time derivatives of the two types of photocurrents, usually referred as linear (**j***L*) and nonlinear (**j***NL*) ones [15]:

$$\mathbf{E}\_{THz}(t) \sim \frac{\partial \mathbf{j}\_L(t)}{\partial t} + \frac{\partial \mathbf{j}\_{NL}(t)}{\partial t}. \tag{2}$$

In the frame of the simplest classical description, both types of currents should depend on temporal behaviour of the carrier's concentration *N*(*t*), mobility *μ*, and some specific field **<sup>~</sup> E** as:

$$\mathbf{j}\_{L,NL}(t) = \epsilon \mu \mathbf{N}(t) \tilde{\mathbf{E}}.\tag{3}$$

In our case of above-bandgap photo-excitation, the amplitude of the *N*(*t*) pulse scaled up with the pump pulse energy. As was reasonably argued in [35], the contribution from photo-induced electrons to both types of currents in BSTS was considerably more than the contribution from holes. A presence of non-zero dc field is necessary for directional motion of charge carriers in this description, regardless of whether it is applied externally or originates due to specific internal processes. The origin of, and the character of its possible temporal variation, are different for different THz generation mechanisms.

In case of linear currents **<sup>j</sup>***L*, the temporal variation of **<sup>~</sup> E** was negligible. In a photoconductive antenna, **<sup>~</sup> E** = **E***dc* is created by an external bias voltage source. With significantly smaller magnitudes, **<sup>~</sup> E** also exists as a surface depletion field or due to the photo-Dember effect [15], regardless of whether an additional lateral external field is applied. The surface depletion and photo-Dember fields are directed along the normal to the TI surface and determine the motion of volume carriers even in case of zero applied voltage. In addition, some surface built-in field can exist in the lateral direction and be responsible for the specific contribution of surface carriers to THz generation. For all generation effects caused by different-type linear currents, the THz waveforms should have almost the same shape, repeating the shape of *∂N*(*t*)/*∂t*. This shape is clearly presented in waveforms like those in Figure 6a. The waveforms were obtained in the case where the high external bias field made **j***<sup>L</sup>* more than other nonlinear contributions to the net photo-induced current. It was seen that changing the bias voltage sign did not cause any observable changes in the THz field magnitude, apart from reversing its sign. Moreover, both curves in Figure 6b demonstrate the zero residual THz field at delay times, when contribution of linear currents should be maximal. Thus, we concluded that the effects of lateral and longitudinal built-in fields were negligible at zero voltage, and were not linearly enhanced when the bias voltage was applied to the TI antenna.

By comparing the mean photocurrents detected in the TI antenna and the semiconductor PCA at the same bias voltage (Figure 5b), we obtained a ratio between the photocurrents (~1:7), which roughly corresponded to the ratio between the mobilities of bulk photoelectrons in both materials, *<sup>μ</sup>semi* = <sup>30</sup> cm2/(<sup>V</sup> · <sup>s</sup>) in our semiconductor InGaAs/InAlAs superlattice [33], and *<sup>μ</sup>T I* = <sup>166</sup> cm2/(<sup>V</sup> · <sup>s</sup>) in BSTS [36]. According to (3) this meant that the mean concentrations of photo-induced bulk electrons were the same in both materials. However, the peak-to-peak THz field amplitudes detected in TI and semiconductor PCAs (Figure 4a) refered to each other as 1.6:1. This indicates that the photocurrent change rate in BSTS was smaller than in the InGaAs/InAlAs superlattice. Thus, we estimated the ratio between the electron relaxation times in the both materials as *τT I*/*τsemi* ∼ (*ETHz*,*semi*/*ETHz*,*T I*)(*μT I*/*μsemi*) ∼ 3.5. Taking the previously measured value of the characteristic relaxation time for the InGaAs/InAlAs superlattice *τsemi* = 1.7 ps, we obtained the relaxation time for the bulk photo-induced electrons in BSTS as approximately *τT I* ≈ 6 ps.

Let us consider which relaxation process this time describes. In the case of BSTS, with extremely low initial concentration of free bulk carriers, the THz generation process began with the absorption of pump photons and the formation of electrons in the conduction band (Figure 7). The characteristic time of this process was of the order of the pump duration *t*0. Time *t*<sup>1</sup> was of the order of a few picoseconds and, within this interval, a relaxation of bulk electrons took place due to the phonon emission [37]. The second type of relaxation process was an interband transition from the bulk conduction band to the surface states at the Dirac cone. As the Fermi level *Ef* lies in the band of surface states (SSs) in a BSTS with a composition near the Ren's curve, SSs above *Ef* were primarily unoccupied. The characteristic time *t*<sup>2</sup> of this process is rather long, approximately 5–10 ps [37,38]. Finally, the relaxation of SSs was the third relaxation mechanism, with time *t*<sup>3</sup> as hundreds of femtoseconds or several picoseconds [9,39]. The direct interband transitions from the conduction band to the valence band are rather long and usually last from hundreds to thousands of picoseconds. These slow processes do not significantly contribute to generation at THz frequencies. Our estimate of the relaxation time corresponds to *t*2. Thus, we concluded that the process of population of the edge states by photo-induced bulk electrons made up the main contribution to the formation of the THz generation spectrum of the BSTS TI PCA.

The nonlinear **j***NL* currents are known to appear in unbiased TIs due to photo-galvanic (PG) and photon-drag (PD) effects [10–15,40,41]. Currents induced in these processes should quadratically depend on the laser pump field, both under sub-bandgap excitation [40] and under above-bandgap [10,13] laser excitation. Phenomenologically, dependences of these currents on the laser electric field for the non-stationary case [42] are described as:

$$\mathbf{j\_{NL}^{PC}}(t) = \int\_{-\infty}^{t} \widehat{\boldsymbol{\beta}}\left(t - t', t - t''\right) : \mathbf{E}(t') \mathbf{E}^\*\left(t''\right) dt' dt'' + c.c.\tag{4}$$

$$\mathbf{j}\_{NL}^{PD}(t) = \int\_{-\infty}^{t} \widehat{\boldsymbol{\gamma}}\left(\mathbf{t} - \mathbf{t}', \mathbf{t} - \mathbf{t}''\right) : \mathbf{E}(\mathbf{t}') \frac{\partial \mathbf{E}^\*\left(\mathbf{t}''\right)}{\partial \mathbf{r}} dt' dt'' + c.c. \tag{5}$$

**Figure 7.** Relaxation of carriers in BSTS film.

The PG effect takes place due to third-order tensor - *β*(*t* − *t* , *t* − *t*), which is non-zero only at the surface of TI. It is tied directly to the specific surface carriers, while both the bulk and surface electrons take part in PD effect via the fourth-order tensor - *γ*(*t* − *t* , *t* − *t*). As it was shown in previous experimental works [40,41], in case of the normal incidence of the pump beam on BSTS, PD effect is negligible in comparison with PG generation. In our case, at zero bias voltage we detected the same bipolar shapes of the temporal waveforms (Figure 6b) as in [15]. Thus, we can relate the THz fields observed in the unbiased TI to the PG effect.

By comparing expression (4) for PG current with the general presentation of the induced currents in form (3), one can see that (4) seemingly depicts an effect of resonant nonlinear generation of an effective field **<sup>~</sup> E**, which is responsible for the directional motion of free carriers. More accurate calculations, performed by considering the kinetic Boltzmann distribution equation for the electron distribution function within the semi-classical approach [40], can be treated so that an effective field **<sup>~</sup> E** appears here as a result of two processes: an alignment of carrier moments along the pump electric field, and an asymmetric scattering of carriers at the surface of TI [41]. However, this theory describes quadratic dependence on the pump field for THz field generated under below-bandgap excitation,

but needs further assumptions to explain generation under above-bandgap pumping. Indeed, the below-bandgap excitation did not change the carrier's concentration, *N(t)* was almost constant in (3), and only the temporal change of effective **<sup>~</sup> E** determined a short PG current pulse, which scaled up quadratically with the pump electric field. At the same time, when the pump photon energy exceeded the bandgap, the concentration of charge carriers also grew quadratically with the pump field. This was the case for bulk electrons, while a saturation of the concentration of the surface electrons may occur. However, no fourth-order dependence on the pump field was observed under above-bandgap excitation.

So, taking all the above considerations into account, we can conclude that: (1) the impact of the PG effect, and accompanying effective PG field **<sup>~</sup> E**, into THz generation in the biased THz antenna was negligible. Generation occurred due to photo-excited *bulk* carriers and its relaxation through the surface states in the presence of the constant field **E***dc*. The temporal shape of *N*(*t*) determined THz generation waveform and the width of the antenna spectral response; and (2) in the absence of an external biased field, THz generation took place due to the PG effect by *surface* electrons, which had almost the same concentration during the whole generation pulse. The temporal shape of effective **<sup>~</sup> E**(*t*) determined the THz generation specific waveform and the width of the BSTS spectral response.

#### **5. Conclusions**

In conclusion, we demonstrated a working photoconductive antenna with a dynamic range of order of 60 dB based on the nanofilm of the TI Bi2−xSbxTe3−ySey. In addition to the known nonlinear effects, the photoconductive mechanism of THz generation was realized in TIs because of the relaxation of bulk electrons through the surface states. A comparison of photoconductive antennas based on TI and semiconductor heterostructure showed that, despite the great difference in the thicknesses by more than one order, the THz fields of both PCAs were comparable in amplitude. The time-averaged photocurrent and dark currents arising in the TI PCA were measured and their linear dependences on the bias voltage were demonstrated.

TI antennas represent promising tools for generating THz radiation. Due to being extremely thin, they can be easily integrated into nanophotonic devices. They are inexpensive to manufacture, as the growing of a TI film takes several minutes without the need for difficult growth conditions, such as those required for MBE-technology. Their conversion efficiency can be further increased by applying plasmon gratings. Lastly, TI antennas are able to withstand large dark currents without being destroyed.

**Author Contributions:** Conceptualization, K.A.K., and P.I.K.; methodology, G.K.K.; software, D.A.S.; validation, K.A.K., and D.A.S.; formal analysis, G.K.K.; investigation, K.A.K., D.A.S., and G.K.K.; sample growth and characterization, P.I.K.; writing—original draft preparation, K.A.K., and G.K.K.; writing—review and editing, K.A.K., G.K.K., and D.A.S.; visualization, D.A.S.; funding acquisition, K.A.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Russian Foundation of Basic Research, grant numbers 18-29-20101 and 19-02-00598.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Acknowledgments:** The authors are grateful to D.S. Ponomarev, A.N. Klochkov, D.V. Lavrukhin, V.B. Novikov, and S.N. Molotkov for helpful discussions.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


### *Communication* **Tiling Photonic Topological Insulator for Laser Applications**

**Petr N. Kim 1,2, Dmitry P. Fedchenko 1,2, Natalya V. Rudakova 1,2 and Ivan V. Timofeev 1,2,\***


#### **Featured Application: A new class of active topological photonic devices and laser arrays.**

**Abstract:** A photonic topological insulator is a structure that isolates radiation in the bulk rather than at the edge (surface). Paradoxically, applications of such an insulator focus on its conducting edge states, which are robust against structural defects. We suggest a tiling photonic topological insulator constructed from identical prism resonators connected to each other. The light beam circulates inside the tiling bulk without propagation. However, we experimentally demonstrate a topologically-protected propagating state due to the disconnected faces of the edge resonators. The investigated state is robust against removing or attaching prism resonators. Moreover, the protection principle is phase-free and therefore highly scalable both in wavelength and resonator size. The tiling is suggested for active topological photonic devices and laser arrays.

**Keywords:** photonic topological insulator; total internal reflection; topological insulator laser

#### **1. Introduction**

Recently, a topological insulator laser was demonstrated [1,2] which exhibits scatterfree edge-state transport of light in the laser cavity, immune to perturbations and disorder. The topological feature forces injection locking of many laser emitters to act as a single coherent laser. The concept led to a variety of configurations: electrical pumping of a quantum cascade laser with valley modes [3]; vertical emission [4]; and bulk and vortex lasing [5,6]. Simultaneously, one-dimensional active resonator arrays were described by a Su–Schrieffer–Heeger model [7], and then implemented and optimized for robust singlemode high-power lasers [8–10].

Topological invariance of a physical process means that it is described by some highly robust conserved quantity that does not change under continuous deformations in the parametric space [11]. For example, the number of holes of a connected smooth compact surface does not change as the surface deforms, without cutting or gluing. In particular, Emmy Noether's theorem connects symmetries to the existence of the corresponding conserved quantities, such as energy, momentum, angular momentum, electric charge, and others. Parametric deformations can break the symmetry, still preserving the topological invariant. Almost forty years ago, a topological invariant was introduced for a single-particle electron state in a combined periodic potential and out-of-plane magnetic field [12,13]. The similar wave-like behavior is inherent to the photon state in the periodic potential of the photonic crystal [14]. As the Bloch wavenumber adiabatically passes the loop trajectory within the Brillouin zone of the crystal, its wave function acquires some topological phase that defines the topological invariant of the photonic band, separated by an insulating bandgap from neighboring bands. According to the bulk-edge correspondence principle [15], the number of edge states in the bandgap is equal to the difference of topological invariants in neighboring bands. Here, one assumes the *spatial edge* of the array rather than frequency band edge. As usual, in the optical frequency range, the magnetic response is weak. Instead, a spin–orbit coupling [16], dynamical modulation [17], or gain-loss materials [2] can also give

**Citation:** Kim, P.N.; Fedchenko, D.P.; Rudakova, N.V.; Timofeev, I.V. Tiling Photonic Topological Insulator for Laser Applications. *Appl. Sci.* **2023**, *13*, 4004. https://doi.org/10.3390/ app13064004

Academic Editor: Vladimir M. Fomin

Received: 22 February 2023 Revised: 16 March 2023 Accepted: 20 March 2023 Published: 21 March 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

rise to nonzero topological phases separated by an insulating bandgap. This idea was easily transferred from photonic crystal to waveguides, including ring resonator platforms [18].

Quartz prism resonators serve well instead of ring resonators, as the excitation can propagate between prisms by the *frustrated total internal reflection* mechanism. For the latter structure, additional edge solutions arise at different incident angles [19]. Nonetheless, there is the question of realizing such a complex coupling utilizing synthetic dimensions [20], or in the microring fashion [21,22]. If the structure period is comparable to radiation wavelength, then the description engages the topological phase. Otherwise, when the resonators are much larger than the wavelength, a phase-free explanation of the edge state is appropriate in terms of the *edge trajectory* of the beam [19].

In this paper, we suggest a *tiling photonic topological insulator* (TPhTI) constructed from identical prism resonators. Compared to [19], this new design suggests a continuous connection of neighboring resonators without spatial gaps. The light beam circulates within a few prisms inside the tiling bulk, penetrating through the mutual faces of the prisms or turning the propagation direction by total internal reflection at the open faces. However, a topologically-propagating state occurs at the edge of the array due to the disconnected faces of edge prisms. This propagating state persists against removing or attaching new prism resonators.

Furthermore, we fabricated the TPhTI and demonstrated the topologically-protected propagating state experimentally. We also speculated on laser applications of the TPhTI containing the gain material.

#### **2. Materials and Methods**

To fabricate the TPhTI we used a detailed concept similar to [19]. Rectangular prism resonators (Figure 1a) were manufactured from quartz glass with a refractive index of 1.43. Their linear dimensions of 12 × <sup>12</sup> × 8 mm3 were ensured by the Maksutov method [23] with 10 um accuracy. To avoid accuracy problems with the half-wavelength gap and multilayer covering, we chose the zero gap. The immersion liquid infiltrated the unintentional air gaps between the prism resonators to suppress the parasitic reflection and to ensure the lossless beam penetration between the resonators. Therefore, a liquid with a refractive index close to the refractive index of quartz glass was selected.

**Figure 1.** (**a**) The prism resonator made of quartz glass with a refractive index of 1.43. (**b**) A model of the tiling photonic topological insulator (TPhTI) composed of 28 prism resonators. (**c**) The TPhTI, composed of seven prism resonators.

The prism resonator tiling was precisely positioned on a flat platform, <sup>200</sup> × 200 mm2 in size. A rectangular triangular prism was used as a coupler to lead the light beam into and out of the quartz glass at the angle of total internal reflection. The angle of total internal reflection is 44.37◦ according to Snell's law. The resonators were fixed on an adhesive composition of a mixture of vinyl acetate (30%) and acetone (70%) copolymers. The immersion liquid was an aqueous solution of glycerin with a density of 1.228 g per cubic centimeter. The refractive index of the immersion liquid was 1.45. No more than 0.01 mL of immersion liquid covered each face to avoid a meniscus on adjacent vertical

faces, producing scattering and deviation of the beam. Before applying the immersion liquid, each prism was cleaned of dust and stains using crepe paper impregnated with a solution of water (80%), isopropanol (10%), metaxypropanol (5%), and nonionic surfactant (5%). Then, rectangular quartz prisms were connected, strictly in the order of numbering, as denoted in Figure 1b. After connecting each new segment, the operability of the tiling was checked using violet (405 nm) and red (650 nm) lasers (Figure 1c). Each prism was adjusted according to three degrees of freedom, namely one rotation and two translations along the axes X and Y (Figure 1a). The glass platform with assembled tiling and a triangular coupler was fixed on an optical bench next to the laser source.

#### **3. Results**

Figure 2 schematically demonstrates the stability of the beam trajectory; resonator #3, as denoted in Figure 1b, was removed in order to experimentally create the lattice defect of the TPhTI. Here, the green color indicates the trajectory of the beam. *In* and *Out* denote the entry and exit points of the beam, respectively. The input and output can be swapped; this does not affect the beam trajectory in any way. In the considered case, when removing nine resonators (#8–#9, #12–#16 and #19–#20), we observe an ordinary waveguide. However, while preserving the structure, we can observe robust beam trajectory relative to the removal of resonator #3 from the TPhTI. In this case, resonators #8, #9, and #13–15 are used to compensate for the absence of resonator #3. Obviously, all nine internal resonators have the same purpose with respect to other restructurings. For example, the removal of resonator #22 is compensated for by resonators #12, #13, and #19. This is the main topological insulator feature; an ordinary waveguide lacks this feature and behaves unstably with respect to the mentioned restructurings.

**Figure 2.** (**a**) The beam trajectory inside a smooth TPhTI model. (**b**) The corrected trajectory inside the TPhTI without prism resonator #3, as denoted in (**b**). The model shows that the light beam successfully bends around the defect of TPhTI.

The topological properties of the prism array yield a robustness to restructuring. Similar photonic topological insulators are theoretically described in [17–19,24], and practically implemented [18,24] on several platforms. Due to the angle of incidence of the beam trajectory, the prism array is a practical implementation of Rudner's toy [17], which provides a simple example of a topological insulator. As a class of restructuring, we chose the addition and removal of resonators from the array. Deeper explanations behind the topology are included in the Supplementary Materials.

Figure 3 shows that the laser beam bypasses the defect and exits the triangular coupler. The beam trajectory passes along the surface of the TPhTI structure due to the effect of total internal reflection on the faces of the prism resonators and exits back, as evidenced by the bright spot in the upper left corner of Figure 3b. The propagating state persists against removing (Figure 3b,d) or attaching new prism resonators (Figure 3e).

(**e**)

**Figure 3.** Beam trajectory photographs. The trajectory for smooth TPhTI (**a**,**c**) is robust against a defect obtained by removing prism resonator #3 (**b**,**d**) or attaching a new prism resonator below resonator #28 (**e**). Light beams for both a violet laser of 405 nm wavelength (**a**,**b**) and green laser of 532 nm (**c**–**e**) act in the same manner, proving the wavelength independence of the TPhTI principle.

Figure 4 shows that the presence of a topological state does not depend on prism resonator size. To demonstrate this scalability, the rectangular prism resonators were made in two versions. The first set was manufactured from quartz glass with a refractive index of 1.43, with linear dimensions 12 × <sup>12</sup> × 8 mm3 (Figure 4a). Their linear dimensions were ensured by the Maksutov method [23] with 10 um accuracy. The second set was manufactured from Chinese crown glass K9 with a refractive index of 1.517 and linear dimensions 30 × <sup>30</sup> × 30 mm3, with 30 um accuracy (Figure 4b).

**Figure 4.** Scalability of the TPhTI is manifested by comparing two resonator sizes: (**a**) <sup>12</sup> <sup>×</sup> <sup>12</sup> <sup>×</sup> 8 mm3. (**b**) 30 <sup>×</sup> <sup>30</sup> <sup>×</sup> 30 mm3. Both trajectories are homothetic and proportional to prism linear dimensions.

In Figure 5, the scalability of the TPhTI principle is stressed. First, it works for every wavelength in the visible range, as long as the refractive index is sufficiently high. Second, the resonator size was fixed at the centimeter scale; nonetheless, the principle is valid for arbitrary sizes larger than the wavelength and the beam cross-section. Please see additional trajectories for different wavelengths, resonator sizes, and tiling configurations in the Supplementary Materials.

**Figure 5.** Wavelength-independent beam trajectory. Laser beams of RGB-colors pass the same trajectory through a TPhTI made of seven prism resonators: (**a**) red 650 nm, (**b**) green 532 nm, and (**c**) blue 405 nm.

#### **4. Discussion**

In practical implementation, the TPhTI turned out to be sensitive to the following parameters of the experiment:


Quantitatively, TPhTI performance is proportional to the beam intensity along the trajectory, as shown in Table 1 for the smooth TPhTI (28 resonators, Figure 3a,c) and defective TPhTI, with one resonator taken away (27 resonators, Figure 3b,d). The relative intensity is normalized to the intensity of the beam passed through the reference waveguide, consisting of eight resonators (Figure 5). Throughout the visible range, the smooth TPhTI secures more than half of the radiation, while the defective TPhTI loses 10–20% more. The best performance is seen in the middle wavelength. The first reason for this is the refractive index dispersion for the prism material, coupler material, and immersion liquid. The second reason is the difference in beam cross-section of the used sources. Altogether, these reasons are technical and have no deep physical impact.

**Table 1.** TPhTI performance is measured as the relative beam intensity of the edge trajectory.


The effect of stability of the trajectory of the light beam relative to the defect introduced into the TPhTI is experimentally confirmed. Table 2 summarizes the stability of trajectories shown in Figures 3–5. Figure 4 shows the perfect scalability of the phenomenon. Therefore, the minus sign '-' declares that the linear dimensions of the prism resonator do not affect the trajectory stability. The refractive indices are not important until the total internal reflection and immersion conditions are satisfied. Therefore, they share the plus–minus sign '±'. The angle of beam incidence is exactly 45 degrees. This is critical, as the trajectory has to pass between certain corners or the beam will split and enter the array bulk. The partial impact of laser wavelength is shown in Table 1 and Figure 5.


**Table 2.** Experimental parameters and their impact on beam trajectory stability.

#### **5. Conclusions**

Here we focused on a new type of photonic topological insulator. We suggested a tiling photonic topological insulator constructed from identical prism resonators connected to each other. We experimentally demonstrated a topologically-protected propagating beam trajectory due to the disconnected faces of edge resonators. Then we removed or attached some prism resonators to destruct the trajectory. Nonetheless, the complete trajectory remained the same outside the destructed area. Overall, the main benefit is a novel platform for the practical implementation of Rudner's toy [17]: a tiling photonic topological insulator. Other benefits are as follows: experimental demonstration of the novel platform, its robustness, phase-free concept, and laser array application. As a direction for possible further research, it is worth noting that, along with quadrangular TPhTIs, triangular and hexagonal prism resonator tiling can be experimentally implemented by zero gap, in accordance with the theoretical prediction [19]. One of the advantages of the hexagonal TPhTI is that the

reflection angle is 60◦. Therefore, this type of insulator can be experimentally implemented with optical material with a refractive index less than 1.43; hence, no less than 1.15. On the other hand, the simplest geometric considerations show that, under certain conditions in a hexagonal TPhTI, a diagonal transition occurs in fewer jumps between resonators than in a quadrangular TPhTI. The TPhTI can be described in the language of trajectories, as well as in the language of differential wave equations natural for graphene-like materials [25], secondary quantization operators, or cellular automata [26]. For some certain incidence angles, the edge solutions reversed the direction upon scattering by edge defects. This case may be indicative of the existence of higher-order states [27].

This tiling is suggested for active topological photonic devices and laser arrays, while topological features force unidirectional propagation. In the visible range, the magnetooptic effects are generally weak, which prohibits the conventional unidirectional propagation mechanism. Instead, the imbedding of gain and loss materials inside the resonator provides another type of unidirectionality [1,2]. The conducted research paves the way to transfer the gain–loss unidirectional mechanism from photonic crystals and waveguides to phase-free theory for macroscopic prism resonators.

**Supplementary Materials:** The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/app13064004/s1, Figures S1–S7: beam trajectory when passing through the TPhTI; Figures S4 and S5: trajectory that bends around the defect in the structure of the TPhTI; Figures S6 and S7: trajectory that bends around the defect in the structure of the TPhTI with resonators of a different size; Figures S8–S10: operation of Snell's law; Figure S11: scattering matrix formalism to explain topological protection [17,24,28–31].

**Author Contributions:** Sample preparation, experimental setup, and measurement, P.N.K., N.V.R. and I.V.T.; software, D.P.F. and I.V.T.; validation, P.N.K.; conceptualization and methodology, D.P.F. and I.V.T.; writing—review and editing, P.N.K., D.P.F., N.V.R. and I.V.T.; supervision, I.V.T. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Russian Science Foundation (project no. 22-42-08003).

**Data Availability Statement:** The data presented in this study are available upon reasonable request from the corresponding author.

**Acknowledgments:** The authors are grateful to V.M. Sventitskii for useful discussions and materials used for experiment.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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