**Picosecond Laser-Induced Hierarchical Periodic Nearand Deep-Subwavelength Ripples on Stainless-Steel Surfaces**

#### **Shijie Ding 1,**†**, Dehua Zhu 2,**†**, Wei Xue 1, Wenwen Liu <sup>1</sup> and Yu Cao 2,\***


Received: 5 December 2019; Accepted: 23 December 2019; Published: 26 December 2019

**Abstract:** Ultrafast laser-induced periodic surface subwavelength ripples, categorized based on the ripple period into near-subwavelength ripples (NSRs) and deep-subwavelength ripples (DSRs), are increasingly found in the variety of materials such as metals, semiconductors and dielectrics. The fabrication of hierarchical periodic NSRs and DSRs on the same laser-irradiated area is still a challenge since the connection between the two remains a puzzle. Here we present an experimental study of linearly polarized picosecond laser-induced hierarchical periodic NSRs and DSRs on stainless-steel surfaces. While experiencing peak power density higher than a threshold value of 91.9 GW/cm2, in the laser-scanned area appear the hierarchical periodic NSRs and DSRs (in particular, the DSRs are vertically located in the valley of parallel NSRs). A large area of the uniformly hierarchical periodic NSRs and DSRs, with the spatial periods 356 ± 17 nm and 58 ± 15 nm, respectively, is fabricated by a set of optimized laser-scanning parameters. A qualitative explanation based on the surface plasmon polariton (SPP) modulated periodic coulomb explosion is proposed for unified interpretation of the formation mechanism of hierarchical periodic NSRs and DSRs, which includes lattice orientation of grains as a factor at low peak power density, so that the initial DSRs formed have a clear conformance with the metallic grains.

**Keywords:** laser induced subwavelength ripples; surface plasmon polaritons; coulomb explosion; stainless steel

#### **1. Introduction**

The laser-induced periodic surface structure (LIPSS) [1,2], a by-product effect of laser material processing applications is at its inception, but in the past few years has been a research hotspot that involves multiple branches of physics such as wave optics, non-linear optics, fluid dynamics and thermodynamics. With the rapid development in particular of ultrafast laser-matter interaction in both science and engineering, the ultrafast laser-induced periodic surface subwavelength ripples [3–5] which can be categorized based on the ripple period (Λ) into near-subwavelength ripples (NSRs, 0.4 < Λ/λ < 1) and deep-subwavelength ripples (DSRs, Λ/λ < 0.4) [3], have been reported increasingly on a variety of materials such as metals [5,6], semiconductors [7,8] and dielectrics [3,9].

However, the existing formation mechanisms for construction of NSRs and DSRs are considered completely different, and their theoretical models have been in a state of debate and development [3, 10,11]. The NSRs (sometimes called classical ripples) are found to be formed by a wide range of pulse durations from a few hundred nanosecond (ns) to femtosecond (fs) laser irradiation on the solid material

surface, which makes it seem like a universal pulse laser-induced material response. The orientation of NSRs, which were found always parallel or perpendicular to the incident laser polarization, is usually ascribed to the periodic electric field modulation by the incident laser beam interference with surface scattering laser wave due to the sample surface roughness [12,13]. The excitation of surface plasmon polaritons (SPPs) by incident laser pulses is also widely used for the explanation of NSR formation [3]. Huang et al. [3] compared experiments with metal, semiconductor and dielectric and assumed the grating-assisted surface plasmon (SP)-laser coupling should be responsible for the origination of NSRs. Reif et al. [14,15] considered the ion sputtering and thin liquid film, and proposed the self-organized effect of the non-stable material to explain the formation of subwavelength ripples. Instead of easy production and observation of the NSRs, DSRs are only rarely found in ultra-short laser pulse (duration less than 100 picoseconds) irradiation of some selected materials, including fused silica [16], silicon [8,10,17], graphite [11] and some other materials [10,18,19]. Diverse mechanisms are proposed for explanation of the origins of DSRs, such as second and higher harmonic generation [10,20], SPPs [11] and self-organized effect [14,21].

The relationship between the formation mechanisms of NSRs and DSRs still remains a puzzle. The interference model of incident and surface scattered laser beam can effectively explain the correlation between the spatial period of NSRs and the incident angle, wavelength of laser irradiation, but not fit the period of the DSRs. The SPPs model excited from the rough surface by scattering with local defects is doubted as its intensity distribution is not at regularity but intricacy [22]. Rudenko A. gave a reasonable opinion that the surface scatter electromagnetic waves have been demonstrated to consist of the SPP, an evanescent cylindrical wave, and a Norton wave [23]. The DSRs models like second and higher harmonic generation [10] and grating-assisted SP-laser coupling [3,10] are not compatible with the spatial period of NSRs. The self-organized theory based on the ion sputtering and instability of thin liquid films is theoretically compatible with various ripple periods for any NSRs and DSRs, which attribute the directional asymmetry of laser-induced ripples to a spatial asymmetry of the excited-electron kinetic energies [21]. But it can only meet with the subwavelength periodic ripples that are perpendicular to the incident laser electric polarization. This does not agree with the scenario of ripples' orientation parallel with laser polarization that is observed in dielectric materials [24], metals and semiconductor materials [10,25,26].

Another interesting subject of debate is whether the hierarchical periodic NSRs and DSRs can be constructed simultaneously on the same laser-irradiated area, which should be helpful to reveal the connection between the two, and to discover a unified theoretical model. Rare reports took notice of the mechanism and regularity of hierarchical periodic NSRs and DSRs formation. Yao et al. [27] used femtosecond laser scanning to fabricate large area subwavelength ripples on stainless-steel surfaces for a reinforced antireflection property. The induced ripples included both NSRs and DSRs, but the DSRs were not noted by the authors since the DSRs were not clear. Ji et al. [28] reported cross-periodic structures (NSRs and DSRs) on the silicon surface that the DSRs induced by a low laser pulse repetition rate of 1 kHz were not distinct and the formation mechanism remains in doubt. In contrast with the fabrication of NSRs, the DSRs usually need a higher repetition rate of the ultrashort laser pulse (above 76 MHz) [10] or an underwater environment [29,30]. Ahsan et al. [31] and Romano et al. [32] reported that the laser irradiation dose and the transient process had a significant influence on the ripple formation, suitable adjustment of the ultrafast laser-induced surface subwavelength ripples could offer a variety of colors. Gurevich et al. [33] proposed that the ripples formation cannot be explained in the frames of pure plasmonic theory and hydrodynamic instabilities are an important influence in the ripple formation. Liao et al. [34] reported that excitation of standing plasma waves at the interfaces between areas modified and unmodified by the femtosecond laser irradiation plays a crucial role in promoting the growth of periodic nanoripples. In fact, there are many diverse mechanisms proposed for the origins of laser-induced DSRs and NSRs, such as the second and higher harmonic generation [10,20], SPPs [11] and self-organized effect [14,21], so far no model can satisfy all the phenomena observed. Hence, the fabrication of in situ hierarchical periodic NSRs and DSRs remains a challenge when exploring their physical mechanisms and potential applications.

In this work, we present a picosecond (ps) laser induced hierarchical periodic NSRs and DSRs on stainless-steel surfaces. The evolution of DSRs to NSRs with laser peak power density deposition was observed, and the lattice orientation as the intrinsic characteristic of the stainless-steel material shows a significant role in the evolutionary process of DSRs to NSRs. A qualitative explanation of the ps laser-induced hierarchical periodic DSR and NSR formation mechanism is discussed and compared with a self-organized effect and the grating-assisted SP-laser coupling theory.

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

Stainless steel is one of the most extensively studied metals because of its versatility in industry and daily life. It has been reported that periodic NSRs are induced by the ultrashort pulse laser irradiation on stainless steel surface [35], but so far no DSRs. AISI 316L stainless steel sheets with dimensions of 50 mm × 50 mm and 1 mm of thickness were used in the experiment. Samples were mechanically polished and divided into two groups A and B. The group A samples were directly subject to the laser irradiation and the group B samples were firstly corroded by the surface erosion agent (HF 20 %vol. + HNO3 10 %vol. + H2O 70 %vol.) before the subsequent laser irradiation. After the corrosion, the group B samples revealed the metallographic lattice structure on the surface. Before the laser irradiation, all the samples were cleaned by ultrasonic ethanol bath for 10 min. The same laser processing parameters were used for the fabrication of the hierarchical periodic NSRs and DSRs on the non-corroded (group A) and corroded (group B) sample surfaces.

The schematic setup of the experimental ps laser-scanning system is shown in Figure 1. The as-prepared samples were irradiated with a linearly polarized ps laser (Trumicro5050, TRUMPF Company, Ditzingen, Germany) with the repetition rate of 400 kHz and the pulse duration of 10 ps. The BBO (Beta barium borate, β-BaB2O4) crystal was utilized for frequency doubling of the incident laser beam from the wavelength of 1030 nm to 515 nm. Also, we set up the beam expander in order to achieve smaller focal spot size and higher laser fluence. A 2-D galvanometric scanner (SCANLab Company, Puchheim, Germany) with F-theta objective lens was used for the focused laser beam scanning in *x*-*y* directions. A *z*-direction stage was used to control the focal length of the laser beam spot since the laser beam was set perpendicular to the surface of samples. The focal spot diameter, defined as the gaussian-profile laser beam at 1/e2 of its maximum intensity, was approximately 16 μm. Different scanning speeds and power density were selected for fabrication of the hierarchical periodic dual subwavelength ripples. Large-area hierarchical periodic NSRs and DSRs were prepared by laser parallel line scanning on the sample surfaces.

**Figure 1.** Schematic setup of the picosecond (ps) laser scanning system for fabrication of hierarchical periodic near-subwavelength ripples (NSRs) and deep-subwavelength ripples (DSRs).

The micro-morphologies of the prepared stainless-steel sample surfaces were investigated by laser-scanning confocal microscopy (OSL4100, OLYMPUS, Tokyo, Japan) and a scanning electron microscope (SEM, QUANTA 200F, FEI, Hillsboro, OR, USA), and the spatial period of the NSRs and DSRs were estimated from the high-magnification morphology images. Since there are reports that the single ripple line seems not always to be straight and perpendicular or parallel to laser polariton [36], which means the laser induced subwavelength ripples have bending and bifurcation, the orientation variation of ripple formation were also investigated.

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

#### *3.1. Preparation of Hierarchical Periodic Near-Subwavelength Ripples (NSRs) and Deep-Subwavelength Ripples (DSRs)*

During the interaction between pulsed laser and solid material, the cumulative history of receiving laser irradiation by a solid surface is essentially affected by the transient laser power density of single laser pulse (space factor) and the superposition rate of multiple laser pulses (time factor). Therefore, our experimental exploration was started by counted ps laser pulses stacking hitting a fixed point on the stainless-steel sample surface for investigation of the influences of space-time characteristics on laser-induced NSRs/DSRs, then expanded to line scanning for fabrication of large area hierarchical periodic NSRs and DSRs.

Figure 2 shows the SEM images of the ps laser induced surface subwavelength ripples at fixed points, each irradiated by 4 laser pulses with the single pulse energy of 1.9 μJ. The average laser power adopted in the experiment was 0.76 W. The schematic power density correlation of two adjacent ablation spots is illustrated in Figure 2h, where L is the center distance between two adjacent pulse points which equals 20 μm, 10 μm and 5 μm in Figure 2a–c, respectively. The laser power density *I(r)* at a certain point in the focal spot associating the material thermo-physical properties can be defined as the following equation:

$$P = \int\_0^{2\pi} \int\_0^{+\infty} I\_0 e^{-2r^2/w\_0^2} r dr d\theta = \pi w\_0^2 I\_0/2 \tag{1}$$

$$I(r) = I\_0 \times e^{-2r^2/w\_0^2} \tag{2}$$

where *p* = *E*/*tp* is the peak laser power, *E* is the single pulse energy, *tp* is the pulse duration, *I*<sup>0</sup> is the maximum power density in the center of the focal spot and *w*<sup>0</sup> is the waist radius of the laser beam.

The results clearly suggest the peak power density plays an important role in the formation of subwavelength ripples. Figure 2a shows the surface morphologies of two separate ablation craters with hatch distance *L* = 20 μm. The ablated crater presents a central, circular region with a radius of 8 μm can be characterized by two concentric rings, namely the dual DSRs + NSRs inner zone I and the single DSRs outer ring II, as shown in Figure 2d. In the inner zone I, the NSRs preferentially aligned perpendicular with the incident laser polarization (marked with the arrow *E*), which has a spatial period of 381 ± 23 nm as measured in the magnified Figure 2d. The DSRs situate in the valley of NSRs with orientation parallel to the incident laser polarization has a spatial period of 381 ± 23 nm. Considering the gaussian profile of the focal spot energy distribution, the laser peak power density threshold value of the inner zone I was calculated to be 91.9 GW/cm2. The ridges of the NSRs were steep and there were nano-particles on both the valleys and ridges. The outer ring II presents the characteristic texture of DSRs with a thickness of about 2 μm aligned along the laser polarization as shown in Figure 2g. The laser peak power density threshold value of the outer ring II with DSRs was calculated as 55 GW/cm2. As shown in Figure 2b, the hatch distance L is set to 10 μm and the overlapping rate is 33% (only the outer ring II of two ablated craters overlapped). In Figure 2e, it is clearly shown that more nanoparticles are dispersed on the DSRs and more DSRs formed in the valley of NSRs close to the overlapping area. With high laser peak power density in the center of the focal spot, the NSRs can be fabricated without pulse overlapping. Due to the low power density in the

periphery of the focal spot, the DSRs formed without pulse overlapping while the NSRs formed with pulse overlapping. These phenomena are in accord with the reported theory that the threshold of multiple laser pulse material ablation is less than of single laser pulse ablation [37]. As shown in Figure 2c, the hatch distance L is set to 5 μm and the overlapping rate is 66%. The overlapping area consisted of the outer ring II and the inner zone I of the two ablated craters. A similar morphology can be seen in the non-overlapped area in Figure 2f, but the overlapping area of two adjacent craters were observed with the higher laser peak power density irradiation and the appearance of the hierarchical periodic NSRs and DSRs (in particular, the DSRs were vertically located in the valley of parallel NSRs). The ridge profile became coarse and the groove became narrow accompanied with the aggregation of plenty of nanoparticles on the ridge, and the coarsened ridge period changed from 201 nm to 249 nm at different locations. For applications, the evolutionary morphology from the periphery to the center of the crater due to the gaussian beam energy distribution suggests a precision control of the laser peak power density is necessary for fabrication of distinct hierarchical periodic NSRs and DSRs.

**Figure 2.** Scanning electron microscope (SEM) images of ps laser induced surface subwavelength ripples. Each of spot was carried out by 4 pulses with single pulse energy of 1.9 μJ and the hatch distance of the two spots was set as: (**a**) 20 μm, (**b**) 10 μm and (**c**) 5 μm. (**d**–**g**) The corresponding images of magnified areas separately. (**h**) The schematic of peak power density profile correlation with laser spots.

For the preparation of large-area hierarchical periodic NSRs and DSRs, it is worth exploring the relationship between the scanning speed and resultant morphology. The preparation of large-area hierarchical periodic NSRs and DSRs was implemented by a line-by-line laser scanning process. The spacing between the filled parallel lines was set to 10 μm. A series of laser scanning speeds from 50 mm/s to 1000 mm/s under the average laser power of 0.76 W were chosen to investigate the effect of space-time characteristic on large area laser-induced hierarchical periodic NSRs and DSRs. The numbers of overlapping laser pulses at any place of the laser scanning line path can be calculated by *N* = *D* \* *fp*/*v*, where *D* = 16 μm is the diameter of focused Gaussian spot, *fp* = 400 kHz is the laser pulse

repetition rate and *v* is the laser scanning speed as 50, 100, 300, 500, 800, 1000, 1300, and 1500 mm/s. Thus, the calculated overlapping pulse numbers (N) were 128, 64, 21, 13, 8, 6, 5 and 4, respectively.

The SEM images of the prepared hierarchical periodic NSRs and DSRs with increasing laser scanning speed are shown in Figure 3. As shown in Figure 3a, there were multiple nanoparticles redeposited on the ridge of the NSRs and, and the NSRs nearly disappeared for the high power density pulse repeated irradiation under a relatively low scanning speed of 50 mm/s. The DSRs in the valley of the NSRs cannot be observed or have vanished due to the absorption of exceeded pulse energy irradiation. When the laser scanning speed was increased to 100 mm/s, the uniformity NSRs and DSRs could be captured easily from the zoomed view of Figure 3b. With the scanning speed increased up to 500 mm/s, the smooth and clean NSRs and rarely nanoparticles redeposition fabricated accompany with more regular DSRs formed in the valley of the NSRs. When the scanning speed was higher than 500 mm/s and lower than 1000 mm/s, the continuity of the DSRs and NSRs became worse and the bending of the DSRs was pronounced. When the scanning speed increased to 1300 mm/s and 1500 mm/s, the nanoripples formed were more blurred. It can be seen from Figure 3g,h that although the periodic ripples formed were not strictly along one direction, but the disorderly DSRs cross with NSRs could still be observed.

**Figure 3.** SEM images of subwavelength ripples prepared by different laser scanning speed and the fixed line spacing of 10 μm. The laser scanning speed of (**a**–**h**) is set to 50, 100, 300, 500, 800, 1000, 1300, and 1500 mm/s, respectively. The insets are zoomed views of the selected areas. The polarization of incident laser is indicated by the white double-headed arrow.

As shown in Figure 4, the spatial period of the NSRs and the DSRs which irradiated at average power of 0.76 W and various scanning speeds from 50 mm/s to 1000 mm/s were measured. The influence of pulse energy overlapping in the charge of the scanning speed was investigated by means of the line and symbol chart. The spatial period of the NSRs shows a small increment from 356.8 ± 17 nm to 411.4 ± 19 nm as the scanning speed increased. This scenario is similar to the previous findings that the spatial period of the NSRs decreases with increasing pulse energy [8,35]. An efficient amount of high power density and its distribution which deposited on the pre-existing ripple could decrease the spatial period and the ridge of the ripple could become coarser for its inevitable pulse overlapping offset. When the scanning speed was higher than 500 mm/s, the spatial period reached a higher limit value of 411.4 ± 19 nm. We assume that the few pulses overlapping that of the low power density in the periphery of the follow-up pulse, interferes with the NSRs formation under that of high power density. Moreover, the DSRs in the valley formed this superimposed effect in chaos, too. The spatial period of the DSRs shows no obvious trend and fluctuates within a range of 44 nm to 74.6 nm.

**Figure 4.** The spatial period of NSRs and DSRs irradiated at an average power of 0.76 W and various scanning speeds from 50 mm/s to 1000 mm/s.

Figure 5 shows the surface morphology evolution of ps laser-induced subwavelength ripples by increasing the average laser power from 0.49 W to 4.55 W at a fixed scanning speed of 500 mm/s, namely the peak power density increases from 60.9 GW/cm2 to 565.7 GW/cm2. As shown in Figure 5a, the surface is covered with uniform DSRs with orientation parallel to the incident laser polarization, since the peak power density is as low as 60.9 GW/cm<sup>2</sup> (average laser power of 0.49 W). It is interesting that the DSRs induced at low peak power density are not straight lines in succession and are similar to dendrite or well-known hydrodynamic instabilities of thin liquid films [21]. By increasing the laser peak power density to 94.5 GW/cm2 (average laser power of 0.76 W), both the NSRs and DSRs were fabricated as illustrated in Figure 5b. More uniformity and regularity including continuous lines were observed on the samples when the laser peak power density was higher than 94.5 GW/cm2. In agreement with the previous reports, a correlation between the electric field polarization direction and the NSRs orientation was observed in all cases [3,10]. Due to the ultrashort pulse laser irradiation, the time of

the pulse duration is not enough for the excited electron transfer energy to lattice and thermalization. All the nano-ripples were fabricated by the "cold" process with few heating effects, which is why so much high power density without molten pool but only more and more nano-particle aggregation.

**Figure 5.** SEM image of the subwavelength ripples induced by different laser peak power density of (**a**) 60.9 GW/cm2, (**b**) 94.5 GW/cm2, (**c**) 161.6 GW/cm2, (**d**) 304.6 GW/cm2, (**e**) 425.3 GW/cm<sup>2</sup> and (**f**) 565.7 GW/cm2, while the scanning speed is set to 500 mm/s and the line spacing is set to 10 μm.

As shown in Figure 5, the variation of laser peak power density has a great influence on the eventual morphology of the hierarchical periodic NSRs and DSRs. The spatial period is one of the most important topology parameters of the hierarchical periodic NSRs and DSRs, which may play a crucial role in its potential application such as superhydrophobicity, friction control and structural color.

The spatial period tendencies of NSRs and DSRs with incident laser peak power density and scanning speed are shown in Figure 6. The spatial period of the NSRs decreases as the incident laser peak power density increases. Under the scanning speed of 50 mm/s, when the laser peak power density increases from 60.9 GW/cm2 to 161.6 GW/cm2, the period of the NSRs decreases from 389 <sup>±</sup> 11 nm to 352 <sup>±</sup> 12 nm. When the laser peak power density is greater than 161.6 GW/cm2, since the scanning speed is relatively low, the much greater pulse overlap results in the preformed periodic ripples' disappearance. A similar scenario can be observed when the scanning speed is 100 mm/s and the laser peak power density greater than 675.2 GW/cm2. Moreover, the spatial period of the NSRs increases as the scanning speed increases, which agrees with the previous section. When the scanning speed is between 300 mm/s and 1000 mm/s, the NSRs were fabricated on the surface of the sample, and the period of the NSRs decreases from 430 ± 10 nm to 382 ± 14 nm with the laser peak power density increase.

On the other hand, the period of DSRs fluctuates at 65 ± 21 nm, and there is no obvious trend with the incident laser peak power density and scanning speed. The formation of the DSRs precedes the NSRs when the incident laser power density is slightly larger than the ablation threshold of the material. The periodic fluctuation is related to the local transient free electron density fluctuation of the material. The spatial period of the subwavelength ripples fabricated at different laser peak power density share a similar tendency with the scanning speed, which means the power density of incident laser has a decisive role in the light–matter interaction.

Finally, a large area of the hierarchical periodic NSRs and DSRs was fabricated on the stainless-steel surfaces by a set of optimized laser-scanning parameters. The scanning speed of 500 mm/s and the laser average power of 0.76 W were chosen. Figure 7 shows the SEM micrographs of the prepared large area hierarchical periodic NSRs and DSRs. The spatial period of obtained NSRs and DSRs were 356 ± 17 nm and 58 ± 15 nm, respectively.

**Figure 6.** Comparison of the spatial period tendency of NSRs and DSRs with incident laser peak power density and scanning speed.

**Figure 7.** SEM micrographs of the prepared large-area hierarchical periodic NSRs and DSRs on the stainless-steel sample surface. (**a**–**d**) is the magnified picture of the selected area which indicated by a rectangular of white line.

#### *3.2. Lattice Orientation of Grains as a Factor in the ps Laser-Induced Hierarchical Periodic NSRs and DSRs*

An interesting phenomenon has been found in that the lattice orientation of grains is a factor in the ps laser-induced hierarchical periodic NSRs and DSRs on the stainless-steel surfaces. The evolutionary differences of the subwavelength periodic ripples with decreasing laser scanning speed under low peak power density (60.9 GW/cm2, average laser power of 0.49 W) are revealed in Figure 8. By comparing Figure 8a,b we see that with the decrease of laser scanning speed (an increase of the overlapping pulse number N and laser energy absorption), the DSRs can be observed on stainless steel sample surface irradiated with all the different laser-scanning speeds (300~1000 mm/s), but the NSRs that are perpendicularly oriented only appear at low scanning speed (<300 mm/s, Figure 8d). With the high laser scanning speed of 1000 mm/s, the obscured DSRs were generated on the pristine surface and the spatial period of the nano-ripples was 58 nm. The ridges and valleys of the ripples are very smooth and these blurred DSRs show a regular arrangement that seems to be influenced by the lattice orientation of the material characteristics, as shown in Figure 8a,b. The initial DSRs formed at low peak power density have a conformance with the metallic grains, which has never been reported before. As shown in Figure 8a,b, the formation of DSRs has preferentially occurred in some "blocks", which is clearly related to the lattice orientation of the material itself. When the laser-scanning speed is decreased to 500 mm/s, the DSRs became distinct and the area induced by the lattice orientation became unclear because the power density from the laser pulses is high enough for the valence electrons excitation upon reaching the material ablation threshold [37]. When the laser-scanning speed is lower than 300 mm/s, the hierarchical periodic NSRs and DSRs are uniformly generated, as shown in Figure 8d. But at the scanning line overlapping area of Figure 8d, which is similar to the Figure 2b scenario as the two adjacent DSRs outer rings overlapped, only DSRs are fabricated because the peak power density is lower than the threshold value of 91.9 GW/cm2.

**Figure 8.** SEM images of subwavelength ripples prepared by different laser scanning speed and the fixed line spacing of 10 μm. The laser scanning speed is set to (**a**) 1000 mm/s, (**b**) 800 mm/s, (**c**) 500 mm/s, and (**d**) 300 mm/s, respectively. The insets are zoomed views of the selected areas. The polarization of the incident laser is indicated by the white double-headed arrow.

To further verify this hypothesis, we performed a pre-corrosion treatment on the stainless-steel samples in order to reveal the metallographic lattice structure on the surface. Hydrofluoric acid–nitric acid aqueous solution was selected on account of the grain of 304 stainless steel which is austenite grain. The metallographic lattice structure before and after the laser scanning treatment are shown in the confocal laser scanning microscope images of Figure 9a,b, respectively. Some grains turned a dark grey color after the ps laser irradiation, since the laser induced nano-scale ripples always present dark color in optical microscopes.

**Figure 9.** The metallographic lattice structure before and after the laser scanning treatment of 0.49 W and 1000 mm/s are shown in the confocal laser-scanning microscope images, (**a**): before, (**b**): after.

Figure 10 shows the SEM micrograph of the same sample of Figure 9b, where the DSRs similar to those in Figure 8a–c can be observed, and the formation of DSRs is affected by the lattice orientation of stainless steel. On the different grains of the stainless-steel sample, the DSRs are selectively generated. The DSRs are found in adjacent grains with little differences in orientation, as shown in Figure 8a,b. The lattice orientation variations, which are the manifestation of grain atomic bulk density differences, are believed to have an intrinsic fluence on the initial formation of DSRs. Moreover, the DSRs formation conformance with the grain structures is sensitive to the peak power density irradiation of the material. In this study, the energy threshold of the lattice orientation and the atomic bulk density affects the DSRs' formation. When the power density goes beyond the lattice binding energy of the stainless steel, the effect of the lattice on the initial formation behavior of DSRs disappears.

**Figure 10.** SEM images of the same sample of Figure 9b. (**a**–**d**) is the magnified picture of the selected area which indicated by a rectangular of white line.

#### *3.3. Mechanism for the Picosecond (ps) Laser-Induced Hierarchical Periodic NSRs and DSRs*

According to the above discussed facts, a feasible mechanism model should be compatible with the three clues that are discussed above: (a) DSRs can be independently generated at a relatively low peak power density, but the generation of NSRs need much higher peak power density and accompanied by DSRs in the valleys of the NSRs. (b) The orientation of the periodic DSRs is parallel to the polarization of incident laser and perpendicular to the orientation of the periodic NSRs which coincides with the laser-induced SPPs. (c) The formation of the DSRs at low peak power density has a conformance with the metallic grain structures, and preferentially occurs in the interior of the grains that have low surface atomic planar densities. Neither the classical scattering wave theory nor the SPPs excitation theory can explain the formation of DSRs in which spatial period much smaller than the incident laser wavelength [11]. The shortcoming of the self-organization theory is the influence of asymmetric ionization kinetic energy affected by the polarization of the laser electric field, which cannot explain the hierarchy and polarization dependence of different ripples in this experiment [21]. Second-harmonic generation (SHG) is only found during the irradiation of certain materials, the present experiments cannot clearly show that SHG is involved in the formation of DSRs on any surface [38].

A qualitative explanation based on SPP modulated periodic coulomb explosion is proposed for the formation mechanism of hierarchical periodic NSRs and DSRs. As shown in Figure 11, the atomic arrangement of the grains of 304 austenitic stainless steel is indicated in the dotted frame A. The white double-headed arrow shows the polarization of the incident laser. During a picosecond laser pulse duration, electron-absorbing photon ionization is always present, and the free electrons after ionization move in the direction of the electric field under the action of the laser electric field, forming a free electron gas limited to the surface movement. However, the concentration of free electrons on the surface of the sample is not uniformly distributed due to the surface roughness and defects, which lead to the initiation of the local non-thermal phase change coulomb explosion [39] at the place where local electron ionization intensity is large enough. As shown in Figure 11b, the material removal of coulomb explosion then makes the free electron gas movement blocked and concentrated at the adjacent place along the laser electric field, which results in the subsequent coulomb explosion chain that forms the DSRs. When the incident laser power density increases to a high threshold value, the laser electric field (Transverse Magnetic wave, TM wave) induced constraint SPPs will propagate along the metallic surface but perpendicular to the laser electric field orientation, and attenuate along the vertical direction of the metallic surface [40]. The dotted line frame B in Figure 11a shows the surface plasmon standing wave field induced at high energy density during laser irradiation. When the incident light is irradiated to a defect on the surface of the stainless steel, the SPPs are excited by the coupling of the surface electron plasma oscillation, and the surface plasmon standing wave is induced when the adjacent surface defects are separated by a certain distance.

Figure 11c shows that the surface energy field of the stainless-steel sample was being periodically modulated by the surface plasmon standing wave action, which made the free electron concentration increase and a strong coulomb explosion occurred. The subsequent free electrons under the SPP-modulated electric field are blocked and concentrated at the adjacent place along the SPPs' propagation direction, which results in the subsequent coulomb explosion chain that forms the NSRs with orientation vertical to the laser polarization directions. The weak electron concentration in the valley after the strong coulomb explosion is likely to form a micro coulomb explosion, thereby forming the DSRs in the valley. For the inevitable pulse overlapping offset, when the peak power density is too high, the hierarchical periodic NSRs and DSRs structures will be partly destroyed and formed in chaos.

*Nanomaterials* **2020**, *10*, 62

**Figure 11.** Schematic of the surface plasmon polariton (SPP)-modulated periodic coulomb explosion for the formation mechanism of hierarchical periodic NSRs and DSRs. (**a**) The picosecond laser irradiated on the stainless-steel surface. The dotted frame (**A**) indicated the atomic arrangement of the grains of 304 austenitic stainless steel. The dotted frame (**B**) shows the surface plasmon standing wave field induced at high energy density during laser irradiation. (**b**) The formation of DSRs under the material removal of coulomb explosion. (**c**) The NSRs induced by the periodically modulated by the surface plasmon standing wave.

#### **4. Conclusions**

Although many notable works have been undertaken over the years to investigate ultrafast laser-induced periodic surface subwavelength ripples (NSRs and DSRs), how to simultaneously construct large-scale hierarchical periodic NSRs and DSRs still remains a challenge. The preparation regulation of the picosecond laser induced hierarchical periodic NSRs and DSRs on stainless-steel surfaces is investigated, and a unified qualitative explanation based on a SPP-modulated periodic coulomb explosion is proposed in this work. The main conclusions obtained are as follows:


metallic surface makes the free electron concentration increase and a strong coulomb explosion chain occurs that forms the NSRs with orientation vertical to the laser polarization direction.


**Author Contributions:** All authors have read and agreed to the published version of the manuscript. Formal analysis, S.D., D.Z. and W.L.; Funding acquisition, W.X. and Y.C.; Investigation, S.D.; Methodology, D.Z., W.L. and Y.C.; Project administration, W.X. and Y.C.; Writing—original draft, S.D. and D.Z.; Writing—review & editing, Y.C.

**Funding:** This research was funded by National Natural Science Foundation of China (Grant numbers U1609209,11704285) and the Zhejiang Provincial Natural Science Foundation (Grant numbers LZ20E050003, LQ17F050001).

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

#### **References**


© 2019 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 (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Miniaturized GaAs Nanowire Laser with a Metal Grating Reflector**

**Wei Wei 1,2,\*, Xin Yan <sup>3</sup> and Xia Zhang <sup>3</sup>**


Received: 26 February 2020; Accepted: 30 March 2020; Published: 4 April 2020

**Abstract:** This work proposed a miniaturized nanowire laser with high end-facet reflection. The high end-facet reflection was realized by integrating an Ag grating between the nanowire and the substrate. Its propagation and reflection properties were calculated using the finite elements method. The simulation results show that the reflectivity can be as high as 77.6% for a nanowire diameter of 200 nm and a period of 20, which is nearly three times larger than that of the nanowire without a metal grating reflector. For an equal length of nanowire with/without the metal grating reflector, the corresponding threshold gain is approximately a quarter of that of the nanowire without the metal grating reflector. Owing to the high reflection, the length of the nanowire can be reduced to 0.9 μm for the period of 5, resulting in a genuine nanolaser, composed of nanowire, with three dimensions smaller than 1 μm (the diameter is 200 nm). The proposed nanowire laser with a lowered threshold and reduced dimensions would be of great significance in on-chip information systems and networks.

**Keywords:** nanowire; nanolaser; metal grating

#### **1. Introduction**

Nanolasers hold the key position in on-chip sensing, optical interconnection and computing systems [1–5]. With cylindrical geometry and strong two-dimensional confinement of electrons, holes and photons, the independent semiconductor nanowire is one of the ideal candidates for nanolasers [6–8]. To date, room-temperature lasing emission has been realized in ZnO, GaN, CdS and GaAs nanowires, covering the optical spectrum from ultra-violet to near-infrared [9–14]. Among them, GaAs nanowires, with a direct band gap and high electron mobility, are considered to be a prime candidate for advanced opto-electronic devices [15]. However, due to the nanowires' small size compared with their emission wavelength, ranging from 800 to 900 nm, the end facets of the nanowire display weak reflection at the near-infrared region, resulting in significant mirror losses [16]. Therefore, the light propagation in the nanowire has to be long enough to overcome a threshold loss induced by the weak facet reflectivities. The distinct index contrast reduces the diameter of the nanowires down to 200 nm, and even below the diffraction limit with the contribution of surface plasmons (collective electron oscillations) [17–19]. To keep the lasing emission from the nanowires at a relatively low threshold level, the nanowire's length becomes too long compared with its diameter, which may impede its potential applications in nanophotonics and high-density photonics integration.

In this paper, an Ag grating with a short period number is proposed to enhance the end-facet reflection and lower the mirror loss of GaAs nanowires. The grating is employed as a high-quality reflector and placed at only one end facet to shrink the length of the nanowires. The other end-facet reflection is provided by the Au cap. The Ag grating and Au cap compose the optical resonant cavity. In

that cavity, two mirrors of Ag grating and Au cap face each other, forming an optical resonator in which a light wave can be resonantly enhanced. To reveal the mechanism of the enhanced reflection by the short-period Ag grating, the finite elements method (FEM) is applied to a numerical simulation of the reflection and cavity properties. With the optimized structural parameters of the grating, the reflected spectrum can be located within the gain spectrum of the GaAs nanowires to generate an increase in feedback. Consequently, the lasing threshold will be lower than that without active feedback, and the nanowire's length can be shortened while maintaining the laser's power.

#### **2. Structure of GaAs Nanowire with Ag Grating**

The schematic diagram of the GaAs nanowire with the Ag grating is shown in Figure 1. On the silica substrate there is an Ag grating, the permittivity of which is described by the Drude-Lorentz model

$$\kappa(\omega) = 1 + \sum\_{k} \frac{\Delta \varepsilon\_k}{-\omega^2 - a\_k(i\omega) + b\_k} \tag{1}$$

where Δε*k*, *ak* and *bk* are constants that provide the best fit for silver, when compared with the optical constant data of silver given by Palik et al. [20]. The terms *ak* and *bk* denote the damping frequency of the electron gas and the effective electron collision frequency, respectively. The Drude-Lorentz model is an extended Drude model, incorporating additional Lorentz terms [21–23]. Both of the models are classic models which describe the transport properties of electrons in metals. Figure 1 illustrates that Λ is the grating period; the width and height of the metal grating are denoted by *Wg* and *Hg*, respectively. The duty cycle of the grating was fixed at 50% during the simulation. The GaAs nanowire is placed on the top of the grating. The part close to the dielectric interface is on the grating, to make the light propagated inside the nanowire interact with the metal grating. Meanwhile, the other part close to the Au cap is left suspended in the air. The Au cap on one top end of the nanowire is the Au particle, which is used as a catalyst during the growth of GaAs nanowires [14,24,25]. Its diameter is approximately equal to that of the nanowire. Due to the high reflection of the metal/dielectric interface, the Au cap is employed here as a high-quality reflector. Its reflectivity can be higher than 70%, depending on the nanowire's diameter [13]. The Au cap naturally decreases the threshold and the nanowire's length. The other end of the nanowire is cleaved, and the mirror is formed by the GaAs/air interface. The reflectivity of the dielectric interface for the fundamental mode is lower than 50%, and decreases with the shrinking nanowire diameter. It becomes less than 30% when the diameter is 200 nm. Therefore, only one end of the nanowire is located on the grating and the other end is left. Owing to the high modal confinement provided by the unique 1D geometry, the nanowire is employed both as the waveguide and gain medium. The Au cap and metal grating act as reflectors, forming the optical resonant cavity.

**Figure 1.** Schematic diagrams of the nanowire with the Ag grating reflector. 3D model (**a**), lateral view (**b**) and top view (**c**) of the proposed structure.

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

When the nanowire is placed on the Ag grating, the light wave will be reflected by the grating, forming the gain feedback, which is shown in Figure 2. The large index difference of the waveguide mode *HE11a* for the nanowire in the air and that on the grating tooth enables the reflection of the light wave by the grating. The reflected spectrum of the grating is shown in Figure 2c, where the period and period number are 140 nm and 20, which makes the spectrum within the gain spectrum of the GaAs nanowire. The reflected spectrum has a wide bandwidth of 64 nm. Owing to the high index contrast, the grating, with a short period number of 20, can provide a maximum reflectivity of 74.5%. As shown in Figure 2d, the profile of *H*z of the propagating mode is highly reflected by the Ag grating, and very little electromagnetic energy is transmitted through the nanowire.

**Figure 2.** Modal profiles of *HE11a* for the nanowire in the air (**a**) and on the grating tooth (**b**). (**c**) Reflected spectrum of the grating. (**d**) Profile of *H*z of the propagating mode. Numbers in (**a**) and (**b**) are modal effective indices. The pseudo-colors indicate the intensity of the magnetic field of *H*z.

The reflected spectrum, including bandwidth and peak, is dependent on the structural parameters of the grating. As depicted in Figure 3a, the grating height varies from 10 to 50 nm. The reflection is weakest for a grating height of 10 nm. It is significant to be note that due to the limitation of the classic Drude model and its extensions of the adopted Drude-Lorentz model at the order of ~10 nm, the simulation result values may not be very accurate [26]. The reflection curve of 10 nm here is only to demonstrate the varying trend as the grating height decreases. With the increasing height, the reflection becomes higher, and the bandwidth of the reflected spectrum becomes wider. However, reflection stays nearly similar when the height increases from 30 to 40 nm, and then becomes weaker at 50 nm. This can be attributed to the effective index contrast. The index contrast increases along with the height, resulting in higher reflection. However, when the grating height gets too large, the very high index contrast and the metal tooth are similar to a cliff or wall for the guided mode inside the nanowire, impeding the propagation and reflection of the mode. The period number is a direct factor in deciding the reflectivity of the grating. In Figure 3b, the reflection gets stronger with the increasing period number, from 10 to 30. When the period number increases from 25 to 30, the reflectivity increases by a very small amount. To be different from the dielectric grating with a small index contrast, the metal grating only needs a short period number to realize high reflection. The reflection capability of the grating gets saturated at a period number of 25. Furthermore, a long period number brings a long grating length, which also increases the nanowire's cavity length. This is contradictory to the purpose of the integration with the metal grating. Thus, the period number would be 20 or 25. In the following calculation, all the period numbers are assumed to be 20. The grating period Λ, or width, is crucial to the peak of the reflected spectrum. As depicted in Figure 3c, the reflection peak displays red-shift with the increasing Λ By optimizing the period Λ or width, the reflected spectrum of the grating can be adjusted within, or to cover, the gain spectrum of the gain medium. The wavelength of the lasing

emission from a GaAs nanowire most probably ranges from 850 to 880 nm [14]. Therefore, all of the structural parameters were selected to cover or partly cover that spectral region.

**Figure 3.** Reflected spectra of the grating for different grating heights (**a**), period numbers (**b**) and Λ (**c**). \* Due to the limitation of classic model of Drude-Lorentz at the order of ~10 nm, the simulation result values may not be very accurate. The results given here are only to show the varying trend of reflection intensity as the grating height decreases.

The photonic integration is going towards high density, requiring reduced dimensions of photonic components. As the nanowire diameter decreases to the limit of fundamental modes, the reflectivity decreases dramatically, together with the threshold gain. The metal grating reflector is more meaningful for nanowires with smaller diameters. The reflected spectra for nanowire diameters of 300 nm, 250 nm, 230 nm, and 200 nm are shown in Figure 4, where the other structural parameters of the grating height, duty cycle and period number are the same. The grating period or width are slightly tuned, to keep the spectra within the gain spectrum of the GaAs nanowire. The bandwidth and intensity of the reflection spectrum have negative relationships with the diameter, due to the index contrast increasing with the decreasing diameter. As the diameter decreases, the electromagnetic wave guided inside the nanowire has a more intense interaction with the metal grating tooth, resulting in a larger modal effective index, together with index contrast.

**Figure 4.** Reflected spectra for nanowire diameters of 300 nm (**a**), 250 nm (**b**), 230 nm (**c**) and 200 nm (**d**).

To compare the reflection between the Ag grating, end facet, and Au cap, functions of the Ag-grating reflectivity, end-facet reflectivity and Au-cap reflectivity on nanowire diameter are depicted in Figure 5a. The end-facet reflection is very weak and gets weaker for diameters of 200 nm and 220 nm. At a diameter of 200 nm, the end-facet reflectivity is below 30%. In contrast, for the Au-cap reflection, it is very strong even at a diameter of 200 nm. Its reflectivity can be 80% at larger diameters, and more than 65% at a diameter of 200 nm. Thus, the Au cap can provide excellent reflection for the propagated light wave with extremely small dimensions. This can be an additional advantage of the Au-catalyst growth method. For the reflection of the Ag grating, it is much stronger than the end-facet reflection. Its reflectivity is two times larger than its end-facet reflectivity. For small nanowire diameters below 260 nm, the reflectivity of Ag grating is even greater than Au-cap reflectivity. The introduction of the metal grating reflector is to compensate for the end-facet reflection, resulting in the reduced nanowire length or lowered threshold gain. The lasing threshold is the lowest excitation level, at which laser output is dominated by stimulated emission rather than spontaneous emission. The threshold gain *gth*, which describes the required gain per unit length for lasing, is defined as [27]

$$g\_{th} = \frac{1}{\Gamma\_{w\chi}} \left[ \alpha\_i + \frac{1}{L} \ln \left( \frac{1}{R} \right) \right] \tag{2}$$

where *R* denotes the geometric mean of the reflectivity of the end facets of the nanowire, and *L* is the length of the nanowire's optical resonant cavity. Γ*wg* is the modal confinement factor, which is an indicator of how well the mode overlaps with the gain medium, and is defined as the ratio between the modal gain and material gain in the active region [28–30]

$$\Gamma\_{w\chi} = \frac{\frac{n\_d}{2\eta\_0} \int\_{A\_d} d\rho \left| E(\rho) \right|^2}{\int\_{A\_d} d\rho \frac{1}{2} \text{Re}[E(\rho) \times H^\*(\rho)] \cdot 2} \tag{3}$$

where η<sup>0</sup> is the intrinsic impedance, *na* is the index of the active region, *Aa* is the cross section of the active region, *A* is the whole cross section ideally extending to infinity, and *E* and *H* are the complex electric and magnetic fields of the guided modes. The threshold gains of a nanowire laser with and without metal grating for diameters varying from 200 to 300 nm are shown in Figure 5b. Three lengths were chosen to demonstrate the threshold performance of the nanowire laser. As lasing emission is easily output from nanowires with lengths from 5–10 μm, lengths of 6 and 9 μm are typical parameters for a nanowire laser. A nanowire of 6 μm length without grating has a relatively high threshold gain, around 800 cm<sup>−</sup>1, and increases to about 1000 cm−<sup>1</sup> when the diameter decreases to 200 nm. This is not beneficial for lasing emission from nanowire and requires high-power pump. If the length is changed to 9 μm, the threshold gain becomes moderate, ranging from 600 to 800 cm−1, which is helpful for lasing emission. However, for nanowire with metal grating, threshold gains for lengths of 6 and 9 μm are both low. The threshold gain of nanowire with a length of 6 μm ranges from 300 to 400 cm<sup>−</sup>1. For nanowire with a length of 9 μm, threshold gain can go down to 200 to 250 cm<sup>−</sup>1. At this threshold level, the laser can be easily lased without a high-power pump. To shrink the nanowire's length, we make the length 3 μm, at which lasing emission requires a high-power pump. Its threshold gain ranges from 1600 to 2000 cm<sup>−</sup>1. With the metal grating, the threshold gain can go down to 600 to 800 cm−1, decreasing threshold gain by more than 2 times. At this threshold level, lasing is not hard to realize. Thus, the length of the nanowire laser can be shortened to 3 μm under moderate pump power. In high-density photonic integration, a nanolaser with three dimensions at nanoscale is preferred. Therefore, we make the length of the nanowire laser 900 nm by shortening the period number of the metal grating to 5. As shown in Figure 5c, the bandwidth becomes wider and the reflection becomes weaker than nanowire of 3 μm length. The maximum reflectivity decreases from 77.6% to 69.2%, and the corresponding threshold gain increases from 756 to 2978 cm−1. Lasing at a threshold gain of ~3000 cm−<sup>1</sup> requires a high-power pump. Although the threshold gain is not low, a nanowire laser can be shortened to within 1 micron and is promising to lase under a high-power pump. In future research, if some additional techniques, like surface plasmons, were added onto the nanowire with metal grating, the confinement factor would be increased by more than 1.5 times, lowering the threshold gain further [31,32].

**Figure 5.** (**a**) Reflected spectra of the Ag grating, end facet and Au cap for nanowire diameter vary from 200 to 300 nm. (**b**) Threshold gain of nanowire with and without Ag grating for nanowire diameters varying from 200 to 300 nm. (**c**) Reflected spectrum for a period number of 5. Pseudo-colors indicate the intensity of the magnetic field of *H*z.

#### **4. Conclusions**

In summary, we proposed a metal grating with a short period to provide high reflection for the light wave propagating inside the nanowire. The metal grating is placed between the silica substrate and the nanowire. To shorten the nanowire's length, the metal grating is only integrated with the end facet of the dielectric interface. The other end-facet reflection is provided by the Au cap, with a high reflectivity of around 70%. When the period number of the metal grating is set to 20, the grating can realize a maximum reflectivity of 81.8%. Moreover, a high reflectivity of 77.6% was realized for the nanowire diameter of 200 nm. The reflectivity is nearly three times larger than that without metal grating. Owing to the high reflection of the metal grating, the threshold gain of the nanowire laser can be decreased by more than 2.5 times. The length of the nanowire laser can be shortened to 3 μm under moderate pump power. With a high-power pump, the length of the nanowire laser could be shortened down to 900 nm, which is promising for the realization of lasing emission at a threshold gain of 2978 cm−1. Consequently, all of the three dimensions of the nanowire laser, especially the length, could be reduced below 1 micron. The proposed miniaturized nanowire laser with metal grating would be promising for use in on-chip sensing, optical interconnection and computing systems.

**Author Contributions:** Conceptualization, W.W.; methodology, W.W. and X.Y.; software, W.W.; writing—original draft preparation, W.W. and X.Y.; writing—review and editing, W.W. and X.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was funded by the National Natural Science Foundation of China (61905045, 61774021 and 61911530133), the Hong Kong Scholar Program (XJ2018052) and the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (IPOC2019ZT07).

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

#### **References**


© 2020 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 (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Lightning-Rod E**ff**ect of Plasmonic Field Enhancement on Hydrogen-Absorbing Transition Metals**

#### **Norihiko Fukuoka and Katsuaki Tanabe \***

Department of Chemical Engineering, Kyoto University, Kyoto 615-8510, Japan **\*** Correspondence: tanabe@cheme.kyoto-u.ac.jp

Received: 1 August 2019; Accepted: 27 August 2019; Published: 30 August 2019

**Abstract:** The plasmonic enhancement of electromagnetic field energy density at the sharp tips of nanoparticles or nanoscale surface roughnesses of hydrogen-absorbing transition metals, Pd, Ti, and Ni, is quantitatively investigated. A large degree of energy focusing is observed for these transition metals in the microwave region, even surpassing the enhancement for noble metals according to the conditions. Pd, for instance, exhibits peak field enhancement factors of 6000 and 2 <sup>×</sup> 10<sup>8</sup> in air for morphological aspect ratios of 10 and 100, respectively. Metal surfaces possibly contain such degrees of nano- or micro-scale native random roughnesses, and, therefore, the field enhancement effect may have been unknowingly produced in existing electrical and optical systems. In addition, for future devices under development, particularly in hydrogen-related applications, it is desirable to design and optimize the systems, including the choice of materials, structures, and operating conditions, by accounting for the plasmonic local energy enhancement effect around the metal surfaces.

**Keywords:** transition metal; surface plasmon; nanoparticle; nanophotonics; hydrogen storage; sensing; nuclear fusion; energy device

#### **1. Introduction**

Free electrons in metallic materials, particularly around metal surfaces or interfaces with dielectric media, exhibit a strong interaction with electromagnetic fields or light in the form of collective oscillation, named "surface plasmons" [1–3]. Surface-plasmon-induced electromagnetic field enhancement on metal surfaces [4–7] has been utilized for various applications, such as chemical/biomedical sensing [8–10], photodetectors [11–13], light-emitting diodes [14–16], nanolasers [17–19], solar cells [16,20–22], and optical cloaking [23–25]. Recently, we found through numerical analysis that a large degree of energy focusing, with enhancement factors over several hundred, is available for planar surfaces of hydrogen-absorbing transition metals, Pd, Ti, and Ni, in the microwave region, even surpassing the enhancement for noble metals [26]. We therein discussed the potential applications of the plasmonic field enhancement effect on hydrogen-absorbing transition metals, such as hydrogen storage [27–31], sensing [32–34], and nuclear fusion [35–38]. In contrast to the studied plasmonic field enhancement effect on planar metal surfaces, it is known that surfaces with sharp curvatures allow the electromagnetic field to concentrate further, called the "lightning-rod effect" [39–43]. In the present study, we numerically investigate the plasmonic field enhancement on sharp surfaces of hydrogen-absorbing transition metals, Pd, Ti, and Ni.

#### **2. Theory and Calculation Methods**

We calculate the field enhancement factors, which represent the intensity ratios for fields around the object (metals in this case) to those in the absence of the object, or the original incident fields, for prolate-spheroidal metal nanoparticles in air, H2, or vacuum, and H2O. We specifically calculate the field enhancement factors at the tips of the prolate-spheroidal metal nanoparticles, to represent sharp-curvature metal surfaces. These calculations, based on the classical electromagnetic field theory in the quasistatic limit [7,44], quantitatively show how much energy can be concentrated from the incident optical or electric power. The intensities of electromagnetic fields around subwavelength-size metal nanoparticles can be described by the formalism below in the quasistatic limit [44]. Consider a homogeneous, prolate spheroid with radii of the major and minor axes *a* and *b*, respectively, placed in a medium in which there exists a uniform static electric field <sup>→</sup> *E*<sup>0</sup> applied along the major axis of the spheroid, as schematically depicted in Figure 1. If the permittivities or dielectric constants of the spheroid and the medium are different, a charge will be induced on the surface of the spheroid. The initially uniform field will, therefore, be distorted by the introduction of the spheroid. Based on the calculation schemes described in earlier articles [7,42,44,45], in short, the electric field outside the

spheroid and at the tip of the prolate spheroid is given by

$$
\stackrel{\rightarrow}{E}\_{tlip} = \frac{\iota\_1(\lambda)}{\iota\_m(\lambda) + L\_1\{\iota\_1(\lambda) - \iota\_m(\lambda)\}} \stackrel{\rightarrow}{E}\_{0\prime} \tag{1}
$$

where ε<sup>1</sup> and ε*<sup>m</sup>* are the frequency-dependent complex permittivities or dielectric functions of the spheroid and the surrounding medium, respectively. *L*<sup>1</sup> is the geometrical factor for the major axis of the prolate spheroid, calculated as

$$L\_1 = \frac{1 - \mathfrak{c}^2}{\mathfrak{c}^2} \left( -1 + \frac{1}{2\mathfrak{c}} \ln \frac{1 + \mathfrak{c}}{1 - \mathfrak{c}} \right), \tag{2}$$

where *e* is the eccentricity of the particle shape:

$$e = \sqrt{1 - \frac{b^2}{a^2}}.\tag{3}$$

The field enhancement factor is then calculated as

$$\eta \equiv \frac{\left| \stackrel{\rightarrow}{E\_{t\phi}} \right|^2}{\left| \stackrel{\rightarrow}{E\_{\phi}} \right|^2} = \left| \frac{\iota\_1(\lambda)}{\iota\_m(\lambda) + L\_1 \{ \iota\_1(\lambda) - \iota\_m(\lambda) \}} \right|^2. \tag{4}$$

Note that this field enhancement factor is defined as the ratio of field intensities and not field magnitudes. Incidentally, for the spherical case, which provides *L*<sup>1</sup> = 1/3, η reduces to the equation of the field enhancement factor derived in Reference [7]. The empirical complex dielectric functions of metals and of the surroundings on the frequencies listed in References [7] and [26] are used for the computations in this study. We assume that ε = 1 and ε" = 0 throughout the entire frequencies for air, H2, and vacuum. The electrostatic calculations carried out in this study are valid for particle sizes in the range of 10–100 nm, for which the phase retardation is negligible throughout the particle, the field enhancement will be largest, and metal nanoparticles and nanoscale roughnesses will, therefore, become most applicable, as discussed in the Results and Discussion section.

**Figure 1.** Schematic bird's-eye view of the system considered in this study for the calculations of field enhancement factors.

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

Firstly, as a reference, we present in Figure 2 the calculated electromagnetic field enhancement factors for the simple, spherical nanoparticle case, which corresponds to the spheroid's aspect ratio, *a*/*b*, of one. The peaks seen in these spectra are associated with the resonance or surface mode, characterized by internal electric fields with no radial nodes. A local energy enhancement around 10 times is decently observed for the hydrogen-absorbing transition metals, Pd, Ni, and Ti, in this spherical-shape case. Incidentally, the results in Figure 2 for shorter wavelengths are consistent with those reported in Reference [7]. It should be noted that the field enhancement factors, for our calculations, are independent of the particle size under the quasistatic approximation, and are valid for particle diameters around the range of 10–100 nm [7]. Figure 3 shows the field enhancement factors for spheroidal metal nanoparticles with an aspect ratio of three. It is observed that even for such a relatively small aspect ratio or morphological surface sharpness, enhancement factors over 100 are attainable for Pd, Ni, and Ti for a wide range of frequencies, through visible to infrared. Such nanoparticles or nanoscale surface roughness thus concentrate electromagnetic or optical energy in their vicinity like antennae. The artifact discontinuities for the curves for Cu and Ti around 1 and 4 μm, respectively, in Figures 3 and 4 are incidentally because of the discontinuities in the source empirical data of the dielectric functions. Remarkably, electromagnetic field enhancement factors of several thousand are observed for Pd, Ni, and Ti for the aspect ratio of 10 (Figure 4). The resonant peak enhancement factors for Au, Ag, and Cu are observed to be even larger, on the order of 105. Among the whole metal elements, Al and the noble metals Ag, Au, and Cu are known to exhibit distinctively higher field enhancement factors than other metals because of their high electrical conductivities [7,46]. Therefore, the combination of such noble-metal spheroidal nanoparticles and hydrogen-absorbed transition metals, available, for instance, by coating bulk metal surfaces by colloidal metal nanoparticles, may be another strategy for applications to harvest the photonic or electromagnetic energy focusing effect. Strikingly, as observed in Figure 5, the field enhancement factor of Pd for the sharp particle or surface morphology case of an aspect ratio of 100 reaches the order of 10<sup>8</sup> in the infrared region, even exceeding those for the noble metals. This consequence is consistent with the results reported in Reference [26] that the plasmonic field enhancement factors of the hydrogen-absorbing transition metals become higher than those of noble metals for planar metal surfaces. Incidentally, the peak or resonant wavelength of Ti may unfortunately locate outside of the range of frequencies handled in this study. Figures 6 and 7 summarize the dependence of the peak field enhancement factors and wavelengths, respectively, on the aspect ratio. It is observed that the electromagnetic field enhancement factors dramatically increase with the aspect ratio, namely, with the sharpness of the metal surfaces. As the sharpness increases, the resonant peak wavelength red-shifts. Large-aspect-ratio metal particles or high-curvature edges of surface irregularities exhibit high polarizabilities and, thus, large dipole moments, particularly at the resonance, to produce strong local field enhancement in the vicinity of such edges [44,47]. To discuss the electromagnetic similarity between isolated metal spheroidal particles and rough surfaces, it is worth mentioning that the detailed numerical calculation results reported in Reference [40], where rough metal surfaces were modeled as prolate hemispheroids protruding from a grounded flat plane, are quantitatively similar to our results in Figures 6 and 7, for the peak field enhancement factors and wavelengths.

The large field-enhancement effect on the hydrogen-absorbing transition metals, Pd, Ni, and Ti, observed in the series of calculations in this study can be used for various hydrogen-energy applications. As discussed in Reference [26], potential applications include hydrogen storage, sensing [48,49], laser fusion [46], and condensed-matter fusion. In addition, for the reported experiments so far, for instance, in the condensed-matter nuclear fusion field, it is highly possible that the deuterium-absorbed Pd, Ni, and Ti surfaces contained certain degrees of nano- or micro-scale native random roughnesses [39,40,50,51] corresponding to such morphological aspect ratios as those studied in this article. Therefore, some of the experimental material systems may have unknowingly benefited from the plasmonic field enhancement effect. The electrostatic calculation results shown in this paper are valid for particle sizes smaller than the

fields' wavelengths at which the phase retardation is negligible throughout the particle object. In addition, the dielectric functions of materials used for our calculations are empirical values for bulk materials, whose validity is debatable when the particle sizes become smaller than 10 nm, because of the electron mean free path limitation or scattering of conduction electrons off particle surfaces [44,47,52,53]. The calculation results for optical wavelengths under the quasistatic approximation are, therefore, valid for metal particles with diameters in the range of 10–100 nm. Metal particles with sizes smaller and larger than these limits both exhibit broader plasmon resonances and smaller field enhancements, because of the surface scattering losses and the radiative losses or electrodynamic damping, respectively [47,52,53]. Therefore, the choice of particle sizes, 10–100 nm, for our calculations is most suitable for plasmon-enhanced electromagnetic and optical applications, because of the largest field enhancements. This size aspect should, therefore, also be accounted for in the optimized design of the material structures in potential applications. In addition, surface plasmons located in between multiple metallic objects with nanoscale separation distances, or so-called "gap plasmons" [54–56], would also provide large field enhancements on the conditions. The gap-plasmon effect for hydrogen-energy applications is important partially because gap plasmons are also commonly observed in real structures such as rough metal surfaces, and will be discussed in future work.

**Figure 2.** Calculated electromagnetic field enhancement factors around spherical nanoparticles of Au, Ag, Cu, Pd, Ti, and Ni in (**left**) air/H2/vacuum and (**right**) H2O. The insets are the clarified plots for Ag.

μ μ **Figure 3.** Calculated electromagnetic field enhancement factors at the tips of spheroidal nanoparticles of Au, Ag, Cu, Pd, Ti, and Ni with an aspect ratio of 3 in (**left**) air/H2/vacuum and (**right**) H2O. The insets are the clarified plots for Au, Ag, and Cu.

μ μ

μ μ

μ

μ μ

μ μ

**Figure 4.** Calculated electromagnetic field enhancement factors at the tips of spheroidal nanoparticles of Au, Ag, Cu, Pd, Ti, and Ni with an aspect ratio of 10 in (**left**) air/H2/vacuum and (**right**) H2O. The insets are the clarified plots for Au, Ag, and Cu.

**Figure 5.** Calculated electromagnetic field enhancement factors at the tips of spheroidal nanoparticles of Au, Ag, Cu, Pd, Ti, and Ni with an aspect ratio of 100 in (**left**) air/H2/vacuum and (**right**) H2O. The inset of (**left**) is the clarified plot for Pd.

**Figure 6.** Dependence of the peak electromagnetic field enhancement factors at the tips of spheroidal nanoparticles of Au, Ag, Cu, Pd, Ti, and Ni on the aspect ratio in (**left**) air/H2/vacuum and (**right**) H2O.

μ

**Figure 7.** Dependence of the peak wavelength of the electromagnetic field enhancement factors at the tips of spheroidal nanoparticles of Au, Ag, Cu, Pd, Ti, and Ni on the aspect ratio in (**left**) air/H2/vacuum and (**right**) H2O.

#### **4. Conclusions**

In this work, we numerically investigated the lightning-rod effect of plasmonic field enhancement on hydrogen-absorbing transition metals. A large degree of energy focusing was observed for these transition metals in the microwave region, even surpassing the enhancement for noble metals according to the conditions. Pd, for instance, exhibited peak field enhancement factors of 6000 and 2 <sup>×</sup> <sup>10</sup><sup>8</sup> in air for morphological aspect ratios of 10 and 100, respectively. The metal surfaces possibly contained such degrees of nano- or micro-scale native random roughnesses, and, therefore, the field enhancement effect may have been unknowingly produced in existing electrical and optical systems. Active utilization of the plasmonic local energy enhancement effect around the metal surfaces by proper material and structure choices, such as the introduction of sharp nanoparticles or sharply roughened surfaces, can potentially improve hydrogen-related device performance.

**Author Contributions:** K.T. conceived the idea for the study. N.F. carried out the calculations and analyzed the data. Both authors contributed to discussion of the results and composed the manuscript.

**Funding:** This research was funded by the Thermal & Electric Energy Technology Foundation and the Research Foundation for Opto-Science and Technology.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **References**


© 2019 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 (http://creativecommons.org/licenses/by/4.0/).
