Second-Harmonic Generation in Aggregates of Lithium Niobate Particles Formed upon Suspension Freezing

Abstract

This paper demonstrates a significant increase in the efficiency of second-harmonic generation in a suspension of lithium niobate (LiNbO₃) particles during freezing at nano and picosecond pum pulse durations. The amplification is caused by the formation of close-packed structures during the solidification process. The energy dependences of the second-harmonic generation, the angular distributions of the scattering intensity, conversion coefficients and the scattering regime in a suspension and in other lithium niobate particle-based samples are studied. This effect can be used for phase transition sensing in a medium, visualization of the particle organization process in ice-templating, and significantly increasing the efficiency of other nonlinear effects in particle matter.

1. Introduction

The study of the second-harmonic generation (SHG) features in various nanostructures is very relevant for various fields of nanophotonics [1]. In particular, harmonic nanoparticles (HNP) from oxides with a non-centrosymmetric structure with a high second-order susceptibility are widely used for applications in bioimaging [2,3,4], holography [5], multiphoton spectroscopy [6,7,8]. The use of HNP makes it possible to avoid the need to fulfill the phase-matching condition, in contrast to the case of SHG in a bulk crystal.

LiNbO₃ nanocrystals are the most efficient in SHG generation, having taken into account the predominantly higher non-linear coefficients of LiNbO₃ (d₃₃ = 34.4 pm/V) and are one of the most widely used nonlinear optical materials for various applications in the field of photonics. The SHG intensity will be maximal for the wavelength where the particle size is the closest to the corresponding calculated coherence length [9,10].

The conversion efficiency and the directional pattern of the SHG process can be controlled by exciting Mie resonances in systems based on nano and submicron particles [11].

The use of ordered structures, such as photonic crystals, makes it possible to obtain quasi-phase-matching conditions and, given the high density of photonic states at the edge of the band gap, can be used for efficient generation of harmonics [12].

If the SHG process is investigated in a randomly inhomogeneous medium, then the presence of multiple scattering in such a medium can significantly enhance the signal of the second harmonic. In disordered media, light is trapped for a long time, and random resonators can be formed which leads to high SHG intensities [13,14]. This mechanism underlies random laser generation, based on various nonlinear phenomena and has already found plenty of practical applications [15,16,17,18].

An important parameter that determines the scattering regime during light propagation in a disordered medium is the scattering mean free path of photons l_s. When l_s decreases compared to the excitation wavelength, a lasing effect may occur at lower threshold values. Such a situation takes place, in particular, in the case of particle agglomeration, which is used to develop sensors for substances that trigger the process [18].

During freezing of a colloidal suspension, the particles are displaced from the growing ice and the subsequent increase in the concentration of particles in the areas of the liquid in front of the freezing interface. This process leads to the formation of close-packed and even ordered structures, and it underlies ice templating [19,20,21,22,23]. Thus, under optical pumping of a frozen suspension, particle densification leads to a decrease in l_s parameter compared to liquid suspension.

In this study, the SHG in suspension of lithium niobate (LN) particles after its freezing due to the displacement of particles and their agglomeration in the process of solidification is demonstrated.

2. Materials and Methods

Samples in the form of a powder, an aqueous suspension, and a thin layer of particles deposited on a glass substrate were used in the current study. Suspension of LN particles (Figure 1 left) was obtained by laser ablation method in water with second harmonic of Nd:YAG laser (λ = 532 nm, τ = 11 ns, E = 0.1 J). The suspension was repeatedly applied to a glass substrate (Figure 1 right) with subsequent drying as a model of a layer of particles formed when the suspension freezes. Additionally, a powder of LN particles was obtained by mechanical grinding of a bulk crystal.

3. Results and Discussion

To excite the second harmonic in the samples, we used two pumping sources: Q-switched Nd:YAG laser (λ = 1064 nm, τ = 11 ns, E = 0.4 J, frequency 10 Hz) and Nd:YAG mode-locked laser (λ = 1064 nm, τ = 30 ps E = 50 mJ, frequency 10 Hz). A portable spectrometer (Ocean Optics) with spectral resolution 1 nm was used for SHG spectra registration.

At a certain concentration of LN particles in the suspension (~10⁸ m⁻³), for each duration of the pump pulse, no SHG signal was observed in the spectrum of transmitted radiation. Then, the suspension was placed on a cold pipeline at liquid nitrogen temperature, and after freezing, a component corresponding to the SHG appeared in the spectrum (Figure 2). A further decrease in temperature did not lead to a change in the intensity of this component.

As shown in [20,21,22,23], during the formation of the crystal structure, the particles accumulate on the surface of the solid front, associated with its displacement during the growth of the solid phase. The mechanism of particle layer migration depends on freezing front speed, initial volume fraction of particles and other parameters, but it always leads to compaction of the particles in local areas of the sample. Decrease in the photon mean free path in densely packed layers of particles compared to its value for the liquid suspension contributes to a sharp increase in the efficiency of the SHG process under optical pumping.

Figure 3 shows the dependences of the intensity of the second harmonic on the pump energy for frozen suspension at nanosecond pump-pulse duration. As is known, second-harmonic output intensity $I_{2\omega }=A\left(d_{eff}{L}^2\right)I_{\omega }{}^2$, where L is the sample’s thickness, A is a proportionality constant, $d_{eff}$—effective SHG coefficient. The experimentally obtained dependence was almost quadratic, with an index of 2.19. Similar dependence was observed for a layer of particles on a substrate and for a powder, at nano- and pica-second pumping durations, which indicates the influence of multiple scattering process on the enhancement caused by the increased trapping of fundamental frequency photons inside the turbid media. At a higher particle concentration, with picosecond pumping, SHG signal was registered, and the dependence of its intensity on the pump energy was also almost quadratic, but with a lower index 1.8. In this case, the influence of the complex absorption and strong scattering inside the particles is not compensated by strong scattering from them.

To characterize the scattering regime in the disordered media, coherent backscattering technique was used. The angular dependence of the scattered light intensity was registered to obtain the photon mean free path, which gives the information about the disordered media properties [24,25,26]. The typical scheme [24] was used for CBS measurement, and the results are shown in Figure 4a. The FWHM of the cone ω ≈ λ/2πℓ, where λ is the light wavelength, and ℓ is the transport mean free path of light in the medium. The transport mean free path of LN powder, measured in this way, was ℓ ≅ 28 μm, and corresponding scattering mean free path was 15 μm.

To demonstrate the difference in light scattering in a suspension and a dense layer of particles, the dependences of the transmission on the inverse thickness of the sample were measured (Figure 4b). For this, a number of quartz cuvettes of various thicknesses and LN powder were used. From the theory of light propagation in a scattering medium, the dependence of transmission on inverse thickness is linear for the classical diffusion case. For the case when the radiation wavelength is comparable to the free path in the medium (λ~ ℓ), photon localization is possible, and the dependence of the transmission on the inverse thickness becomes quadratic or exponential [27]. As can be seen in Figure 4b, the suspension corresponds to a linear dependence for classical diffusion, while for the powder, the dependence is quadratic, which indicates the presence of localization transition in the medium. From linear dependency parameter ℓ could be obtained. Thus, for suspension ℓ~1.5 mm, it is two orders of magnitude higher than the value for powder.

Figure 5 shows the angular distribution for a liquid suspension, a thin layer of particles on a glass substrate (thickness ~10 μm), and a powder (thickness 2 mm) at picosecond pumping. The radiation in the suspension is predominantly directed toward the pump. In the case of a thin layer of particles, the directionality disappears, and scattering also occurs in the opposite direction. As the layer thickness increases, the scattering ratio increases in favor of the backward direction, which corresponds to theoretical calculations for the stationary diffusion model of SHG in multiple scattering media [28]. For the powder, the angular dependence of the radiation intensity at the fundamental wavelength is also shown. The efficiencies of conversion into second-harmonic radiation for a liquid suspension, a thin layer of particles, and a powder were 10⁻⁴ %, 10⁻³ % and 0.1%, respectively.

4. Conclusions

As was shown, the generation of the second harmonic accompanies the phase transition of the liquid component of the suspension. Thus, by incorporating of HNP into an optically transparent substance, the process of amplification by multiple scattering can be used to study various phase transitions or as sensors for such transitions in a medium. The method can also be used to study the processes of particle organization in ice-templating.

SHG signal enhancement is affected both by an increase in the number of particles interacting with radiation with an increase in their concentration, and by the processes of photon trapping due to multiple scattering and a significant decrease in the photon mean free path value. Thus, freezing of liquid suspensions can significantly increase the efficiency of other nonlinear effects in particle matter, such as Raman scattering, higher harmonic generation, and luminescence.