Comprehensive Model for Randomly Phase-Matched Frequency Conversion in Zinc-Blende Polycrystals and Experimental Results for ZnSe

Abstract

Second-order nonlinear interactions in disordered materials based on random phase matching suggest intriguing opportunities for extremely broadband frequency conversion. Here we present a quantitative realistic model for random phase matching in zinc-blende polycrystals (ZnSe, ZnS, GaAs, GaP, etc.) that takes into account effects of random crystal orientation, grain size fluctuations, and includes polarization analysis of the generated output. Our simulations are based on rigorous transformation of the second-order susceptibility tensor in randomly rotated coordinates − to account for random orientation of crystalline domains, and demonstrate a good agreement with our experimental data for ZnSe using a nanosecond λ = 4.7 µm source − in terms of variations of the strength and polarizations of the output fields. Also, it is revealed that random phase matching is most suitable for ultrafast (sub-100-fs) interactions with focused beams, e.g. second harmonic generation, sum and difference frequency generation, and optical parametric oscillation, that typically require short (< 1 mm) interaction lengths, where disordered polycrystals can be on par, in terms of conversion yield, with ideal quasi phase matched crystals.

Effects of Grain Morphology on Nonlinear Conversion Efficiency of Random Quasi-Phase Matching in Polycrystalline Materials

“…The second-order susceptibility tensor of ZnSe, denoted as matrix dijk with six identical nonzero components under Kleinman symmetry, is modulated by the random grain orientations. Assuming the input electric field oscillates along the x axis and the polarizations of the SHG fields can be along both the x and y axis, the resulting effective nonlinear coefficients in an arbitrary grain are given by the following two different forms [2], [12]:…”

“…Earlier methods considered the fluctuation of field phase and effective nonlinear coefficient (deff) in different grains, but the grain morphology was supposed to follow simple Gaussian distribution and the deff was simply averaged [1], [7]- [10], instead of modeling the actual situation of realistic polycrystalline samples. Some basic conclusions such as the peak efficiency should fulfill the condition that the average grain size is close to the coherence length (Lcoh), the output signal grows linearly with the sample length, and RQPM possesses a broad bandwidth as well, have been widely accepted [1], [11], [12]. In recent years, novel modeling approaches that are much more sophisticated have been proposed, providing precise methods to simulate RQPM process, especially the cases with thin samples and ultrashort pulses [12], [13].…”

“…Some basic conclusions such as the peak efficiency should fulfill the condition that the average grain size is close to the coherence length (Lcoh), the output signal grows linearly with the sample length, and RQPM possesses a broad bandwidth as well, have been widely accepted [1], [11], [12]. In recent years, novel modeling approaches that are much more sophisticated have been proposed, providing precise methods to simulate RQPM process, especially the cases with thin samples and ultrashort pulses [12], [13]. Different from PM and QPM with regular structures, the randomness and complexity of the grain morphology in polycrystals plays an important role in RQPM, which is also the key point in modeling.…”

“…Figure2demonstrates several polycrystalline ZnSe models directly generated by "Neper" based on the grain growth module. There are two key factors to characterize polycrystals, the grain size and sphericity, which are both better fitted by the lognormal function[12],[17] rather than the Gaussian function[1],[2],[7], and a complete description requires both the mean value (μ) and standard deviation (σ). The size (diameter) of a grain polyhedron is defined as the diameter of a sphere of equivalent volume, and the sphericity is the ratio of the surface area of a sphere to that of the polyhedron with equivalent volume.…”

Fourier Transform Analysis on Random Quasi-Phase-Matched Nonlinear Optical Interactions

“…Early theories assumed the grain size to follow Gaussian distribution with averaged deff, from which some basic rules for RQPM like the optimal grain size and the conversion efficiency versus interaction length, were concluded [1,7]. Comprehensive models were also proposed for harmonic and supercontinuum generation pumped by ultrashort pulses [8,9]. Recently, professional ceramic modeling tools were introduced to create realistic samples, and the reliable statistical analyzation by full-space scanned integrations allowed us to see RQPM more clearly through the second harmonic generation (SHG) process [10].…”