Modeling of Random Quasi-Phase-Matching in Birefringent Disordered Media

TL;DR

This paper develops a vectorial model to simulate second-harmonic generation in birefringent disordered media, revealing how birefringence influences efficiency and phase matching, with implications for material characterization techniques.

Contribution

The paper introduces a novel vectorial model for SHG in birefringent disordered media and analyzes how birefringence affects phase matching and efficiency scaling.

Findings

Birefringence relaxes grain-size dependence of SHG efficiency in monodispersed assemblies.

Birefringent grains can enhance SHG efficiency by up to 54% in polydispersed assemblies.

SHG scaling with grain size becomes material-specific when grains are smaller than the coherence length.

Abstract

We provide a vectorial model to simulate second-harmonic generation (SHG) in birefringent, transparent media with an arbitrary configuration of non-linear ($\chi^{(2)}$) crystalline grains. We apply this model on disordered assemblies of LiNbO$_3$ and BaTiO$_3$ grains to identify the influence of the birefringence on the random quasi-phase-matching process. We show that in monodispersed assemblies, the birefringence relaxes the grain-size dependence of the SHG efficiency. In polydispersed assemblies with sufficiently large grains, we find that the birefringence introduces an SHG efficiency enhancement of up to 54% compared to isotropic reference crystals, which is grain size independent. This enhancement increases linearly with the grain size, if the birefringent grains can be phase matched. These two different scaling behaviours are used in Kurtz and Perry's powder-technique to identify the phase-matchability of a material. We show on the example of LiNbO$_3$ and ADP that this technique cannot be applied when the grains get smaller than the coherence length, because the SHG scaling with the grain size becomes material specific.