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

We provide a vectorial model to simulate second-harmonic generation (SHG) in birefringent, transpar-ent media with an arbitrary configuration of nonlinear (χ (2)) crystalline domains. We apply this model ondisordered assemblies of LiNbO3 and BaTiO3 to identify the influence of the birefringence on the ran-dom quasi-phase-matching process. We show that in monodispersed assemblies, the birefringence relaxesthe domain size dependence of the SHG efficiency. In polydispersed assemblies with sufficiently largedomains, we find that the birefringence introduces a SHG efficiency enhancement of up to 54% comparedto isotropic reference crystals. This enhancement is domain size independent in non-phase-matchablematerials, while it increases linearly with the domain size if the domains can be phase matched. Thesetwo different scaling behaviors are used in Kurtz and Perry’s (KP) powder technique to identify the phasematchability of a material. We show on the example of LiNbO3 and ammonium dihydrogen phosphatethat the KP technique cannot be applied to domains smaller than the coherence length, because then the