Modeling of Random Quasi-Phase-Matching in Birefringent Disordered Media
Jolanda S. Müller, Andrea Morandi, Rachel Grange, Romolo Savo
Abstract
We provide a vectorial model to simulate second-harmonic generation (SHG) in birefringent, transparent media with an arbitrary configuration of nonlinear (${\ensuremath{\chi}}^{(2)}$) crystalline domains. We apply this model on disordered assemblies of ${\mathrm{Li}\mathrm{Nb}\mathrm{O}}_{3}$ and ${\mathrm{Ba}\mathrm{Ti}\mathrm{O}}_{3}$ to identify the influence of the birefringence on the random quasi-phase-matching process. We show that in monodispersed assemblies, the birefringence relaxes the domain size dependence of the SHG efficiency. In polydispersed assemblies with sufficiently large domains, we find that the birefringence introduces a SHG efficiency enhancement of up to 54% compared to isotropic reference crystals. This enhancement is domain size independent in non-phase-matchable materials, while it increases linearly with the domain size if the domains can be phase matched. These two different scaling behaviors are used in Kurtz and Perry's (KP) powder technique to identify the phase matchability of a material. We show on the example of ${\mathrm{Li}\mathrm{Nb}\mathrm{O}}_{3}$ and ammonium dihydrogen phosphate that the KP technique cannot be applied to domains smaller than the coherence length, because then the SHG scaling with the domain size becomes material specific.