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

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. apply this on disordered assemblies LiNbO$_3$ and BaTiO$_3$ grains identify the influence birefringence random quasi-phase-matching process. show that monodispersed assemblies, relaxes grain-size dependence SHG efficiency. In polydispersed sufficiently large grains, we find introduces efficiency enhancement up 54% compared isotropic reference crystals, which is grain size independent. This increases linearly size, if birefringent can be phase matched. These two different scaling behaviours are used Kurtz Perry's powder-technique phase-matchability material. example ADP technique cannot applied when get smaller than coherence length, because becomes material specific.