Modulation instability induced by quadratic nonlinearity in optically anisotropic medium

In anisotropic crystals, the inherent breakdown of circular symmetry due to anisotropy significantly impacts optical phenomena. This study theoretically investigates the effects of anisotropic diffraction on modulation instability (MI) spectra and subsequent optical filament formation. We model an anisotropic medium with quadratic nonlinearity, exhibiting noncritical phase-matched second-harmonic generation, using coupled nonlinear Schrödinger equations. Through linear stability analysis and numerical simulations, we examine MI in quasi-isotropic and anisotropic quadratic nonlinear media. Our results reveal that anisotropic diffraction induces asymmetry in the MI gain spectrum, leading to the formation of elliptical optical filaments for both fundamental and second harmonics. Notably, this asymmetry in the MI gain spectrum facilitates the generation of multiple filaments in high-gain MI region.