Modulational instability in liquid crystals with competing nonlinearities

Abstract

We analytically investigate modulational instability (MI) of plane waves in liquid crystals with competing nonlinearities. We find that the competition between thermal nonlinearity and reorientational nonlinearity leads to unique stability of the plane waves. We also find that both the nonlocality of the orientational effect (${\sigma _1}$σ1) and the opt-thermal nonlinearity ($\gamma $γ) tend to suppress the MI by decreasing both the gain bandwidth and the maximum gain. Particularly, due to the competing nonlinearities, we find that the MI is closely related to the critical power, which is only related to the opt-thermal nonlinearity coefficient ($\gamma $γ) but irrelevant to the profile of the nonlocal response function when ${\sigma_1} = {\sigma_2}$σ1=σ2. Interestingly, the plane wave is always stable, providing its power is larger than the critical power. Our analytical results are confirmed by numerical simulations. These results may provide insight to the theoretical and experimental studies of the solitons in liquid crystals with competing nonlinearities.