Self-trapping and periodic modulation of beam propagation in semiconductor photorefractive medium

Abstract

We have deduced a two-level form of beam evolution in photonic lattices of semiconductor photorefractive medium and its classical canonical form of the two-level equation. We analytically calculate the fixed points of the classical canonical aligns, analyze its stability and calculate the critical value of topology changes. According to the classical canonical form of the two-level equation, we make space phase diagram, further analyze the self-trapping of beam propagation in semiconductor photorefractive medium and find two kinds of self-trapping: 1) Both the population difference and the relative phase in energy levels oscillate near an equilibrium point in the phase space. 2) The population difference in energy levels oscillate near an equilibrium point while the relative phase increases monotonously. From the three aspects of high frequency, low frequency, and intermediate frequency, we investigate how an external periodic field influences the self-trapping and find that the external high frequency periodic field may dramatically modulate the critical points at which the transition to self-trapping occurs. It makes the self-trapping occur with small nonlinear effect when the beam propagates in semiconductor photorefractive medium.