Nonlinear optical solitary waves in a photonic band gap

Abstract

It is suggested that solitary wave solutions exist in the gap region of photonic band gap materials with a Kerr nonlinearity. Using a variational trial function we estimate the amplitude, size scale, and the nature of phase modulation of these nonlinear waves. In two dimensions, we predict the occurrence of a variety of finite energy solitary waves associated with the different symmetry points of the crystalline Brillouin zone. Solutions which preserve the symmetry of the crystal exist for both positive and negative Kerr coefficient whereas solutions which break the symmetry occur only for positive nonlinearity. These states are relevant to the bistable switching properties of photonic band gap materials.