Wave propagation in nonlinear photonic band-gap materials

We study theoretically the propagation of electromagnetic waves through periodic structures consistent of layered materials with an intensity-dependent dielectric constant. We find the transmission properties to be strongly modulated by both frequency and intensity in the presence of nonlinearity. The transmission diagram in the frequency versus amplitude plane exhibits distinctive features depending upon whether the Kerr coefficient is positive or negative. These features, though complicated, can be understood through the analysis of stable periodic orbits of the corresponding nonlinear mapping. These systems exhibit bistability and multistability most strongly near the upper band edges and between the basins of stable periodic orbits. Resonance transmissions via soliton formation are analyzed through a simple mechanical analogy. We also discuss the switching threshold and the feasibility of making a switch utilizing such a structure.