Multistability and Switching in Nonlinear Layered Optical and Electronic Media

Abstract

Photonic crystals that possess a Photonic Band Gap (PBG) are systems with very intersting physical properties and, in addition, are very important in applications. As a result of numerous efforts [1, 2, 3, 4, 5, 6] both in the experimental and theoretical direction it is now well established that PBG systems can be realized in practice. Possible applications include resonance cavities, perfect refractive mirrors, antennas and electromagnetic wave filters with broad frequency range from ultraviolet to microwave. Most PBG studies so far have addressed almost exclusively PGB structures where nonlinearity in the dielectric constant of the constituting matertial is negligible.[7] One reason for this is that in the presence of nonlinearity the superposition principle does not hold any more, rendering the calculations more difficult and also turning familar concepts such as that of bands and gaps essentially meaningless. In the present paper we present recen-t results obtained through a simple periodic model concerning nonlinear effects in one dimensional PBG crystals and other nonlinear periodic lattice systems.[8, 9] The nonlinear Kronig-Penney (KP) model that we use shows that in the electromagentic case of wave propagation in one dimension occurrence of shifts in the linear stop gaps as a result of nonlinearity, the onset of bistability as well as switching properties.[10]