Transmission anomalies in Kerr media photonic crystal circuits: Intrinsic localized modes

Abstract

A study is made of the exact solutions of a system of nonlinear difference equations that model the propagation of electromagnetic radiation in photonic crystal waveguides and networks of interconnecting photonic crystal waveguides (photonic crystal circuits) containing Kerr nonlinear dielectric media. The transmission properties of a waveguide formed of linear dielectric material and containing a barrier of Kerr nonlinear material are determined and shown to exhibit anomalies similar to those due to gap solitons in layered Kerr nonlinear optical media. Similar discussions for a nonlinear segment bisected by a waveguide composed of linear dielectric media are given. The transmission properties of a junction formed from Kerr nonlinear media connecting three semi-infinite waveguides formed from linear dielectric materials are also determined. The transmission of electromagnetic energy through the junction is found to exhibit anomalies similar to those due to gap solitons in layered Kerr nonlinear media. The transmission anomalies in the systems we study are shown to arise from intrinsic localized modes that are found in the Kerr nonlinear media of the system. Intrinsic localized modes are solitonlike modes that can only exist in nonlinear systems. Previous transmission studies presented by us have concentrated on systems formed of linear media, and no previous transmission studies have been presented by us on systems supporting intrinsic localized modes. The central focus of this paper and new results presented are the study of resonant transmission anomalies in photonic crystal circuits containing Kerr media and the identification of some of these resonances with intrinsic localized modes that exist is the Kerr media.