Abstract

Multiple-scale analysis is employed for the study of nonlinear wave propagation in periodic layered media. In a first step, wave propagation in each individual layer is modeled by a corresponding equivalent nonlinear transmission line. The multiple-scale analysis is then employed to establish a system of nonlinear equations for the amplitudes of the forward and backward waves in the transmission lines of the model mentioned. This system of nonlinear equations is solved with the aid of a continuation technique for derivation of transmission characteristics of the periodic structure. To study optical bistability, a parameter-switching algorithm is utilized for obtaining the solutions of the system including both stable and unstable ones. For the sake of verification, we have also utilized a nonlinear finite-difference time-domain (NFDTD) method to analyze the wave propagation in the aforementioned structure. While there is an acceptable agreement between the bistability results obtained using our method and the NFDTD, there is a considerable difference between our results and the ones derived using the conventional coupled-mode theory.

© 2007 Optical Society of America

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