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

Multiple-scale coupled-mode theory for second-harmonic generation in one-dimensional periodic structures

Costantino De Angelis, Gianfranco Nalesso, Daniele Modotto, Michele Midrio, Andrea Locatelli, and J. Stewart Aitchison
J. Opt. Soc. Am. B 20(9) 1853-1865 (2003)

Perturbation analysis of plane-wave transmission through a dielectric slab with Kerr-type nonlinearity

Kiarash Zamani Aghaie and Mahmoud Shahabadi
Opt. Express 13(17) 6587-6596 (2005)

Stable all-optical limiting in nonlinear periodic structures. I. Analysis

Dmitry Pelinovsky, Jason Sears, Lukasz Brzozowski, and Edward H. Sargent
J. Opt. Soc. Am. B 19(1) 43-53 (2002)

Fourier modal method for the analysis of second-harmonic generation in two-dimensionally periodic structures containing anisotropic materials

Benfeng Bai and Jari Turunen
J. Opt. Soc. Am. B 24(5) 1105-1112 (2007)

Variational analysis and angular bistability in layered nonlinear Kerr media with phase conjugation

T. A. Laine and A. T. Friberg
J. Opt. Soc. Am. B 17(6) 977-984 (2000)