volume | PIER Journals

2005-08-23

Multiple-Scale Analysis of Plane Wave Refraction at a Dielectric Slab with Kerr-Type Nonlinearity

Kiarash Aghaie,

Dr. Kiarash Aghaie

Department of Electrical and Computer Engineering

University of Tehran

Iran

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Mahmoud Shahabadi

Dr. Mahmoud Shahabadi

School of Electrical and Computer Engineering

University of Tehran

Iran

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Progress In Electromagnetics Research, Vol. 56, 81-92, 2006

doi:10.2528/PIER05051701

Abstract

Multiple-scale analysis is employed for the analysis of plane wave refraction at a nonlinear slab. It will be demonstrated that the perturbation method will lead to a nonuniformly valid approximation to the solution of the nonlinear wave equation. To construct a uniformly valid approximation, we will exploit multiplescale analysis. Using this method, we will derive the zerothorder approximation to the solution of the nonlinear wave equation analytically. This approximate solution clearly shows the effects of self-phase modulation (SPM) and cross-phase modulation (XPM) on plane wave refraction at the nonlinear slab. In fact, the obtained zeroth-order approximation is very accurate and there is not any need for derivation of higher-order approximations. As will be shown, the proposed method can be generalized to the rigorous study of nonlinear wave propagation in one-dimensional photonic band-gap structures.

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Kiarash Aghaie, and Mahmoud Shahabadi, "Multiple-Scale Analysis of Plane Wave Refraction at a Dielectric Slab with Kerr-Type Nonlinearity," Progress In Electromagnetics Research, Vol. 56, 81-92, 2006.
doi:10.2528/PIER05051701

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