Perturbation Theory of Nonlinear Electromagnetic Wave Propagation

Abstract

A perturbation method, previously employed to treat nonlinear boundary-value problems involving partial differential equations, is used to study nonlinear electromagnetic wave propagation. The problems considered are I. electromagnetic wave propagation in a waveguide containing a nonlinear isotropic medium; II. electromagnetic oscillations in a cavity containing a nonlinear dispersive anisotropic medium; III. propagation and interaction of electromagnetic waves in a nonlinear dispersive anisotropic medium; IV. reflection of an electromagnetic wave from a nonlinear dispersive uniaxial medium. The method avoids secular terms, which arise in some perturbation treatments. The results show how the wave number, propagation velocity, and angle of refraction of a wave depend upon its amplitude.