Perturbation analysis of axially nonuniform electromagnetic structures using nonlinear phase progression.

Abstract

A perturbation technique is developed to deal with axial, as well as transverse, perturbations of an electromagnetic propagating structure which is otherwise axially uniform. The method, an adaptation and extension of time-dependent perturbation theory of quantum mechanics, uses a nonlinear phase progression term in the axial propagating factor of the fields to accommodate and readily calculate, without secular terms, corrections to the progressive phase delay along the perturbed structure. The technique admits inhomogeneities and anisotropy and does not depend upon quasi-static or quasi-optic assumptions. It is particularly useful for axially dependent perturbations which give rise to a phase shift, or to radiation, or to any other effect of interest which is strongly dependent on the phase progression of the wave. The method is first illustrated by an analysis of simple axial loading of a waveguide, and then by a calculation of the radiation from a surface wave structure with a ridged dielectric binding medium. Finally, the casting of Maxwell's equations for general situations into a form appropriate for the application of this perturbation analysis is discussed.