On the Representation of Electromagnetic Fields in Discontinuously Filled Closed Waveguides by Means of Continuous Potentials

Abstract: A closed waveguide of a constant cross section S with perfectly conducting walls is considered. It is assumed that its filling is described by function ε and µ invariable along the waveguide axis and piecewise continuous over the waveguide cross section. The aim of the paper is to show that, in such a system, it is possible to make a change of variables that makes it possible to work only with continuous functions. Instead of discontinuous transverse components of the electromagnetic field E, it is proposed to use potentials u e and v e related to the field as (Formula Presented.) and, instead of discontinuous transverse components of the magnetic field H, to use the potentials u h and v h related to the field as (Formula Presented.). It is proven that any field in the waveguide admits the representation in this form if the potentials u e ,u h are elements of the Sobolev space (Formula Presented.) and v e ,v h are elements of the space W 2 1 (S). © 2019, Pleiades Publishing, Ltd.