Analysis of a cylindrical dielectric waveguide with three regions by use of an invariant mode-definition parameter

Abstract

Boundary conditions at a dielectric interface are expressed in terms of electrodynamic vector and scalar potentials that are expressed in terms of two-dimensional scalar solutions to the wave equation. Possible field configurations are expressed in terms of linear combinations of the scalar solutions. Their behavior at a dielectric interface and within a region of constant permittivity is investigated, and a parameter that is used to define propagation modes in cylindrical dielectric waveguides is shown to have the same value in regions with different permittivities. Scalar expressions that include this parameter are used to calculate exact expressions for fields and propagation constants in a cylindrical dielectric waveguide with three coaxial regions. The characteristics of propagation modes in these waveguides are discussed.