TE-wave propagation in a graded waveguide structure

TL;DR

This paper derives exact analytical formulas for TE-wave propagation, reflection, and transmission in graded hollow waveguides with arbitrary cross sections, enabling precise modeling of smooth dielectric transitions.

Contribution

It introduces a general analytical approach for TE-wave analysis in graded waveguides with arbitrary shapes, simplifying calculations and improving modeling accuracy.

Findings

Exact formulas for electric field components in graded waveguides.

Analytical reflection and transmission coefficients for arbitrary cross sections.

Asymptotic agreement with thin dielectric layer models.

Abstract

We investigate TE-wave propagation in a hollow waveguide with a graded dielectric layer, described using a hyperbolic tangent function. General formulae for the electric field components of the TE-waves, applicable to hollow waveguides with arbitrary cross sectional shapes, are presented. We illustrate the exact analytical results for the electric field components in the special case of a rectangular waveguide. Furthermore, we derive exact analytical results for the reflection and transmission coefficients valid for waveguides of arbitrary cross sectional shapes. Finally, we show that the obtained reflection and transmission coefficients are in exact asymptotic agreement with those obtained for a very thin homogeneous dielectric layer using mode-matching and cascading. The proposed method is tractable since it gives analytical results that are directly applicable without the need of mode-matching, and it has the ability to model realistic, smooth transitions.