Parametric representation of wave propagation in nonuniform media (both in transmission and stop bands)

TL;DR

This paper introduces an analytical parametric method to describe wave propagation in nonuniform media, covering both transmission and stop bands, and establishes a link to Floquet solutions.

Contribution

It extends the parametric antiresonance theory to include Bloch wave behavior in transmission bands, providing exact solutions and their relation to Floquet theory.

Findings

Derived a wide class of exact solutions for wave propagation.

Established correspondence between parametric solutions and Floquet solutions.

Enhanced understanding of wave behavior in nonuniform media.

Abstract

An analytical approach based on the parametric representation of the wave propagation in nonuniform media was considered. In addition to the previously developed theory of parametric antiresonance describing the field attenuation in stop bands, in the present paper the behaviour of the Bloch wave in a transmission band was investigated. A wide class of exact solutions was found and the correspondence to the quasi-periodic Floquet solutions was shown.