Generation of a reflected wave in an inhomogeneous medium

TL;DR

This paper uses a generalized WKB method to analyze electric field distribution in inhomogeneous media, revealing the nature of reflected waves and their phase characteristics, with implications for dielectric waveguides and particle reflection.

Contribution

It introduces a novel application of the generalized WKB method to distinguish wave components in inhomogeneous media, clarifying the nature of reflected waves.

Findings

The second wave component is not a nonuniform left-traveling wave.

Phase distribution of the reflected component increases similarly to the right-traveling wave.

Results are applicable to dielectric waveguide development and particle reflection analysis.

Abstract

In this work we present the results of calculation of the electric field distribution in the inhomogeneous media based on the generalized WKB method. In this approach the field is represented as the sum of two components, one of which is associated with the right-travelling WKB solution and the other with the left-travelling WKB solution. It has been shown that the second component is not a left-travelling nonuniform wave. Calculation results showed that the phase distribution of this component has an increasing character, similar to the phase distribution of the right-travelling wave component. Obtained results can be useful during the development of dielectric accelerating waveguides. The obtained results may also indicate the location where a semiclassical particle with energy greater than the barrier height can reflect from a smooth potential barrier.