Diffraction of a mode close to its cut-off by a transversal screen in a planar waveguide

TL;DR

This paper analyzes how a waveguide mode near its cut-off frequency diffracts when encountering a thin Neumann screen, deriving formulas for reflection and transmission coefficients using advanced mathematical methods.

Contribution

It introduces a new approach to compute diffraction coefficients for modes close to cut-off in planar waveguides, including asymptotics for small gaps.

Findings

Derived explicit formulas for reflection and transmission coefficients.

Established asymptotics of edge Green's function directivities.

Validated the asymptotic formulas against known results.

Abstract

The problem of diffraction of a waveguide mode by a thin Neumann screen is considered. The incident mode is assumed to have frequency close to the cut-off. The problem is reduced to a propagation problem on a branched surface and then is considered in the parabolic approximation. Using the embedding formula approach, the reflection and transmission coefficients are expressed through the directivities of the edge Green's function of the propagation problem. The asymptotics of the directivities of the edge Green's functions are constructed for the case of small gaps between the screen and the walls of the waveguide. As the result, the reflection and transmission coefficients are found. The validity of known asymptotics of these coefficients is studied.