Electromagnetic field near the common edge of a perfectly conducting wedge and a resistive half-plane

TL;DR

This paper analyzes the electromagnetic field behavior near the edge where a resistive half-plane meets a perfectly conducting wedge, revealing conditions for logarithmic versus power-law field components and validating findings through waveguide mode calculations.

Contribution

It identifies specific geometric conditions under which logarithmic terms appear in the field expansion and demonstrates the applicability of the Meixner method for general cases.

Findings

Logarithmic functions appear only at specific angles between the resistive plane and wedge sides.

Main field components are predominantly power-law unless at particular angles.

Calculated waveguide mode wave numbers support the theoretical field distribution laws.

Abstract

The behavior of the electromagnetic field near a common edge of a resistive half-plane and a perfectly conducting wedge is investigated. The possible appearance besides power terms also of logarithmic functions in the field expansions at specific angles between a resistive plane and the sides of the wedge is indicated. It is shown that in the main terms of the electric or magnetic field components perpendicular to the edge, logarithmic functions appear only in two particular cases: when a half-plane forms a straight angle with one of the sides of the conducting wedge, or when the external angle of the conducting wedge is a right one. Otherwise, the main terms of all components have a purely power character and can be determined by the Meixner method. To confirm the efficiency of accounting for the found field distribution law, transversal wave numbers of the dominant mode of a rectangular waveguide with a resistive film in the diagonal plane is calculated.