Generalization of conformal mapping to scattering of electromagnetic waves from surfaces: An example of a triangle

TL;DR

This paper extends conformal mapping techniques to analyze electromagnetic scattering from arbitrarily shaped metallic surfaces, exemplified by an equilateral triangle, revealing insights into resonance, vorticity, and boundary effects.

Contribution

It introduces a conformal mapping approach for electromagnetic scattering analysis of arbitrary shapes, providing a simpler alternative to traditional numerical methods.

Findings

Good agreement with traditional numerical results

Insights into vorticity and eddy currents

Clarification of electric field divergence at boundaries

Abstract

We discuss a way to exploit the conformal mapping to study the response of a finite metallic element of arbitrary shape to an external electromagnetic field at finite frequencies. This provides a simple way to study different physics issues and provides new insights that include the issue of vorticity and eddy current, and the nature of the divergent electric field at the boundaries and at corners. The nature of the resonance can be directly addressed and clarified. We study an example of an equilateral triangle and found good agreement with results obtained with traditional numerical techniques.