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

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.