Response of Elliptical Scatterer Due to Perfect Magnetic Material

TL;DR

This work addresses electromagnetic scattering from an infinitely long elliptic cylinder bounded by a Perfect Magnetic Conductor. It develops a fully analytic separation-of-variables approach in elliptic coordinates using radial and angular Mathieu functions to obtain TM and TE field representations and to satisfy PMC boundary conditions. The study derives far-field expressions and the bistatic echo width, showing that TE polarization yields stronger, more directional scattering with a backscatter peak at $180^{\circ}$, while TM shows maxima at $120^{\circ}$ and $240^{\circ}$ and exhibits nonlinear growth with size. These results enhance understanding of EM interactions with complex geometries and high-permeability materials, and provide benchmarks for solver validation across optics, acoustics, meteorology, and radar applications, with potential practical implications for PMC-based devices and analyses.

Abstract

The effects on the bistatic echo width of an elliptical cylinder due to a perfect magnetic material are reported in this article. The configuration is analyzed using the separation of variables method and Mathieu functions. In this approach, the structural geometry is illuminated by an electromagnetic field. Radial and angular Mathieu functions have been used in the formulation. Notably, the maxima of the scattered elliptic transfer electric mode ($θ= 180^{\circ}$) are much higher than those of the scattered transfer magnetic mode, comparable to terms $θ= 120^{\circ}$ and $θ= 240^{\circ}$, respectively. It can be observed that an increase in the in-plane radial component leads to the linearity principle for the transfer electric mode, while non-linear behavior is investigated for the elliptic transfer magnetic mode. Therefore, the unidirectional bistatic echo width is subject to non-directional behavior. These analogous results may have applications in the fields of optics, meteorology, acoustics, radio astronomy, collision physics, and other disciplines where wave scattering phenomena play a crucial role. Furthermore, the findings of this study contribute to the fundamental understanding of electromagnetic interactions with complex geometries and materials

Figures (8)

• Figure 1: Configuration for TM polarization
• Figure 2: Configuration for TE polarization
• Figure 3: Validation and comparison results
• Figure 4: Validation and comparison results
• Figure 5: Backscattering width variation