Scattering-Based Characteristic Mode Theory for Structures in Arbitrary Background: Computation, Benchmarks, and Applications

Abstract

This paper presents a novel approach for computing substructure characteristic modes. This method leverages electromagnetic scattering matrices and spherical wave expansion to directly decompose electromagnetic fields. Unlike conventional methods that rely on the impedance matrix generated by the method of moments (MoM), our technique simplifies the problem into a small-scale ordinary eigenvalue problem, improving numerical dynamics and computational efficiency. We have developed analytical substructure characteristic mode solutions for a scenario involving two spheres, which can serve as benchmarks for evaluating other numerical solvers. A key advantage of our method is its independence from specific MoM frameworks, allowing for the use of various numerical methods. This flexibility paves the way for substructure characteristic mode decomposition to become a universal frequency-domain technique.

Figures (14)

• Figure 1: Configuration of the scattering matrices in \ref{['eq16']}. To solve for $\mathbf{S}_b$, the key structure must be set to free space (i.e., removed).
• Figure 2: Schematic of dual-sphere scattering. $\vec{r}_1$ and $\vec{r}_2$ are their centers.
• Figure 3: Modal significance, where the line labeled $\mathbf{Z}$ is obtained by impedance matrix-based method; the line labeled $\mathbf{S(Z)}$ is obtained using \ref{['eq11']}, \ref{['eq12']} and \ref{['eq20']}; the line labeled "Ana." is obtained by the analytical methods. (a) involves two PEC spheres, (b) involves two dielectric spheres with one being lossy, and (c) involves one PEC sphere and one layered sphere.
• Figure 4: Characteristic values of BCMs for benchmark case Sec. \ref{['benchcase1']}.
• Figure 5: Characteristic far-field patterns for the dominant mode of benchmark case Sec. \ref{['benchcase2']} at $k2R=1$. (a) impedance matrix based method, (b) scattering-based method, (c) analytic method.