Unified Theory of Characteristic Modes: Part I -- Fundamentals

TL;DR

This paper introduces a unified theoretical framework for characteristic mode decomposition applicable to all method-of-moment formulations, enabling broader application and improved numerical stability in electromagnetic scattering analysis.

Contribution

It develops a unified theory linking impedance and transition matrices, extending characteristic mode analysis to various frequency-domain solvers and improving computational robustness.

Findings

Unified characteristic mode formulation derived

Applicable to all method-of-moment and transition matrix methods

Demonstrated improved numerical stability and convergence

Abstract

A unification of characteristic mode decomposition for all method-of-moment formulations of field integral equations describing free-space scattering is derived. The work is based on an algebraic link between impedance and transition matrices, the latter of which was used in early definitions of characteristic modes and is uniquely defined for all scattering scenarios. This also makes it possible to extend the known application domain of characteristic mode decomposition to any other frequency-domain solver capable of generating transition matrices, such as finite difference or finite element methods. The formulation of characteristic modes using a transition matrix allows for the decomposition of induced currents and scattered fields from arbitrarily shaped objects, providing high numerical dynamics and increased stability, removing the issue of spurious modes, and offering good control of convergence. This first part of a two-part paper introduces the entire theory, extensively discusses its properties and offers its basic numerical validation.