Unified Theory of Characteristic Modes—Part I: Fundamentals

A unification of characteristic mode decomposition for all method-of-moment (MoM) formulations of the field integral equations describing free-space scattering is derived. The work is based on an algebraic link between the impedance and transition matrices, the latter of which was used in early definitions of characteristic modes and is uniquely defined for all the 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 the 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 article introduces the entire theory, extensively discusses its properties, and offers its basic numerical validation.