Unified Theory of Characteristic Modes

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, offering good control of convergence, and significantly simplifying modal tracking. Algebraic properties of the transition matrix are utilized to show that characteristic mode decomposition of lossy objects fails to deliver orthogonal far fields. All aforementioned properties and steps are demonstrated on several numerical examples for both surface- and volume-based method-of-moment formulations.