Characteristic modes for nonconducting bodies having mutually orthogonal symmetry planes

Abstract

We consider the characteristic modes of lossy or loss‐free dielectric and / or magnetic bodies symmetric with respect to mutually orthogonal symmetry planes. For such cases, we show that the moment method can be applied to the eigenvalue equation defining the modes, transforming it into a matrix eigenvalue equation involving matrices partitioned into diagonal blocks.

Some numerical aspects of characteristic mode decomposition

“…Complicating the process of modal tracking are degeneracies and crossing avoidances (associated with modal coupling) [47]- [50] near frequencies where multiple eigenvalues approach the same value. Though a system's symmetry [39], [51], [52] may be employed to analytically distinguish degeneracies and crossing avoidances [40] and enable smooth tracking of complex modal systems [41], the sensitivity of these phenomena to vanishingly small symmetry-destroying perturbations raises questions regarding the physical relevance of tracking modes across frequency. Regardless of physical interpretation, one special case stands out among results related to symmetry-based tracking: modal eigenvalues of completely asymmetric (C 1 symmetry) structures are infinitely unlikely to The von Neumann-Wigner theorem [38] gives rise to several important results related to modal tracking and symmetry.…”