On Characteristic Eigenvalues of Complex Media in Surface Integral Formulations

Abstract

Abstract-Although surface integral equations (SIEs) have been extensively used in solving electromagnetic problems of penetrable objects, there are still open issues relating to their application to the Theory of Characteristic Modes. This work demonstrates that when an SIE is used to solve for the characteristic modes (CMs) of a dielectric or magnetic object, the resulting eigenvalues are unrelated to the reactive power of the object, unlike the eigenvalues of perfect electric conductors. However, it is proposed that the classical eigenvalues, which provide useful physical insights, can be extracted from the SIE CM solution using Poynting's theorem. Large discrepancies between the SIE CM eigenvalues and the proposed eigenvalues, as well as eigenvalue-derived characteristic quantities, are highlighted using a numerical example. The modal resonances as predicted by the proposed eigenvalues closely match those obtained for natural resonance modes.

Theory of characteristic modes for lossy structures: Formulation and interpretation of eigenvalues

“…It is often argued that the eigenvalues of this type of CM formulation give the ratio of stored and radiated power of a mode. 6,30 As a generalization of this result for lossy structures, we presume that the eigenvalues have the following interpretation:…”

“…It is often argued that the eigenvalues of this type of CM formulation give the ratio of stored and radiated power of a mode . As a generalization of this result for lossy structures, we presume that the eigenvalues have the following interpretation: where is extinction power, radiated plus dissipated power, and reactive power (stored in the near field) is used instead of the stored one.…”

Restoring characteristic eigenvalues as reactive powers for simple and complex media in surface integral formulations

“…Although this inconsistency was explicitly shown to be a problem for VIE CM solutions, the first SIE TCM paper [8] does not examine if a similar problem exists in SIE solutions. However, as detailed in [6], SIE eigenvalues are in fact different in meaning from both traditional eigenvalues for PEC objects as well as VIE eigenvalues. Moreover, it was proven that SIE eigenvalue is inconsistent with the definition of reactive power from Poynting's theorem, and as such it does not provide any direct insight into an object's resonant characteristics.…”

“…In [6], a post-processing method of correctly determining the characteristic eigenvalues of penetrable objects using a full SIE solution which consists of both electric and magnetic currents was proposed. This solution utilizes the method presented in [3] to remove the SIE internal resonances from the CM solution.…”

“…In particular, we first overview the problem that the characteristic eigenvalues from SIE formulations are not equal to the modal reactive powers. Then, we overview a recent proposal which address this problem [6]. This proposed method recalculates the characteristic eigenvalues based on the modal reactive power definition from Poynting's theorem.…”