On characteristic eigenvalues of complex media in surface integral formulations

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.