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

The Theory of Characteristic Modes (TCM) has recently been shown to be beneficial in solving a wide variety of complex electromagnetic problems. However, there are still open issues in using TCM to analyze objects which consist of simple or complex media. Either a volume integral equation (VIE) or a surface integral equation (SIE) is required to solve for the characteristic modes of these objects. Herein, we overview the important issue that the characteristic eigenvalues obtained from SIE formulations are not related to the modal reactive power, unlike the classical TCM definition. A recently proposed solution that restores the modal reactive power interpretation of characteristic eigenvalues is described. A numerical example is provided to demonstrate the differences between the SIE eigenvalues and the restored eigenvalues.