Integral Equation Formulations for Characteristic Modes of Dielectric and Magnetic Bodies

Five types of surface integral equation (IE) formulations are presented to determine the characteristic modes of dielectric and magnetic bodies. It should be noted that these five formulations are derived in a unified manner. Instead of directly using the IE coefficient matrices of scattering problems, this paper presents the formulations in a more natural and rigorous way. The IE formulations result in the generalized real symmetric eigenvalue equations for the characteristic modes. It is found that the eigenvalues of the first four formulations indicate the negative or positive imaginary part of the complex power of the characteristic modes, which are zero at resonance. The first two IE formulations result in two new generalized eigenvalue equations, while the last three IE formulations lead to the same generalized eigenvalue equations as in the references. Moreover, the first two formulations can be immune from spurious modes from which the third and fourth formulations suffer.