Surface integral equation based characteristic mode formulation for dielectric resonators

The characteristic mode (CM) theory for analyzing the resonant behaviors of arbitrarily shaped dielectric bodies is further discussed based on the well-known PMCHW formulation. A careful investigation into the CM formulation developed in the 1970s finds that it fails to provide modal solutions with clear underlying physics for the dielectric resonators. To fix this problem, we propose a new generalized eigenvalue equation involving only the electric current on the equivalent surface. Moreover, a generalized eigenvalue equation involving only the magnetic current is also proposed for the CM analysis of the dielectric resonators. It is actually a dual CM formulation of the previous one. The two generalized eigenvalue equations are independent of each other and yield exactly the same CMs. The CMs can accurately describe the resonant behavior and modal fields of a dielectric resonator. Numerical results are presented to validate the proposed CM formulations.