New look of the mysteries of the characteristic modes

The theory of characteristic modes is being widely used for designing antennas (Y. Chang, and R. F. Harrington, 1977, Antennas and Propagation, IEEE Transactions on, 25(6), 789–795). Regarding to the design of dielectric objects there are still unknown aspects in the interpretation of their solutions. Previous works about characteristic Modes are published for conducting bodies and dielectric Bodies, but a difficulty to understand the solution using the surface integral equations based on Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) formulation appears. It is also found that analyzing a dielectric body using different formulations, different results are obtained as the PMCHWT formulation provides more modes than those obtained using the Volume Integral Equation (VIE). What is observed is that the characteristic eigenvalues obtained with VIE are contained in the PMCHWT solution, resulting in the latter more solutions than in VIE. The observed difference is that PMCHWT provides two eigenvalues for each mode.