Complex variational axial mode matching method for single-mode and overmoded dielectric resonators

The generalization of the axial mode matching method to calculate electromagnetic properties is here considered for single-mode as well as overmoded (whispering gallery) dielectric resonators having geometric cylindrical symmetry but non-diagonal dielectric permittivity and magnetic permeability. In particular, a compact matricial form of the complex-valued variational constraint governing this configuration is calculated. The reliability of this method is prved numerically by the matching of the modes of the fields in two different round media sharing the same transverse surface, the second one by finding the field in one region to match the contiguous layer once this has known field. The reliability of this method is proved numerically by the matching of the Ehrenfest-Boltzmann theorem predictions extended also in the non-perturbative range, and by a filling factor matching test. An experimental measurement is also compared with the results. This method can be applied in new ferromagnetic semiconductors physics that should behave gyroelectromagnetically in the opportune experimental conditions.