A new method for solving nonhermitian perturbation theory for the microdisc resonators with phi-periodic refractive index

The radiation loss in the whispering gallery resonators causes the eigenvalues of the Maxwell equations with the corresponding boundary conditions complex. The corresponding operators are nonhermitian and for these operators the standard perturbation techniques have some difficulties. In this paper by employing the Floquet theorem a new technique for the φ periodic perturbations is developed. The method is applied to obtain the change of resonance frequencies and losses of φ -perturbed microresonators with cylindrical symmetry. The results are compatible with that are obtained by the Volume Current Method.