Complex Frequency Eigenvalue Problem for Circular Dielectric Rod Partially Covered with Graphene

We consider the two-dimensional electromagnetic complex-frequency eigenvalue problem for the natural modes of circular dielectric rod with partial graphene cover. The surface impedance of graphene is characterized by the quantum-theory Kubo equations. To reduce the problem to a well-conditioned determinantal equation, we use the method of analytical regularization based on explicit inversion of the static part of the problem. To find the roots of truncated determinantal equation, we apply the residual inverse iteration method. This analysis reveals the presence of the plasmon modes of the curved strip of graphene and the modes of the circular dielectric rod, perturbed by the presence of the strip. If the rod radius is measured in micrometers, the real parts of all these eigenfrequencies are comparable, however, the plasmon mode Q-factors are higher.