Generalized Perturbation Theory for Weakly Deformed Microdisk Cavities

Abstract

AbstractA perturbation treatment is derived for weakly deformed microdisk cavities in a more generalized scenario, where both resonant and non‐resonant surface scattering processes coexist. It is proved that the originally developed nondegenerate and degenerate perturbation theories are simplified forms of the generalized theory in special cases. The validity of the perturbation theory is verified by the comparison with a full numerical method for two generic classes of deformed microdisk cavities: locally notched microdisks and smooth globally deformed microdisks. The simulation of these two classes of microdisk cavities using the perturbation theory unveils the distinct characteristics of optical modes from the ones predicted by the original nondegenerate and degenerate perturbation theories in the generalized scenario. Furthermore, a hybrid‐scattering‐based exceptional point is introduced for deformed microdisk cavities in the generalized scenario by using the perturbation theory. The exceptional point exhibits higher nonorthogonality over the originally proposed resonant‐scattering‐based exceptional point, as non‐resonant scattering processes provide an additional degree of freedom. Full numerical simulations demonstrate that the exceptional point is more robust against random surface roughness at cavity boundary than the resonant‐scattering‐based exceptional point.