Ray dynamics and wave chaos in circular-side polygonal microcavities

Abstract

We systematically study mode characteristics in circular-side polygonal microcavities (CSPMs), particularly in these cavities with chaotic ray dynamics, in order to gain insights into the wave chaos in the CSPMs. The circular sides could improve the light confinement of the CSPMs as concave mirrors, in that regular islands are formed around the stable fixed points in the Poincar\'e surface of sections (SOS). However, the fixed points become unstable under some specific deformations, and global chaos with quasistable ``star islands'' appears around these fixed points in the Poincar\'e SOS accordingly. The phenomenon can be well explained by the ray dynamic analysis under the second-order approximation, and the results show that the high-order terms play an important role in the motions of light rays and destroy the regular islands in the phase space leading to chaotic ray dynamics. The destruction of regular islands results in degradation of mode quality factors and dispersed mode field distributions according to the finite-element method simulation of the confined modes. Furthermore, an unusual variation of mode quality factor is observed by varying the refractive index of the outside media for the CSPM with chaotic ray dynamics.