LAUSR

The optical resonance problem is an eigenproblem with an exponential-growing boundary condition imposed at infinity. This inconvenient boundary condition is caused by the openness of dielectric systems, and it is explained as the effect of retardation. Following our previous work [Jiang and Xiang, Phys. Rev. A 102, 053704 (2020)2469-992610.1103/PhysRevA.102.053704] where a perfectly-matched-layer method is developed for transverse-magnetic modes, we extend the method in this paper to transverse-electric modes and apply it to study mode symmetries. The method is implemented by introducing an extra layer to absorb outgoing waves at the far-field region, based on which we derive a damping eigenequation. A finite-element-based numerical approach is developed to compute the eigenstates of the damping eigenproblem. Our method is validated by application to the circular cavity and comparison with exact analytical solutions of whispering-gallery modes. We apply the method to the elliptic cavity to study the even- and odd-symmetric optical eigenstates. We also apply the method to trace the evolution of a pair of degenerate eigenstates with cavity shapes smoothly deformed from circles to squares.