Resonances in a circular dielectric cavity

We study resonance distributions in a circular dielectric cavity. It is shown that the decay-rate distribution has a peak structure and the details of the peak are consistent with the classical survival probability time distribution. We also investigate the behavior of the complex resonance positions at the small opening limit. At the large $n$ limit, the real part of complex resonance positions approaches the solutions with different $m$ of Dirichlet problem with a scale $n^{-2}$ and the imaginary part goes zero as $n^{-2m}$ for TM and $n^{-2(m+1)}$ for TE polarization, where $m$ is the order of the resonance.