A Gaussian-optical Approach to Stable Periodic Orbit Resonances of   Partially Chaotic Dielectric Micro-cavities
  The quasi-bound modes localized on stable periodic ray orbits of dielectric micro-cavities are constructed in the short-wavelength limit using the parabolic equation method. These modes are shown to coexist with irregularly spaced "chaotic" modes for the generic case. The wavevector quantization rule for the quasi-bound modes is derived and given a simple physical interpretation in terms of Fresnel reflection; quasi-bound modes are explictly constructed and compared to numerical results. The effect of discrete symmetries of the resonator is analyzed and shown to give rise to quasi-degenerate multiplets; the average splitting of these multiplets is calculated by methods from quantum chaos theory. 
H. E. Tureci, H. G. L. Schwefel, E. E. Narimanov and A. Douglas Stone