Abstract
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.
©2002 Optical Society of America
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