Wave-Chaotic Optical Resonators and Lasers

Deformed cylindrical and spherical dielectric optical resonators and lasers are analyzed from the perspective of non-linear dynamics and quantum chaos theory. In the short-wavelength limit such resonators behave like billiard systems with non-zero escape probability due to refraction. A ray model is introduced to predict the resonance lifetimes and emission patterns from such a cavity. A universal wavelength-independent broadening is predicted and found for large deformations of the cavity. However there are significant wave-chaotic corrections to the model which arise from chaos-assisted tunneling and dynamical localization effects. Highly directional emission from lasers based on these resonators is predicted from chaotic "whispering gallery" modes for index of refraction less than two. The detailed nature of the emission pattern can be understood from the nature of the phase-space flow in the billiard, and a dramatic variation of this pattern with index of refraction is found due to an effect we term "dynamical eclipsing". Semiconductor lasers of this type also show highly directional emission and high output power but from different modes associated with periodic orbits, both stable and unstable. A semiclassical approach to these modes is briefly reviewed. These asymmetric resonant cavities (ARCs) show promise as components in future integrated optical devices, providing perhaps the first application of quantum chaos theory.