Chaotic Light: a Theory of Asymmetric Resonant Cavities Jens U. Nöckel and A. Douglas Stone

Spherical and cylindrical dielectric cavities support high Q whispering gallery modes due to total internal reflection of the trapped light. When such a cavity is deformed smoothly the ray dynamics of these modes becomes chaotic in a manner determined by the KAM theory of classical hamiltonian dynamics. The universal properties of the ray dynamics predicted by KAM theory allow a general understanding of the whispering gallery modes of such asymmetric resonant cavities (ARCs). This theory combined with simulations of the non-linear map describing the ray motion provides the basis for a ray-optics model of the Q-spoiling of these whispering gallery modes for large deformations (greater than 1% of the radius). The model predicts a sharp onset as a function of deformation for significant Q-spoiling of these modes and highly directional emission above this threshold. Solution of the wave equation for typical whispering gallery modes confirms the qualitative behavior predicted by the ray-optics model even when the cavity is only a few times the resonant wavelength. The model explains for the first time the lasing intensity profile of highly deformed lasing droplets. in Optical Processes in Microcavities, edited by R.K.Chang and A.J.Campillo (World Scientific Publishers, 1996)