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Session N18 - Nonlinear Dynamics: Chaos.
MIXED session, Thursday morning, March 21
Room 241, America's Center
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) where perturbation theory cannot be applied and brute force numerical computation is difficult. 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. Both predictions are qualitatively confirmed by numerical solution of the wave equation for typical whispering gallery modes even when the cavity is only a few times the resonant wavelength. The emission directionality shows unambiguous signatures of KAM island structure. The model explains for the first time the anisotropic emission profiles of highly deformed lasing droplets, which are very different for oblate and prolate shapes.
