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Light emission from optical cavities can show strong directionality even for small deformations of a circular cavity. In order to model the emission patterns produced by an elliptical cavity, the invariants of the ray dynamics in the interior of the cavity are introduced. These invariants are then used to extend the wavefunction to the exterior of the cavity using a modified version of Wilkinson's formula. Wilkinson's formula gives a singularity in the limit of zero eccentricity, and so an alternate calculation is also given which can be extended to generic perturbations of a circular cavity. |
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