Differences between emission patterns and internal modes of optical resonators

The evanescent wave field outside an optical resonator is typically strongly directional when the shape deviates even very slightly from being perfectly circular or spherical. In this Rapid Communication we show that the tunneling mechanism underlying escape from such weakly deformed resonators can lead to emission patterns that look quite different to the corresponding internal mode. A direct short-wavelength analysis is not possible because the required complex ray data cannot be found due to the presence of natural boundaries. We show, however, that an approach based on perturbative approximation of the ray families successfully describes this phenomenon. In appropriate limits, the emission pattern allows one effectively to perform a direct observation of solutions of the one-dimensional Schrödinger equation in the complex plane.