Directional emission from weakly eccentric resonators

It is shown that when a circular resonator is deformed in a nonintegrable way, a symmetry breaking of escaping rays occurs which can dramatically modulate the outgoing wave even for small perturbations. The underlying mechanism does not occur in integrable models for which the ray families can be computed exactly and is described in this Letter on the basis of canonical perturbation theory. Emission from deformed resonators is currently of immense practical interest in the context of whispering-gallery optical resonances of dielectric cavities and the approach outlined here promises simple analytical characterisations in the important case of small deformations.