Squeezing light from optical resonators

Whispering gallery modes in optical resonators have recently gained immense practical importance, as a means of producing very small lasers and in other technological applications such as coupling optical fibres and as sensing devices. In the context of lasers, it is particularly important to understand the effects of deforming the shape of the resonator from perfectly cylindrical or spherical since the resultant asymmetric emission pattern is an important feature of that application. Surprisingly, emission patterns for small deformations are poorly understood, despite the fact that the corresponding ray dynamics are almost entirely regular and at first sight show little qualitative difference from the perfectly cylindrical and spherical cases. The essential reason for this is that understanding emission patterns demands that we complexify the whispering-gallery families of rays and this is a difficult problem for nonintegrable systems, so in addition to being of practical importance, the problem is also very interesting mathematically. The project proposes to overcome the inherent difficulties by using canonical perturbation theory to approximate the complexified ray families. The end product of the project should be a general and explicit recipe for calculating emission patterns of whispering-gallery type resonant modes, valid when the radial perturbation is of the order of a wavelength or smaller. Although accurate numerical solutions of such problems are possible, simple analytical predictions of the sort proposed here have been lacking and will be useful in the design and analysis of technological applications of optical resonators.