Inhomogeneous medium as a high-Q resonator

A theoretical analysis is made of the possibility of forming optical resonators from inhomogeneous media. A mode calculation is reported for a toroidal resonator with a quadratic distribution of the refractive index. Estimates are made of the geometrical dimensions of this resonator as a function of the refractive index gradient. It is shown that in gas resonator of this type it should be possible in principle to achieve a photon lifetime of the order of a fraction of a second.