Dispersion compensation in whispering gallery modes

We show that manipulation by a spatial profile of refractive index of a circularly symmetric dielectric cavity results in a novel way of fine tuning frequency separations as well as spatial localizations of high-Q whispering gallery modes excited in the cavity. The method enables dispersion compensation in the modes (spectrum equalization), diminishes the quality-factor limitation by surface roughness and contamination, and enables critical coupling to ultra-high-Q modes without maintaining an air-gap with evanescent couplers.