Three-wave mixing in whispering gallery resonators

We review the progress in the development of frequency converters based on three-wave mixing in whispering gallery resonators (WGRs). The theoretical description, given in a unified notation for all basic processes, reveals that the phase-matching condition known from conventional devices is replaced by several selection rules and, furthermore, the fact that conversion efficiencies of more than 25% can be reached in the overcoupled regime only. Experimentally, the conversion efficiencies exceed 50%already at milliwatt input powers. This is achieved, however, so far in bulk resonators only since today the on-chip devices have two orders of magnitude lower quality factors. Regarding the stability of the conversion process, one has to consider impurities left from the crystal growth and material specific effects like photoconductivity, photorefractivity, and pyroelectricity. The impressive experimental progress paves the way that micrometer-sized frequency converters based on WGRs will find the way out of the lab into real-world applications.