Brillouin lasing in whispering gallery micro-resonators

Thresholds of stimulated Brillouin scattering (SBS) in solid-state whispering gallery mode (WGM) microresonators are analyzed. It is shown that the SBS interaction is substantially different here from that known in the bulk case and in the case of water droplet resonators. The reason is the absence of pure longitudinal acoustic WGMs owing to strong coupling of the longitudinal (l) and transverse (t) acoustic displacements at the surface of the resonator. As a result, a considerable increase of the SBS thresholds takes place, and the lowest thresholds correspond to the hybrid tl-modes with very large radial indices. Nevertheless, the thresholds lie in the mu W range of the pump power. Dependence of the SBS power thresholds on the modal numbers and the possibility of self-tuning to the SBS resonance are analyzed.