Role of geometry in optothermal response of toroidal ultra-high-Q cavities

Ultra-high quality factor (UHQ) resonant cavities are able to store light for long periods of time, resulting in high circulating intensities. As a result, numerous nonlinear optical phenomena appear, such as radiation pressure oscillations and lasing. However, deleterious behaviors also occur, such as optothermal broadening of the resonant linewidth. The degree of distortion is directly related to the circulating power in the cavity, the material absorption, and the thermooptic coefficient of the cavity material. Specifically, a portion of the circulating power is absorbed by the material and converted to heat. This thermal energy is able to induce a refractive index change in the cavity which is experimentally observed as a resonant wavelength change. This behavior has been observed in numerous cavities, but one interesting case is the toroidal cavity, as it has a particularly complex geometry providing multiple thermal transport pathways. To accurately capture this complex behavior, we have developed a COMSOL Multiphysics model which combines the thermal and optical components. The model uses the non-uniform optical mode profile as the heat source. As such, changes in device geometry and wavelength are inherently captured. To verify the modeling, we characterize the optothermal threshold for a series of toroidal cavities across a range of wavelengths and device geometries. Additionally, the thermal time constant of the structure is explored. Of note, the membrane thickness is shown to play a critical role in the optothermal behaviors.