Multiple Time Scale Thermo-Optical Nonlinear Response in Silica Spherical Microresonators

We directly measured the temporal behavior of the thermo-optical frequency shift of the whispering gallery modes (WGMs) of a silica spherical microresonator during its cooling after the pump pulse with a resolution of $\sim 12~\mu $ s. We observed that the thermal response contains a very fast component with a characteristic time scale of 0.1-0.2 ms (much faster than the cooling time of the microresonator as a whole). Numerical modeling, in good agreement with experimental results, showed that the fast component is related to the process of heat diffusion from the mode volume. The magnitude and characteristic timescale of the fast response depend on the mode profile, but the slow part of the response is similar for the fundamental and higher order modes.