Thermal oscillatory behavior analysis and dynamic modulation of refractive index in microspherical resonator

The thermal nonlinear effects in whispering-gallery-mode resonators are characterized by oscillatory behavior in the transmission spectrum. Although the thermal linewidth broadening is proven to be practical in mode-locking and dynamic control of the optical path, the oscillatory behavior always leads to instability of mode-locking and influences the control accuracy. We theoretically and experimentally illustrate the thermal oscillatory behavior using a model that combines slow and fast thermal relaxation processes of the microsphere and fluctuations of the pump wavelength. We also report dynamic modulation of the refractive index based on the fast thermal relaxation process.