Introduction
Small-sized objects experience random temperature fluctuations due to energy exchange with the environment, known as thermal fluctuations. In optical microresonators, these fluctuations lead to variations in the resonant frequency due to the thermo-optic effect. These variations in resonant frequency are known as thermo-refractive noise (TRN).
TRN is a significant source of noise in narrow-linewidth semiconductor lasers. It is often the predominant noise source for offset frequencies between 10 kHz and 100 kHz. Furthermore, TRN presents a challenge for achieving sub-Hz linewidths in integrated lasers at room temperature.
In this note, I will explain how to numerically simulate thermo-refractive noise in a silicon nitride (SiN) microresonator using COMSOL. The simulation file, developed based on the methodologies outlined in references [1] and [2], can be accessed via this link. This webpage only contains the introduction part of the note, the full content is available via this link.