Thermal analysis of optical reference cavities for low sensitivity to environmental temperature fluctuations

The temperature stability of optical reference cavities is significant in state-of-the-art ultra-stable narrow-linewidth laser systems. In this paper, the thermal time constant and thermal sensitivity of reference cavities are analyzed when reference cavities respond to environmental perturbations via heat transfer of thermal conduction and thermal radiation separately. The analysis as well as simulation results indicate that a reference cavity enclosed in multiple layers of thermal shields with larger mass, higher thermal capacity and lower emissivity is found to have a larger thermal time constant and thus a smaller sensitivity to environmental temperature perturbations. The design of thermal shields for reference cavities may vary according to experimentally achievable temperature stability and the coefficient of thermal expansion of reference cavities. A temperature fluctuation-induced length instability of reference cavities as low as 6 × 10^-16 on a day timescale can be achieved if a two-layer thermal shield is inserted between a cavity with the coefficient of thermal expansion of 1 × 10^-10/K and an outer vacuum chamber with temperature fluctuation amplitude of 1 mK and period of 24 hours.