Thermal Analysis Of Optical Reference Cavities For Ultra-stable Laser Systems

Optical reference cavities are widely used in various fields such as high resolution spectroscopy, precision metrology and optical atomic clocks. With the Pound-Drever-Hall (PDH) technique, the frequency of a laser can be stabilized to the resonance of a highly stable, high finesse Fabry-Perot (FP) cavity. With high signal to noise ratio and tight frequency lock, the frequency stability and linewidth of the laser depend entirely on the length stability of the FP reference cavity. Therefore, it is the key in these systems to keep the FP reference cavity as stable as possible. However, environmental disturbance and temperature variation would modulate the length of reference cavity, and thus laser frequency stability. Special geometry and mounting configurations for reference cavities have been developed for less sensitivity to environmental vibration. To reduce the impact of temperature variation, the cavities are usually inserted into the multilayer temperature control devices. In most of ultra-stable laser systems, the laser frequency drifts linearly at tens of mHz/s to several Hz/s on a relatively short timescale, and drifts nonlinearly on hundreds of seconds’ timescale. Except for the aging of the cavity material and optical contact between cavity mirrors and spacers (between 10-17/s and 10-16/s), the temperature fluctuation of reference cavities is the key cause of laser frequency drift. With limited temperature stability of reference cavities, it is essential to reduce its temperature sensitivity.In this paper, we focus on the reduction of thermal sensitivity of reference cavities. By means of finite element analysis, we find that when the mass of thermal shield of reference cavities is bigger, the capacity is higher, the emissivity is smaller, the time constant of reference cavities will be larger and its thermal sensitivity to environmental temperature fluctuation will be lower. Moreover, when enclosed in multiple-layer thermal shields, reference cavities will become less sensitive to environmental temperature fluctuations. According to experimentally achievable temperature stability and the coefficient of thermal expansion of reference cavities, a feasible thermal shield system can be designed.Furthermore, we explore the length stability of reference cavities when its temperature is inhomogeneous and when reference cavities are made from composite materials.