Researching The Stabilization Of Ultra-stable Fabry-Perot Cavities

Ultra-stable cavities are widely used for laser frequency stabilization. In these experiments the laser performance relies on the length stability of the Fabry-Perot cavities. Vibration-induced deformation is one of the dominate factors that affects the stability of ultra-stable optical cavities. We quantitatively analyzed the elastic deformation of Fabry-Perot cavities with various shapes and mounting configurations. Our numerical result facilitates a novel approach for the design of ultra-stable cavities that are insensitive to vibration perturbations. This approach can be applied to many experiments such as laser frequency stabilization, high-precision laser spectroscopy, and optical frequency standard. After these results, we focus on another factor, thermal noise. We numerically analyzed the thermal noise of a widely-used ultra-stable cavity in experiment, based on the mechanical loss of cavity materials and the numerical analysis of the mirror-spacer mechanics with the direct application of the fluctuation dissipation theorem. After calculations, we found the dominate factors that produce the thermal noise, and these factors will be applied to reduced the thermal noise.