Finite element analysis of the zero-crossing temperature of a long Fabry–Perot cavity

An ultra-stable Fabry–Perot (F–P) cavity is designed, whose spacer is made of an ultra-low-expansion (ULE) glass and mirrors made of fused silicon (FS). The spacer aperture is composed of three holes, among which a long and small hole is in the middle, and a short and large hole is on each side. The fused silicon (FS) mirrors are placed in the large holes of the spacer aperture, and the FS rings are mounted on the end face of the spacer. FS mirrors, aperture and FS rings are coaxial. The thermal noise limit of the cavity is 9.1×10-17\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$9.1\times 10^{-17}$$\end{document}. By finite element analysis, the specific FS rings are choose to successfully tune the zero-crossing temperature from −10 to 27 K, which enables the cavity zero-crossing temperature easily be tuned above room temperature. In the meantime, this design makes the machining error has little effect on the zero-crossing temperature of the cavity, and it is convenient to manufacture a long F–P cavity.