The stiffness analysis of vibration-insensitive spherical optical reference cavities

Vibration-insensitive spherical optical reference cavities are important to ultra-stable lasers. Striving for even lower instabilities of ultra-stable lasers, it is essential to study the stiffness analysis of vibration-insensitive optical reference cavities. Theoretically, under the other same conditions, greater stiffness could lead to lower vibration sensitivity and Brownian thermal noise. In this paper, the stiffness of a spherical optical cavity mounted at two support points on a diameter of the spherical spacer are analyzed theoretically. The analysis results show that the maximum values of the three kinds stiffness and bending shearing force are located in the support point of the cavity. Additionally, the minimum of that and the maximum of axial stress present to radius of the cavity. On the whole, five function curves of the stiffness and two key forces are nonlinear as a function of the length of the optical axis. The analysis results in this paper are helpful to optimization design thermal noise and vibration sensitivity of spherical optical reference cavities.