Study of a spherical vibration-insensitive optical reference cavity

We have investigated the vibrational sensitivity of a horizontal-mounted spherical reference cavity, which can be applied to develop an ultra-stable laser. Effects of different magnitudes of height and area as well as acceleration of the cavity support points on the length variation of the cavity are studied. When the cavity support points are totally constrained, the vibration sensitivity can be reduced to below 3.0×10-10/g. After performing extensive numerical simulations, we can find the optimal support position. According to the obtained results we present the mounting scheme of the spherical cavity. Taking into consideration the machining errors, near-horizontal mounting, and unsymmetrical mounting of the cavity, we can describe quantitatively the length variation of the cavity caused by these three factors. We also discuss the contribution of the second order effect to the length variation of the cavity.