Some aspects of simulation and realization of an optical reference cavity

The interrogation of an ultranarrow clock transition of a single trapped ion for optical frequency metrology requires a laser stabilized to a couple of Hz per second with a linewidth of the same order of magnitude. Today, lasers in the visible have reached the Hz-range in frequency stability, if locked onto a high-finesse, ultrastable reference cavity. Vertical mounting of the reference cavity can reduce its sensitivity to vibrations as described in [M. Notcutt, L. Ma, J. Ye, and J. Hall, Opt. Lett. 30, 1815 (2005)]. We have designed a comparable vertical cavity with an overall length of 150 mm resulting in a free spectral range of 1 GHz. Optimization of the cavity design has been carried out with a finite elements method, leading to expected relative length variations below 10(-14) under the influence of gravity acceleration (1g). The variation in different geometric parameters has been studied. The analysis of the different noise sources shows that, for a regime superior to a tenth of a hertz, the fast linewidth of the laser will not be limited by the cavity characteristics.