Some aspects of simulation and realization of an optical reference cavity

TL;DR

This paper discusses the design, simulation, and realization of a vertically mounted ultra-stable optical reference cavity aimed at achieving laser frequency stability suitable for optical clock transitions, emphasizing vibration reduction and noise analysis.

Contribution

It introduces a new vertical cavity design optimized via Finite-Elements Method, achieving low length variation and analyzing noise sources for ultra-stable laser applications.

Findings

Expected relative length variations below 10^{-14} under gravity

Design reduces sensitivity to vibrations compared to horizontal cavities

Fast laser linewidth not limited by cavity characteristics above 0.1 Hz

Abstract

The interrogation of an ultra-narrow 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, ultra-stable reference cavity. Vertical mounting of the reference cavity can reduce its sensitivity to vibrations as described in \cite{notcutt05}. We have designed a comparable vertical cavity with an overall length of 150 mm resulting in a Free Spectral Range of 1GHz. Optimisation 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 (1 $g$). The variation of 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.