Frequency stability of a wavelength meter and applications to laser frequency stabilization

Interferometric wavelength meters have attained frequency resolutions down to the MHz range. In particular, Fizeau interferometers, which have no moving parts, are becoming a popular tool for laser characterization and stabilization. In this article, we characterize such a wavelength meter using an ultra-stable laser in terms of relative frequency instability ${\sigma }_y(\tau )$ and demonstrate that it can achieve a short-term instability ${\sigma }_y(1s)\approx 2\times {10}^{-10}$ and a frequency drift of order $10$ MHz/day. We use this apparatus to demonstrate frequency control of a near-infrared laser, where a frequency instability below $3\times {10}^{-10}$ from 1 s to 2000 s is achieved. Such performance is for example adequate for ions trapping and atoms cooling experiments.