Precision interferometric measurements of mirror birefringence in high-finesse optical resonators

Abstract

High-finesse optical resonators found in ultrasensitive laser spectrometers utilize supermirrors ideally consisting of isotropic high-reflectivity coatings. Strictly speaking, however, the optical coatings are often nonuniformly stressed during the deposition process and therefore do possess some small amount of birefringence. When physically mounted the cavity mirrors can be additionally stressed in such a way that large optical birefringence is induced. Here we report a direct measurement of optical birefringence in a two-mirror Fabry-P\'erot cavity with $R=99.99%$ by observing ${\mathrm{TEM}}_{00}$ mode beating during cavity decays. Experiments were performed at a wavelength of 4.53 $\ensuremath{\mu}\mathrm{m}$, with precision limited by both quantum and technical noise sources. We report a splitting of ${\ensuremath{\delta}}_{\ensuremath{\nu}}=618(1)$ Hz, significantly less than the intrinsic cavity line width of ${\ensuremath{\delta}}_{\text{cav}}\ensuremath{\approx}3$ kHz. With a cavity free spectral range of 96.9 MHz, the equivalent fractional change in mirror refractive index due to birefringence is therefore $\mathrm{\ensuremath{\Delta}}n/n=6.38(1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$.