# Broadband birefringence spectroscopy with sub-kHz precision

## TL;DR

This paper demonstrates a novel method using cavity-mode dispersion spectroscopy with optical frequency combs to measure birefringence in high-finesse cavities, achieving high sensitivity and opening avenues for studying birefringent noise.

## Contribution

It introduces a new application of optical frequency combs for precise static birefringence measurement in crystalline mirror coatings.

## Key findings

- Measured birefringent cavity mode splitting with fractional frequency sensitivity of 5e-14.
- Calculated static birefringent splitting of refractive index at two temperatures.
- Proposed a method to study dispersive birefringent noise using optical frequency combs.

## Abstract

Although current amorphous high-reflective mirror coatings have had tremendous success in metrology applications, they are inherently limited by thermal fluctuations in their coating structure. Alternatively, crystalline coating technology has demonstrated superior thermal noise performance. However, recent studies have revealed birefringent noise sources, raising questions about the limits of frequency stability of high-finesse cryogenic silicon cavities with crystalline mirror coatings. Here, we show the applicability of cavity-mode dispersion spectroscopy to measure birefringent cavity mode splitting. We measured birefringence induced cavity mode splitting by probing the resonance frequencies of a high-finesse, ultra-low expansion glass cavity with all-crystalline mirror coatings, reaching fractional frequency sensitivity of \SI{5e-14}{} utilizing an optical frequency comb for two orthogonal polarizations. Subsequently, we calculated the static birefringent splitting of the refractive index for \SI{23.8}{\celsius} and \SI{31.3}{\celsius} on the order of \SI{305 \pm 3}{ppm} and \SI{294 \pm 3}{ppm} over \SI{30}{nm} respectively. Furthermore, we propose measurements of dispersive birefringent noise based on optical frequency combs. Our results not only extend the use of optical frequency combs to measure static birefringence, but also implicate a possibility to further study spectrally dependent frequency noise.