Optical frequency comb for cryogenic interferometer lock acquisition and calibration

Advanced LIGO uses multi-color cavity metrology to bring several cross-coupled cavities into resonance quickly and robustly. This scheme, known as arm length stabilization (ALS), uses the beatnote between a frequency doubled auxiliary field and the main laser to stabilize the 4-km arm interferometer into its operating point. Third-generation cryogenic gravitational wave (GW) detectors such as Voyager will operate well beyond the Si absorption band, i.e. $\geq 1.3 \,\rm \mu m$, rendering the second harmonic ALS scheme impractical for wavelengths $\sim2\,\rm \mu m$. The auxiliary wavelength is instead chosen to be near 1.5$\,\rm \mu m$ which has no simple relation to main laser that can be bridged over with a single non-linear interaction. Here, we propose using an optical frequency comb as a beatnote measurement tool between the two wavelengths. We consider a feedforward technique to suppress most of the frequency comb intrinsic noise in the beatnote fluctuations detection and derive the stability requirements based on lock acquisition, and for doing differential strain calibration in future cryogenic gravitational-wave detectors.