Higher-order Hermite-Gauss modes for gravitational waves detection
S. Ast, S. Di Pace, Jacques Millo, M. Pichot, M. Turconi, N. Christensen, Walid Chaibi
Abstract
As part of the research on thermal noise reduction in gravitational-wave detectors, we experimentally demonstrate the conversion of a fundamental ${\mathrm{TEM}}_{00}$ laser mode at 1064 nm to higher-order Hermite-Gaussian modes (HG) of arbitrary order via a commercially available liquid crystal spatial light modulator. We particularly studied the ${\mathrm{HG}}_{5,5}/{\mathrm{HG}}_{10,10}/{\mathrm{HG}}_{15,15}$ modes. A two-mirror plano-spherical cavity filters the higher-order modes spatially. We analyze the cleaned modes via a three-mirror diagnosis cavity and measure a mode purity of $96/93/78%$ and a conversion efficiency of $6.6%/3.7%/1.7%$, respectively. A full set of simulations and mathematical proofs are also presented which shows that (i) Hermite-Gauss modes resonate in a two-mirror cavity provided mirrors are properly angled with respect to the impinging mode, and (ii) Hermite-Gauss modes resonate in triangular cavities. Hence, higher-order Hermite-Gauss modes are compatible with ground-based gravitational-wave detectors' architecture and can be employed for the mitigation of mirror thermal noise for the third generation Einstein Telescope or Cosmic Explorer.