Higher-order Hermite-Gauss modes for gravitational waves detection

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