Higher-Order Laguerre-Gauss Mode Generation and Interferometry for Gravitational Wave Detectors

Abstract

We report on the first experimental demonstration of higher-order Laguerre-Gauss (LG(p)(ℓ)) mode generation and interferometry using a method scalable to the requirements of gravitational wave (GW) detection. GW detectors which use higher-order LG(p)(ℓ) modes will be less susceptible to mirror thermal noise, which is expected to limit the sensitivity of all currently planned terrestrial detectors. We used a diffractive optic and a mode-cleaner cavity to convert a fundamental LG(0)(0) Gaussian beam into an LG(3)(3) mode with a purity of 98%. The ratio between the power of the LG(0)(0) mode of our laser and the power of the LG(3)(3) transmitted by the cavity was 36%. By measuring the transmission of our setup using the LG(0)(0), we inferred that the conversion efficiency specific to the LG(3)(3) mode was 49%. We illuminated a Michelson interferometer with the LG(3)(3) beam and achieved a visibility of 97%.

Fabry-Pérot-Michelson interferometer using higher-order Laguerre-Gauss modes

“…The quality of the modes in various points has been estimated by using an adimensional intensity overlap integral γ (already used in [15,16]…”

“…Up to now, two table-top experiments have demonstrated the generation of a high purity LG 33 mode for GW detection using a diffractive element, either a liquidcrystal-on-silicon spatial-light modulator [14] or a fusedsilica plate [15], in combination with a linear mode-cleaner cavity. Two further experiments have investigated this technique at scales closer to a real gravitational wave detector by increasing either the laser power or the length of the optical system: the former [16] was focused on the LG 33 high-power generation by a diffractive phase plate, while the goal of the latter [17] was to inject an LG 33 mode into a suspended 10-m-long Fabry-Pérot cavity in vacuum.…”

Minimum noise optical coatings for interferometric detectors of gravitational waves

“…See [44] for a broad discussion. Gauss-Laguerre modes, in particular, received considerable attention, since they may fit standard spherical-mirror cavities [45], although imposing much tighter mode-matching and astigmatism requirements [46].…”

Effects of mirror aberrations on Laguerre-Gaussian beams in interferometric gravitational-wave detectors

“…Due to the practical advantages associated with the use of spherical mirrors, experimental testing of LG 3,3 modes has begun. It has thus far been demonstrated that these modes can be generated with high efficiency and resonated in tabletop cavities with small mirrors [14,15]. An unpleasant property of higher-order LG modes is that each LG p,l mode is 2p + |l| + 1-fold degenerate, the LG 3,3 mode being 10-fold degenerate.…”