Phase effects due to beam misalignment on diffraction gratings

All-reflective interferometer configurations have been proposed for the next generation of gravitational wave detectors, with diffractive elements replacing transmissive optics. However, an additional phase noise creates more stringent conditions for alignment stability. A framework for alignment stability with the use of diffractive elements was required using a Gaussian model. We successfully create such a framework involving modal decomposition to replicate small displacements of the beam (or grating) and show that the modal model does not contain the phase changes seen in an otherwise geometric planewave approach. The modal decomposition description is justified by verifying experimentally that the phase of a diffracted Gaussian beam is independent of the beam shape, achieved by comparing the phase change between a zero-order and first-order mode beam. To interpret our findings we employ a rigorous time-domain simulation to demonstrate that the phase changes resulting from a modal decomposition are correct, provided that the coordinate system which measures the phase is moved simultaneously with the effective beam displacement. This indeed corresponds to the phase change observed in the geometric planewave model. The change in the coordinate system does not instinctively occur within the analytical framework, and therefore requires either a manual change in the coordinate system or an addition of the geometric planewave phase factor.Comment: 14 pages, 8 figures, submitted to Optics Expres

Experimental demonstration of higher-order Laguerre-Gauss mode interferometry

The compatibility of higher-order Laguerre-Gauss (LG) modes with interferometric technologies commonly used in gravitational wave detectors is investigated. In this paper we present the first experimental results concerning the performance of the LG33 mode in optical resonators. We show that the Pound-Drever-Hall error signal for a LG33 mode in a linear optical resonator is identical to that of the more commonly used LG00 mode, and demonstrate the feedback control of the resonator with a LG33 mode. We succeeded to increase the mode purity of a LG33 mode generated using a spatial-light modulator from 51% to 99% upon transmission through a linear optical resonator. We further report the experimental verification that a triangular optical resonator does not transmit helical LG modes

Remarks on thermoelastic effects at low temperatures and quantum limits in displacement measurements

The noise level of thermoelastic fluctuations of a mirror at low temperature was derived and introduced by M. Cerdonio et al. [Phys. Rev. D 63, 082003 (2001)]. The importance of the paper has become remarkable according to the increasing attention to the low-temperature high-precision measurement device. Here we would like to introduce the analytical form of their equation of thermoelastic noise in the integral form in order to reduce the computational labor

Interferometers for Displacement-Noise-Free Gravitational-Wave Detection

We propose a class of displacement- and laser-noise free gravitational-wave-interferometer configurations, which does not sense non-geodesic mirror motions and laser noises, but provides non-vanishing gravitational-wave signal. Our interferometer consists of 4 mirrors and 2 beamsplitters, which form 4 Mach-Zehnder interferometers. By contrast to previous works, no composite mirrors are required. Each mirror in our configuration is sensed redundantly, by at least two pairs of incident and reflected beams. Displacement- and laser-noise free detection is achieved when output signals from these 4 interferometers are combined appropriately. Our 3-dimensional interferometer configuration has a low-frequency response proportional to f^2, which is better than the f^3 achievable by previous 2-dimensional configurations.Comment: 5 pages, 4 figure

Higher order Laguerre-Gauss mode degeneracy in realistic, high finesse cavities

Higher order Laguerre-Gauss (LG) beams have been proposed for use in future gravitational wave detectors, such as upgrades to the Advanced LIGO detectors and the Einstein Telescope, for their potential to reduce the effects of the thermal noise of the test masses. This paper details the theoretical analysis and simulation work carried out to investigate the behaviour of LG beams in realistic optical setups, in particular the coupling between different LG modes in a linear cavity. We present a new analytical approximation to compute the coupling between modes, using Zernike polynomials to describe mirror surface distortions. We apply this method in a study of the behaviour of the LG33 mode within realistic arm cavities, using measured mirror surface maps from the Advanced LIGO project. We show mode distortions that can be expected to arise due to the degeneracy of higher order spatial modes within such cavities and relate this to the theoretical analysis. Finally we identify the mirror distortions which cause significant coupling from the LG33 mode into other order 9 modes and derive requirements for the mirror surfaces.Comment: 12 pages Submitted to PRD 19/07/201

Residual amplitude modulation in interferometric gravitational wave detectors

The effects of residual amplitude modulation (RAM) in laser interferometers using heterodyne sensing can be substantial and difficult to mitigate. In this work, we analyze the effects of RAM on a complex laser interferometer used for gravitational wave detection. The RAM introduces unwanted offsets in the cavity length signals and thereby shifts the operating point of the optical cavities from the nominal point via feedback control. This shift causes variations in the sensing matrix, and leads to degradation in the performance of the precision noise subtraction scheme of the multiple-degree-of-freedom control system. In addition, such detuned optical cavities produce an optomechanical spring, which also perturbs the sensing matrix. We use our simulations to derive requirements on RAM for the Advanced LIGO (aLIGO) detectors, and show that the RAM expected in aLIGO will not limit its sensitivity

Diagonalizing sensing matrix of broadband RSE

For a broadband-operated RSE interferometer, a simple and smart length sensing and control scheme was newly proposed. The sensing matrix could be diagonal, owing to a simple allocation of two RF modulations and to a macroscopic displacement of cavity mirrors, which cause a detuning of the RF modulation sidebands. In this article, the idea of the sensing scheme and an optimization of the relevant parameters will be described

All-sky search for continuous gravitational waves from isolated neutron stars using Advanced LIGO and Advanced Virgo O3 data

We present results of an all-sky search for continuous gravitational waves which can be produced by spinning neutron stars with an asymmetry around their rotation axis, using data from the third observing run of the Advanced LIGO and Advanced Virgo detectors. Four different analysis methods are used to search in a gravitational-wave frequency band from 10 to 2048 Hz and a first frequency derivative from − 10 − 8 to 10 − 9     Hz / s . No statistically significant periodic gravitational-wave signal is observed by any of the four searches. As a result, upper limits on the gravitational-wave strain amplitude h 0 are calculated. The best upper limits are obtained in the frequency range of 100 to 200 Hz and they are ∼ 1.1 × 10 − 25 at 95% confidence level. The minimum upper limit of 1.10 × 10 − 25 is achieved at a frequency 111.5 Hz. We also place constraints on the rates and abundances of nearby planetary- and asteroid-mass primordial black holes that could give rise to continuous gravitational-wave signals