Piezo-deformable mirrors for active mode matching in advanced LIGO.

The detectors of the laser interferometer gravitational-wave observatory (LIGO) are broadly limited by the quantum noise and rely on the injection of squeezed states of light to achieve their full sensitivity. Squeezing improvement is limited by mode mismatch between the elements of the squeezer and the interferometer. In the current LIGO detectors, there is no way to actively mitigate this mode mismatch. This paper presents a new deformable mirror for wavefront control that meets the active mode matching requirements of advanced LIGO. The active element is a piezo-electric transducer, which actuates on the radius of curvature of a 5 mm thick mirror via an axisymmetric flexure. The operating range of the deformable mirror is 120±8 mD in vacuum and an additional 200 mD adjustment range accessible out of vacuum. Combining the operating range and the adjustable static offset, it is possible to deform a flat mirror from -65 mD to -385 mD. The measured bandwidth of the actuator and driver electronics is 6.8 Hz. The scattering into higher-order modes is measured to be <0.2% over the nominal beam radius. These piezo-deformable mirrors meet the stringent noise and vacuum requirements of advanced LIGO and will be used for the next observing run (O4) to control the mode-matching between the squeezer and the interferometer.

Differential wavefront sensing and control using radio-frequency optical demodulation.

Differential wavefront sensing is an essential technique for optimising the performance of many precision interferometric experiments. Perhaps the most extensive application of this is for alignment sensing using radio-frequency beats measured with quadrant photodiodes. Here we present a new technique that uses optical demodulation to measure such optical beats at high resolutions using commercial laboratory equipment. We experimentally demonstrate that the images captured can be digitally processed to generate wavefront error signals and use these in a closed loop control system for correct wavefront errors for alignment and mode-matching a beam into an optical cavity to 99.9%. This experiment paves the way for the correction of even higher order errors when paired with higher order wavefront actuators. Such a sensing scheme could find use in optimizing complex interferometers consisting of coupled cavities, such as those found in gravitational wave detectors, or simply just for sensing higher order wavefront errors in heterodyne interferometric table-top experiments.

Point absorbers in Advanced LIGO.

Small, highly absorbing points are randomly present on the surfaces of the main interferometer optics in Advanced LIGO. The resulting nanometer scale thermo-elastic deformations and substrate lenses from these micron-scale absorbers significantly reduce the sensitivity of the interferometer directly though a reduction in the power-recycling gain and indirect interactions with the feedback control system. We review the expected surface deformation from point absorbers and provide a pedagogical description of the impact on power buildup in second generation gravitational wave detectors (dual-recycled Fabry-Perot Michelson interferometers). This analysis predicts that the power-dependent reduction in interferometer performance will significantly degrade maximum stored power by up to 50% and, hence, limit GW sensitivity, but it suggests system wide corrections that can be implemented in current and future GW detectors. This is particularly pressing given that future GW detectors call for an order of magnitude more stored power than currently used in Advanced LIGO in Observing Run 3. We briefly review strategies to mitigate the effects of point absorbers in current and future GW wave detectors to maximize the success of these enterprises.

Optical lock-in camera for gravitational wave detectors.

Knowledge of the intensity and phase profiles of spectral components in a coherent optical field is critical for a wide range of high-precision optical applications. One of these is interferometric gravitational wave detectors, which rely on the optical beats between these fields for precise control of the experiment. Here we describe an optical lock-in camera and show that it can be used to record optical beats at MHz or greater frequencies with higher spatial and temporal resolution than previously possible. This improvement is achieved using a Pockels cell as a fast optical switch to transform each pixel on a sCMOS array into an optical lock-in amplifier. We demonstrate that the optical lock-in camera can record fields with 2 Mpx resolution at 10 Hz with a sensitivity of -62 dBc when averaged over 2s.

Enhancing the dynamic range of deformable mirrors with compression bias.

We report the design and testing of a compression-biased thermally-actuated deformable mirror that has a dynamic range larger than the limit imposed by pure-bending stress, negligible higher-order-mode scattering, and a linear defocus response and that is vacuum compatible. The optimum design principles for this class of actuator are described and a mirror with 370 mD dynamic range is demonstrated.

High dynamic range thermally actuated bimorph mirror for gravitational wave detectors.

Adaptive optics are crucial for overcoming the fabrication limits on mirror curvature in high-precision interferometry. We describe a low-cost thermally actuated bimorph mirror with 200 mD linear response, which meets dynamic range and low aberration requirements for the ${\rm{A}} + $A+ upgrade of the Laser Interferometer Gravitational-wave Observatory (LIGO). Its deformation and operation limits were measured and verified against finite element simulation.