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.

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.

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.

Overview of Advanced LIGO adaptive optics.

This is an overview of the adaptive optics used in Advanced LIGO (aLIGO), known as the thermal compensation system (TCS). The TCS was designed to minimize thermally induced spatial distortions in the interferometer optical modes and to provide some correction for static curvature errors in the core optics of aLIGO. The TCS is comprised of ring heater actuators, spatially tunable CO2 laser projectors, and Hartmann wavefront sensors. The system meets the requirements of correcting for nominal distortion in aLIGO to a maximum residual error of 5.4 nm rms, weighted across the laser beam, for up to 125 W of laser input power into the interferometer.

Analytical model for ring heater thermal compensation in the Advanced Laser Interferometer Gravitational-wave Observatory.

Advanced laser interferometer gravitational-wave detectors use high laser power to achieve design sensitivity. A small part of this power is absorbed in the interferometer cavity mirrors where it creates thermal lenses, causing aberrations in the main laser beam that must be minimized by the actuation of "ring heaters," which are additional heater elements that are aimed to reduce the temperature gradients in the mirrors. In this article we derive the first, to the best of our knowledge, analytical model of the temperature field generated by an ideal ring heater. We express the resulting optical aberration contribution to the main laser beam in this axisymmetric case. Used in conjunction with wavefront measurements, our model provides a more complete understanding of the thermal state of the cavity mirrors and will allow a more efficient use of the ring heaters in the Advanced Laser Interferometer Gravitational-wave Observatory.

Observation of Parametric Instability in Advanced LIGO.

Parametric instabilities have long been studied as a potentially limiting effect in high-power interferometric gravitational wave detectors. Until now, however, these instabilities have never been observed in a kilometer-scale interferometer. In this Letter, we describe the first observation of parametric instability in a gravitational wave detector, and the means by which it has been removed as a barrier to progress.

Multicolor cavity metrology.

Long-baseline laser interferometers used for gravitational-wave detection have proven to be very complicated to control. In order to have sufficient sensitivity to astrophysical gravitational waves, a set of multiple coupled optical cavities comprising the interferometer must be brought into resonance with the laser field. A set of multi-input, multi-output servos then lock these cavities into place via feedback control. This procedure, known as lock acquisition, has proven to be a vexing problem and has reduced greatly the reliability and duty factor of the past generation of laser interferometers. In this article, we describe a technique for bringing the interferometer from an uncontrolled state into resonance by using harmonically related external fields to provide a deterministic hierarchical control. This technique reduces the effect of the external seismic disturbances by 4 orders of magnitude and promises to greatly enhance the stability and reliability of the current generation of gravitational-wave detectors. The possibility for using multicolor techniques to overcome current quantum and thermal noise limits is also discussed.

Direct measurement of absorption-induced wavefront distortion in high optical power systems.

Wavefront distortion due to absorption in the substrates and coatings of mirrors in advanced gravitational wave interferometers has the potential to compromise the operation and sensitivity of these interferometers [Opt. Lett.29, 2635-2637 (2004)]. We report the first direct spatially-resolved measurement, to our knowledge, of such wavefront distortion in a high optical power cavity. The measurement was made using an ultrahigh sensitivity Hartmann wavefront sensor on a dedicated test facility. The sensitivity of the sensor was lambda/730, where lambda=800 nm.

Accurate and precise optical testing with a differential Hartmann wavefront sensor.

A novel differential Hartmann sensor is described. It can be used to determine the characteristics of an optic accurately, precisely, and simply without detailed knowledge of the wavefront used to illuminate the optical system or of the geometry of the measurement system. We demonstrate the application of this sensor to both zonal and modal optical testing of lenses. We also describe a dual-camera implementation of the sensor that would enable high-speed optical testing.

Ultra-sensitive wavefront measurement using a Hartmann sensor.

We describe a Hartmann sensor with a sensitivity of lambda /15,500 at lambda= 820nm. We also demonstrate its application to the measurement of an ultra small change in wavefront and show that the result agrees with that expected to within lambda/3,300.