An analysis and visualization of the output mode-matching requirements for squeezing in Advanced LIGO and future gravitational wave detectors

The sensitivity of ground-based gravitational wave (GW) detectors will be improved in the future via the injection of frequency-dependent squeezed vacuum. The achievable improvement is ultimately limited by losses of the interferometer electromagnetic field that carries the GW signal. The analysis and reduction of optical loss in the GW signal chain will be critical for optimal squeezed light-enhanced interferometry. In this work we analyze a strategy for reducing output-side losses due to spatial mode mismatch between optical cavities with the use of adaptive optics. Our goal is not to design a detector from the top down, but rather to minimize losses within the current design. Accordingly, we consider actuation on optics already present and one transmissive optic to be added between the signal recycling mirror and the output mode cleaner. The results of our calculation show that adaptive mode-matching with the current Advanced LIGO design is a suitable strategy for loss reduction that provides less than 2% mean output mode-matching loss. The range of actuation required is +47 uD on SR3, +140 mD on OM1 and OM2, +50 mD on the SRM substrate, and -50 mD on the added new transmissive optic. These requirements are within the demonstrated ranges of real actuators in similar or identical configurations to the proposed implementation. We also present a novel technique that graphically illustrates the matching of interferometer modes and allows for a quantitative comparison of different combinations of actuators.Comment: Matches version accepted in PR

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

Thermal modelling of Advanced LIGO test masses

High-reflectivity fused silica mirrors are at the epicentre of current advanced gravitational wave detectors. In these detectors, the mirrors interact with high power laser beams. As a result of finite absorption in the high reflectivity coatings the mirrors suffer from a variety of thermal effects that impact on the detectors performance. We propose a model of the Advanced LIGO mirrors that introduces an empirical term to account for the radiative heat transfer between the mirror and its surroundings. The mechanical mode frequency is used as a probe for the overall temperature of the mirror. The thermal transient after power build-up in the optical cavities is used to refine and test the model. The model provides a coating absorption estimate of 1.5 to 2.0 ppm and estimates that 0.3 to 1.3 ppm of the circulating light is scattered on to the ring heater.Comment: 14 pages, 9 figure

In-situ characterization of the thermal state of resonant optical interferometers via tracking of their higher-order mode resonances

Thermal lensing in resonant optical interferometers such as those used for gravitational wave detection is a concern due to the negative impact on control signals and instrument sensitivity. In this paper we describe a method for monitoring the thermal state of such interferometers by probing the higher-order spatial mode resonances of the cavities within them. We demonstrate the use of this technique to measure changes in the Advanced LIGO input mode cleaner cavity geometry as a function of input power, and subsequently infer the optical absorption at the mirror surfaces at the level of 1 ppm per mirror. We also demonstrate the generation of a useful error signal for thermal state of the Advanced LIGO power recycling cavity by continuously tracking the first order spatial mode resonance frequency. Such an error signal could be used as an input to thermal compensation systems to maintain the interferometer cavity geometries in the presence of transients in circulating light power levels, thereby maintaining optimal sensitivity and maximizing the duty-cycle of the detectors

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

Multi-color 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 four orders of magnitude and promises to greatly enhance the stability and reliability of the current generation of gravitational wave detector. The possibility for using multi-color techniques to overcome current quantum and thermal noise limits is also discussed

Mid-IR laser for wavefront correction in gravitational wave detectors

The next-generation gravitational wave detectors aim to enhance our understanding of extreme phenomena in the Universe. The high-frequency sensitivity of these detectors will be maximized by injecting squeezed vacuum states into the detector. However, the performance advantages offered by squeezed state injection can be easily degraded by losses in the system. A significant source of loss is the mode mismatch between optical cavities within the interferometer. To overcome this issue, new actuators are required that can produce a highly spherical wavefront change, with minimal higher order aberrations, whist adding low phase noise to the incident beam

Ultra-sensitive wavefront measurement using a Hartmann sensor

We describe a Hartmann sensor with a sensitivity of λ /15,500 at λ= 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 λ/3,300.Aidan F. Brooks, Thu-Lan Kelly, Peter J. Veitch, and Jesper Munc