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 Absorber Limits to Future Gravitational-Wave Detectors.

High-quality optical resonant cavities require low optical loss, typically on the scale of parts per million. However, unintended micron-scale contaminants on the resonator mirrors that absorb the light circulating in the cavity can deform the surface thermoelastically and thus increase losses by scattering light out of the resonant mode. The point absorber effect is a limiting factor in some high-power cavity experiments, for example, the Advanced LIGO gravitational-wave detector. In this Letter, we present a general approach to the point absorber effect from first principles and simulate its contribution to the increased scattering. The achievable circulating power in current and future gravitational-wave detectors is calculated statistically given different point absorber configurations. Our formulation is further confirmed experimentally in comparison with the scattered power in the arm cavity of Advanced LIGO measured by in situ photodiodes. The understanding presented here provides an important tool in the global effort to design future gravitational-wave detectors that support high optical power and thus reduce quantum noise.

Narrow-linewidth fiber amplifier for gravitational-wave detectors.

We report on the design and noise performance of a narrow-linewidth Yb-doped fiber amplifier emitting up to 178 W at 1064 nm for possible use in gravitational-wave (GW) interferometric detectors. The novel design utilizes a specialty large-mode-area gain fiber with confined-core doping and depressed cladding, followed by a smaller-core passive fiber to improve output beam quality. We show that the free-running noise of the system is equal to or better than current Advanced LIGO noise requirements. Finally, we discuss potential improvements for long-term use in GW detectors.

First Demonstration of Electrostatic Damping of Parametric Instability at Advanced LIGO.

Interferometric gravitational wave detectors operate with high optical power in their arms in order to achieve high shot-noise limited strain sensitivity. A significant limitation to increasing the optical power is the phenomenon of three-mode parametric instabilities, in which the laser field in the arm cavities is scattered into higher-order optical modes by acoustic modes of the cavity mirrors. The optical modes can further drive the acoustic modes via radiation pressure, potentially producing an exponential buildup. One proposed technique to stabilize parametric instability is active damping of acoustic modes. We report here the first demonstration of damping a parametrically unstable mode using active feedback forces on the cavity mirror. A 15 538 Hz mode that grew exponentially with a time constant of 182 sec was damped using electrostatic actuation, with a resulting decay time constant of 23 sec. An average control force of 0.03 nN was required to maintain the acoustic mode at its minimum amplitude.

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.

Low scatter and ultra-low reflectivity measured in a fused silica window.

We investigate the reflectivity and optical scattering characteristics at 1064 nm of an antireflection coated fused silica window of the type being used in the Advanced LIGO gravitational-wave detectors. Reflectivity is measured in the ultra-low range of 5-10 ppm (by vendor) and 14-30 ppm (by us). Using an angle-resolved scatterometer we measure the sample's bidirectional scattering distribution function (BSDF) and use this to estimate its transmitted and reflected scatter at roughly 20-40 and 1 ppm, respectively, over the range of angles measured. We further inspect the sample's low backscatter using an imaging scatterometer, measuring an angle resolved BSDF below 10(-6) sr-1 for large angles (10°-80° from incidence in the plane of the beam). We use the associated images to (partially) isolate scatter from different regions of the sample and find that scattering from the bulk fused silica is on par with backscatter from the antireflection coated optical surfaces. To confirm that the bulk scattering is caused by Rayleigh scattering, we perform a separate experiment measuring the scattering intensity versus input polarization angle. We estimate that 0.9-1.3 ppm of the backscatter can be accounted for by Rayleigh scattering of the bulk fused silica. These results indicate that modern antireflection coatings have low enough scatter to not limit the total backscattering of thick fused silica optics.

Balanced homodyne readout for quantum limited gravitational wave detectors.

Balanced homodyne detection is typically used to measure quantum-noise-limited optical beams, including squeezed states of light, at audio-band frequencies. Current designs of advanced gravitational wave interferometers use some type of homodyne readout for signal detection, in part because of its compatibility with the use of squeezed light. The readout scheme used in Advanced LIGO, called DC readout, is however not a balanced detection scheme. Instead, the local oscillator field, generated from a dark fringe offset, co-propagates with the signal field at the anti-symmetric output of the beam splitter. This article examines the alternative of a true balanced homodyne detection for the readout of gravitational wave detectors such as Advanced LIGO. Several practical advantages of the balanced detection scheme are described.

Angular control of optical cavities in a radiation-pressure-dominated regime: the Enhanced LIGO case.

We describe the angular sensing and control (ASC) of 4 km detectors of the Laser Interferometer Gravitational-Wave Observatory (LIGO). Enhanced LIGO, the culmination of the first generation LIGO detectors, operated between 2009 and 2010 with about 40 kW of laser power in the arm cavities. In this regime, radiation-pressure effects are significant and induce instabilities in the angular opto-mechanical transfer functions. Here we present and motivate the ASC design in this extreme case and present the results of its implementation in Enhanced LIGO. Highlights of the ASC performance are successful control of opto-mechanical torsional modes, relative mirror motions of ≤ 1×10(-7) rad rms, and limited impact on in-band strain sensitivity.

Impact of upconverted scattered light on advanced interferometric gravitational wave detectors.

Second generation gravitational wave detectors are being installed in a number of locations globally. These long-baseline, Michelson interferometers increase the sensitivity between 10 and 40 Hz by many orders of magnitude compared with first generation instruments. Control of non-linear noise coupling from scattered light fields is critical to achieve low frequency performance. In this paper we investigate the requirements on the attenuation of scattered light using a novel time-domain analysis and two years of seismic data from the LIGO Livingston Observatory.

Arm-length stabilisation for interferometric gravitational-wave detectors using frequency-doubled auxiliary lasers.

Residual motion of the arm cavity mirrors is expected to prove one of the principal impediments to systematic lock acquisition in advanced gravitational-wave interferometers. We present a technique which overcomes this problem by employing auxiliary lasers at twice the fundamental measurement frequency to pre-stabilise the arm cavities' lengths. Applying this approach, we reduce the apparent length noise of a 1.3 m long, independently suspended Fabry-Perot cavity to 30 pm rms and successfully transfer longitudinal control of the system from the auxiliary laser to the measurement laser.

Tip-tilt mirror suspension: beam steering for advanced laser interferometer gravitational wave observatory sensing and control signals.

We describe the design of a small optic suspension system, referred to as the tip-tilt mirror suspension, used to isolate selected small optics for the interferometer sensing and control beams in the advanced LIGO gravitational wave detectors. The suspended optics are isolated in all 6 degrees of freedom, with eigenmode frequencies between 1.3 Hz and 10 Hz. The suspended optic has voice-coil actuators which provide an angular range of ±4 mrad in the pitch and yaw degrees of freedom.

Active correction of thermal lensing through external radiative thermal actuation.

Absorption of laser beam power in optical elements induces thermal gradients that may cause unwanted phase aberrations. In precision measurement applications, such as laser interferometric gravitational-wave detection, corrective measures that require mechanical contact with or attachments to the optics are precluded by noise considerations. We describe a radiative thermal corrector that can counteract thermal lensing and (or) thermoelastic deformation induced by coating and substrate absorption of collimated Gaussian beams. This radiative system can correct anticipated distortions to a high accuracy, at the cost of an increase in the average temperature of the optic. A quantitative analysis and parameter optimization is supported by results from a simplified proof-of-principle experiment, demonstrating the method's feasibility for our intended application.

Quantum-limited optical phase detection at the 10(-10)-rad level.

Interferometric detection of gravitational waves at a level of astrophysical interest is expected to require measurement of optical phase differences of < or = 10(-10) rad. A fundamental limit to the phase sensing is the statistics of photon detection--Poisson statistics for light in a coherent state. We have built a laboratory-scale interferometer to achieve and investigate the phase detection sensitivity required for the Laser Interferometer Gravitational-Wave Observatory. With 70 W of circulating power, we have obtained a phase sensitivity of 1.28 x 10(-10) rad/square root(Hz) at frequencies above 600 Hz, limited by quantum noise. Below 600 Hz, excess noise above the quantum limit is seen, and we present our investigations into the sources of this excess. Compared with the results of previous such experiments, the phase sensitivity over the full 100-Hz-10-kHz band of interest has been improved by factors of up to 100, with a factor-of-2.5 improvement in the quantum-limited level.