Matrix heater in the gravitational wave observatory GEO 600.

Large scale laser interferometric gravitational wave detectors (GWDs), such as GEO 600 require high quality optics to reach their design sensitivity. The inevitable surface imperfections, inhomogeneities, and light-absorption induced thermal lensing in the optics, can convert laser light from the fundamental mode to unwanted higher order modes, and pose challenges to the operation and sensitivity of the GWDs. Here we demonstrate the practical implementation of a thermal projection system which reduces those unwanted effects via targeted spatial heating of the optics. The thermal projector consists of 108 individually addressable heating elements which are imaged onto the beam splitter of GEO 600. We describe the optimization of the spatial heating profile and present the obtained results.

Translational, rotational, and vibrational coupling into phase in diffractively coupled optical cavities.

All-reflective optical systems are under consideration for future gravitational wave detector topologies. A key feature of these all-reflective systems is the use of Fabry-Perot cavities with diffraction gratings as input couplers; however, theory predicts and experiment has shown that translation of the grating surface across the incident laser light will introduce additional phase into the system. This translation can be induced through simple side-to-side motion of the coupler, yaw motion of the coupler around a central point (i.e., rotation about a vertical axis), and even via internal resonances (i.e., vibration) of the optical element. In this Letter we demonstrate on a prototype-scale suspended cavity that conventional cavity length-sensing techniques used to detect longitudinal changes along the cavity axis will also be sensitive to translational, rotational, and vibrational motion of the diffractive input coupler. We also experimentally verify the amplitude response and frequency dependency of the noise coupling as given by theory.

Experimental demonstration of a suspended diffractively coupled optical cavity.

All-reflective optical systems are under consideration for future gravitational wave detector topologies. One approach in proposed designs is to use diffraction gratings as input couplers for Fabry-Perot cavities. We present an experimental demonstration of a fully suspended diffractively coupled cavity and investigate the use of conventional Pound-Drever-Hall length sensing and control techniques to maintain the required operating condition.

Huddle test measurement of a near Johnson noise limited geophone.

In this paper, the sensor noise of two geophone configurations (L-22D and L-4C geophones from Sercel with custom built amplifiers) was measured by performing two huddle tests. It is shown that the accuracy of the results can be significantly improved by performing the huddle test in a seismically quiet environment and by using a large number of reference sensors to remove the seismic foreground signal from the data. Using these two techniques, the measured sensor noise of the two geophone configurations matched the calculated predictions remarkably well in the bandwidth of interest (0.01 Hz-100 Hz). Low noise operational amplifiers OPA188 were utilized to amplify the L-4C geophone to give a sensor that was characterized to be near Johnson noise limited in the bandwidth of interest with a noise value of 10-11 m/Hz at 1 Hz.

Damping and local control of mirror suspensions for laser interferometric gravitational wave detectors.

The mirrors of laser interferometric gravitational wave detectors hang from multi-stage suspensions. These support the optics against gravity while isolating them from external vibration. Thermal noise must be kept small so mechanical loss must be minimized and the resulting structure has high-Q resonances rigid-body modes, typically in the frequency range between about 0.3 Hz and 20 Hz. Operation of the interferometer requires these resonances to be damped. Active damping provides the design flexibility required to achieve rapid settling with low noise. In practice there is a compromise between sensor performance, and hence cost and complexity, and sophistication of the control algorithm. We introduce a novel approach which combines the new technique of modal damping with methods developed from those applied in GEO 600. This approach is predicted to meet the goals for damping and for noise performance set by the Advanced LIGO project.

Apparatus for dimensional characterization of fused silica fibers for the suspensions of advanced gravitational wave detectors.

Detection of gravitational waves from astrophysical sources remains one of the most challenging problems faced by experimental physicists. A significant limit to the sensitivity of future long-baseline interferometric gravitational wave detectors is thermal displacement noise of the test mass mirrors and their suspensions. Suspension thermal noise results from mechanical dissipation in the fused silica suspension fibers suspending the test mass mirrors and is therefore an important noise source at operating frequencies between ∼10 and 30 Hz. This dissipation occurs due to a combination of thermoelastic damping, surface and bulk losses. Its effects can be reduced by optimizing the thermoelastic and surface loss, and these parameters are a function of the cross sectional dimensions of the fiber along its length. This paper presents a new apparatus capable of high resolution measurements of the cross sectional dimensions of suspension fibers of both rectangular and circular cross section, suitable for use in advanced detector mirror suspensions.

Invited article: CO2 laser production of fused silica fibers for use in interferometric gravitational wave detector mirror suspensions.

In 2000 the first mirror suspensions to use a quasi-monolithic final stage were installed at the GEO600 detector site outside Hannover, pioneering the use of fused silica suspension fibers in long baseline interferometric detectors to reduce suspension thermal noise. Since that time, development of the production methods of fused silica fibers has continued. We present here a review of a novel CO(2) laser-based fiber pulling machine developed for the production of fused silica suspensions for the next generation of interferometric gravitational wave detectors and for use in experiments requiring low thermal noise suspensions. We discuss tolerances, strengths, and thermal noise performance requirements for the next generation of gravitational wave detectors. Measurements made on fibers produced using this machine show a 0.8% variation in vertical stiffness and 0.05% tolerance on length, with average strengths exceeding 4 GPa, and mechanical dissipation which meets the requirements for Advanced LIGO thermal noise performance.

Optical modulation techniques for length sensing and control of optical cavities.

We present a discussion of the use of amplitude modulation techniques with regard to the length sensing and control of optical cavities for laser interferometric gravitational-wave detectors. Traditional radio-frequency amplitude modulation techniques automatically include phase modulation as a product of the modulation process, which can contaminate the signal after demodulation. In particular, with many length-sensing and control schemes the detected signals are demodulated in quadrature, which, in the case of a traditional amplitude modulation scheme, will result in offsets due to the additional phase modulation. We demonstrate this effect using a simple optical cavity configuration and show that minor adjustments to the modulator system can be used to compensate for the extra modulation components and provide additional flexibility.

Response of a Fabry-Perot optical cavity to phase modulation sidebands for use in electro-optic control systems.

The worldwide endeavor to build long baseline laser interferometers to detect and study gravitational radiation is well under way. In the German-British GEO600 project, it is proposed to pass the sidebands induced on the light by an electro-optic phase modulator through a Fabry-Perot optical cavity used in transmission, called a mode cleaner. This can be achieved when the phase modulation frequency is matched to the first longitudinal-mode frequency of the mode cleaner cavity so that both carrier and sidebands are transmitted. The primary function of the mode cleaner is to reduce the geometry fluctuations associated with the light, and thus any such noise induced by the modulation process is also suppressed. We present the results of an experiment that investigates the feasibility of passing modulation sidebands through an optical cavity and the factors limiting its success. In particular, we show that it is possible to avoid introducing excess noise associated with the transmitted sidebands, provided that certain experimental criteria are satisfied. The research was carried out on a prototype mode cleaner cavity built and tested at Glasgow University but which is similar to the equivalent apparatus planned for GEO600.

Light scattering described in the mode picture.

A system of orthonormal functions representing the eigenmodes of an optical resonator with perfectly spherical mirror surfaces has been described in the literature. In real experiments, however, the wave front of the passing beam will be deformed by surface irregularities or index inhomogeneities inside components traversed by the beam. We describe quantitatively the relative power transferred out of the fundamental mode into higher-order modes by these irregularities.