Automatic alignment-control system for a suspended Fabry-Perot cavity

In interferometric gravitational-wave detectors, most of the optical components are suspended by wires so that they are isolated from all kinds of forces except gravity. The requirement for the alignment of optical components to the laser beam is crucial. We have demonstrated a servo system developed for a Fabry-Perot cavity whose mirrors are suspended independently. We use mechanical modulation and a lock-in detection method to detect any misalignment. This system directly detects the relation between the axis of the laser beam and the axis of the cavity and automatically aligns the cavity to the laser beam. We confirmed that the intensity of the reflected light from the suspended Fabry-Perot cavity can be minimized with this system. Automated control of the alignment of the large-scale detectors is also discussed.     

Twin mirrors for laser interferometric gravitational-wave detectors

Gravitational-wave detectors such as Virgo and the laser interferometric gravitational-wave observatory (LIGO) use a long-baseline Michelson interferometer with Fabry-Perot cavities in the arms to search for gravitational waves. The symmetry between the two Fabry-Perot cavities is crucial to reduce the interferometer's sensitivity to the laser amplitude and frequency noise. To this purpose, the transmittance of the mirrors in both cavities should be as close as possible. This paper describes the realization and the characterization of the first twin large low-loss mirrors with transmissions differing by less than 0.01%.     

Shot noise in gravitational-wave detectors with Fabry-Perot arms

Shot-noise-limited sensitivity is calculated for gravitational-wave interferometers with Fabry-Perot arms, similar to those being installed at the Laser Interferometer Gravitational-Wave Observatory (LIGO) and the Italian-French Laser Interferometer Collaboration (VIRGO) facility. This calculation includes the effect of nonstationary shot noise that is due to phase modulation of the light. The resulting formula is experimentally verified by a test interferometer with suspended mirrors in the 40-m arms.     

Experimental demonstration of resonant sideband extraction in a sagnac interferometer

Sagnac interferometers have recently been proposed as a potential alternative to Michelson interferometers for the purpose of large-scale laser interferometric gravitational-wave detectors. We report on an experimental investigation of the Sagnac interferometer in two configurations: with arm cavities, and with resonant sideband extraction. Resonant sideband extraction was shown to increase the signal bandwidth by a factor of 6.5 compared with the arm cavity device, corresponding to an increase in sensitivity of as much as 6 dB for signals outside the arm cavity bandwidth. Moreover, we compare the performance of a Sagnac interferometer with resonant sideband extraction to a Michelson interferometer with resonant sideband extraction.     

Radiation pressure and stability of interferometric gravitational-wave detectors

The effect of radiation pressure on the stability of Fabry-Perot cavities with hanging mirrors is investigated. Such cavities will form an integral part of the laser interferometric gravitational-wave detectors that are being constructed around the globe. The mirrors are hung by means of a pendulum suspension and are locked by servo controls. We assume a realistic servo-control transfer function that satisfies the standard stability criteria. We find that for positive offsets from the resonance of the cavity the system is stable. However, we show that for negative offsets instabilities can occur, although the servo system has the effect of increasing the instability threshold, compared with the nonservoed case. Conditions for stability are finally given, involving the finesse of the cavity, the input power, the mass of the mirrors, the servo gain, and the phase detuning from perfect resonance. Gravitational-wave detectors with arm cavities having a finesse as low as approximately 200 could exhibit instabilities. Some implications for the locking of these detectors are finally given.     

Power-recycled resonant sideband extraction interferometer with polarization detection

Second-generation interferometric gravitational-wave detectors will use a technique called resonant sideband extraction (RSE) to improve the sensitivity in a narrow, tunable, frequency band. We present a configuration in which we use polarization detection to allow a continuously tunable power-recycled RSE interferometer for a control scheme similar to those of the first-generation detectors. A mathematical model describing this configuration and the results from a tabletop prototype are presented that demonstrate this configuration.     

Wavefront distortion of the reflected and diffracted beams produced by the thermoelastic deformation of a diffraction grating heated by a Gaussian laser beam

It may be advantageous in advanced gravitational-wave detectors to replace conventional beam splitters and Fabry-Perot input mirrors with diffractive elements. In each of these applications, the wavefront distortions produced by the absorption and subsequent heating of the grating can limit the maximum useful optical power. We present data on the wavefront distortions induced in a laser probe beam for both the reflected and diffracted beams from a grating that is heated by a Gaussian laser beam and compare these results to a simple theory of the wavefront distortions induced by thermoelastic deformations.     

High-gain power recycling of a Fabry-Perot Michelson interferometer for a gravitational-wave antenna

Power recycling was implemented on a fully suspended prototype interferometer with arm lengths of 20 m. A wave-front-sensing technique for alignment control of the suspended mirrors was also implemented, which allowed for several hours of stable operation. A power-recycling gain of greater than 12 was achieved, a significant increase over the highest gain in a suspended mirror Fabry-Perot Michelson interferometer reported to date.     

Dispersion-free, multiple-beam interferometer

A two-mirror Fabry-Perot interferometer is described haivng a dependence of transmission T? (ω) on frequency that is very different from the dependence T? (l) on the distance l between the mirrors. This feature is due to resonant dielectric mirrors in which the reflection phase and amplitude depend sharply on ω. The function T? (ω) can have several extrema ?T? /?ω = 0. At these points the interferometer becomes insensitive to a frequency change, whereas the dependence on l remains. Interferometer parameters are defined and some examples are considered. The dispersion-free interferometer can be used for measuring very small mechanical displacements with a light source with poor frequency stability. The applications to gravitational wave detectors and sensitive seismometers can be suggested if the small distance between the mirrors is acceptable.     

Signal extraction in a power-recycled michelson interferometer with fabry-perot arm cavities by use of a multiple-carrier frontal modulation scheme

We present a signal extraction scheme for longitudinal sensing and control of an interferometric gravitational-wave detector based on a multiple-frequency heterodyne detection technique. Gravitational-wave detectors use multiple-mirror resonant optical systems where resonance conditions must be satisfied for multiple degrees of freedom that are optically coupled. The multiple-carrier longitudinal-sensing technique provides sensitive signals for all interferometric lengths to be controlled and successfully decouples them. The feasibility of the technique is demonstrated on a tabletop-scale power-recycled Michelson interferometer with Fabry-Perot arm cavities, and the experimentally measured values of the length-sensing signals are in good agreement with theoretical calculations.     

Optical mode cleaner with suspended mirrors

We report on the development of a new type of mode cleaner that reduces any geometric noise of the laser beam in an interferometric gravitational-wave detector. The mode cleaner is a Fabry-Perot cavity that comprises independently suspended mirrors and works as a frequency-stabilization reference as well as a mode selector; the length of the cavity is 1 m. Stand-alone tests have shown at least a 30-dB reduction in the geometric fluctuation of the beam and a 60-dB reduction of the frequency noise of the laser. We have also succeeded in operating a 20-m Fabry-Perot prototype detector (at the National Astronomical Observatory, Tokyo, Japan) by using this mode cleaner.     

Sensing and control in dual-recycling laser interferometer gravitational-wave detectors

We introduce length-sensing and control schemes for the dual-recycled cavity-enhanced Michelson interferometer configuration proposed for the Advanced Laser Interferometer Gravitational Wave Observatory (LIGO). We discuss the principles of this scheme and show methods that allow sensing and control signals to be derived. Experimental verification was carried out in three benchtop experiments that are introduced. We present the implications of the results from these experiments for Advanced LIGO and other future interferometric gravitational-wave detectors.     

Principle of a two-output-difference interferometer for removing the most important interference distortions

This paper presents a two-output-difference interferometer for removing the most important interference distortions caused by nonlinear detectors. These distortions can be removed not only because the resulting interferogram is composed of the difference between the signals of the two detectors, but also because the modulated signals at each output have the same amplitude and opposite phases. Due to the use of two corner-cube mirrors fixed as a single moving element, the tilt and shearing problem will disappear. The effect of the corner-cube mirror deviation angle and the plane mirror tilt angle are investigated in detail, and the formulas of their tolerance are derived by means of modulation depth and phase error. The advantage of the interferometer enables it to be suitable for Fourier transform spectrometers.     

Interferometer Utilizing Free Masses as a Device for Measuring Gravitational Gradients

A Fabry–Perot–Michelson optical interferometer utilizing suspended mirrors is considered as a device for measuring low-frequency variations of the Earth's gravitational field. The operating principles of the instrument, the system for maintaining the angular alignment of the mirrors at the operating point, and a simplified model of the gravitational field are all described. The variations of the field at the location of the interferometer are modeled numerically and estimates are given of the magnitudes of the measurable effects. The results are used as a basis for modeling the operation of the instrument as a whole.     

Nonlinear damping in mechanical resonators made from carbon nanotubes and graphene

The theory of damping is discussed in Newton's Principia and has been tested in objects as diverse as the Foucault pendulum, the mirrors in gravitational-wave detectors and submicrometre mechanical resonators. In general, the damping observed in these systems can be described by a linear damping force. Advances in nanofabrication mean that it is now possible to explore damping in systems with one or more atomic-scale dimensions. Here we study the damping of mechanical resonators based on carbon nanotubes and graphene sheets. The damping is found to strongly depend on the amplitude of motion, and can be described by a nonlinear rather than a linear damping force. We exploit the nonlinear nature of damping in these systems to improve the figures of merit for both nanotube and graphene resonators. For instance, we achieve a quality factor of 100,000 for a graphene resonator.     

Compactness of lateral shearing interferometers

Imaging lateral shearing interferometers are good candidates for airborne or spaceborne Fourier-transform spectral imaging. For such applications, compactness is one key parameter. In this article, we compare the size of four mirror-based interferometers, the Michelson interferometer with roof-top (or corner-cube) mirrors, and the cyclic interferometers with two, three, and four mirrors, focusing more particularly on the last two designs. We give the expression of the translation they induce between the two exiting rays. We then show that the cyclic interferometer with three mirrors can be made quite compact. Nevertheless, the Michelson interferometer is the most compact solution, especially for highly diverging beams.     

Dynamic models of Fabry-Perot interferometers

Long-baseline, high-finesse Fabry-Perot interferometers can be used to make distance measurements that are precise enough to detect gravity waves. This level of sensitivity is achieved in part when the interferometer mirrors are isolated dynamically, with pendulum mounts and high-bandwidth cavity length control servos to reduce the effects of seismic noise. We present dynamical models of the cavity fields and signals of Fabry-Perot interferometers for use in the design and evaluation of length control systems for gravity-wave detectors. Models are described and compared with experimental data.     

Modeling the Dynamics of a Gravitational Interferometer in the Field of the Earth

The results are given of a numerical modeling of the behavior of a Fabry–Perot–Michelson optical interferometer utilizing suspended mirrors in the variable gravitational field of the Earth. The possibility is demonstrated of separating and reconstructing the signals in the interferometer arms and of filtering the coherent noise. A prediction is made of the maximum attainable sensitivity of the apparatus to variations of the gravitational gradient.     

Optical coating without phase dispersion for a Fabry-Perot interferometer

Phase dispersion induced by coatings can be a critical phenomenon in interferometry. We are interested in special mirrors intended for a Fabry-Perot interferometer with a high reflectance region and a low reflectance region in which phase dispersion on reflection must be avoided. We describe how a classical approach that uses the concepts of admittance and symmetrical multilayers allows the design of simple solutions.     

Test station for optical elements exposed to high power synchrotron radiation beams

An experimental setup including a Michelson interferometer and an infrared camera for studying mirrors, crystals and other surfaces exposed to high power synchrotron radiation beams is described. Its performance is illustrated by first results for different test mirrors such as SiC, Cu, Al and monochromator crystals. A short, low-field wiggler in the DORIS II storage ring served as a light source with 25 W/mrad at a particle energy of 3.7 GeV for first tests.