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The arm cavities of real gravitational wave detectors can show small deviations like a tilt or a spatial shift between the cavity mirrors. These deviations lead to a separation of the optical mode centres with respect to the mirrorʼs centre. In this Letter we perform the computation of parametric instable modes considering the described displacement. We further analyse the possibility of parametric oscillatory instability in the Advanced LIGO interferometer for the case of a displaced arm cavity. Our results reveal an additional number of optical and elastic mode combinations due to a displacement that can give rise to the undesirable effect of parametric oscillatory instability.

We discuss the importance of accurate calculation of axially-symmetrical elastic modes frequencies and forms in test masses (mirrors) of Advanced LIGO interferometer using the method of superposition to analyse the effect of parametric oscillatory instability. This method consists in possibility to construct analytical expressions for partial solutions of media motion equation in the cylindrical coordinates which allow to satisfy all zero boundary conditions. Obtained results allow to predict more exactly (in comparison with numerical calculations) the number of combinations of optical and elastic modes that can create undesirable effect of parametric oscillatory instability.

We discuss the importance of accurate numerical calculation of elastic modes in the mirrors of Advanced LIGO to enable precise predictions of the problem of parametric oscillatory instability. We propose accuracy estimations through use of analytical solutions based on Chree–Lamb modes. Small deviations from cylindrical test mass shape may produce splitting of non-axial symmetric elastic modes into doublets. This splitting may increase the possibility of parametric oscillatory instability.

We present analysis of undesirable effect of parametric instability in signal recycled GEO 600 interferometer. The basis for this effect is provided by excitation of additional (Stokes) optical mode, having frequency ω 1 , and mirror elastic mode, having frequency ω m , when the optical energy stored in the main FP cavity mode, having frequency ω 0 , exceeds a certain threshold and detuning Δ = ω 0 − ω 1 − ω m is small. We discuss the potential of observing parametric instability and its precursors in GEO 600 interferometer. This approach provides the best option to get familiar with this phenomenon, to develop experimental methods to depress it and to test the effectiveness of these methods in situ.

The basis of undesirable effect of parametric oscillatory instability in optical interferometer is provided by excitation of the additional (Stokes) optical mode having frequency ω 1 , and the mirror elastic mode, having frequency ω m . It appears when optical energy stored in the main mode, with frequency ω 0 , exceeds a certain threshold and the frequencies are related as ω 0 ≃ ω 1 + ω m . We analyze the time evolution of parametric instability which allows predicting the characteristics of precursors of parametric instability. Observation of such precursors may help avoid parametric instability.

The basis of undesirable effect of parametric oscillatory instability in signal recycled LIGO interferometer is the excitation of the additional (Stokes) optical mode, with frequency ω 1 , and the mirror elastic mode, with frequency ω m , when optical energy stored in the main mode, with frequency ω 0 , exceeds the certain threshold and the frequencies are related as ω 0 ≃ ω 1 + ω m . We analyze parametric instability in the general case when eigen frequencies of Fabry–Perot (FP) cavities in arms of interferometer are detuned from each other and show that parametric instability in this interferometer is relatively small due to small bandwidth of interferometer. We propose to “scan” the frequency range where parametric instability may take place by varying the position of signal recycling mirror.

Synthetic fused silica fibres of rectangular cross section, known as ‘ribbon’ fibres, are currently the baseline design for the suspension elements of the lowest stage of the test mass suspensions for the planned Advanced LIGO detector. In this Letter we present the first measurements of mechanical loss factors of synthetic fused silica ribbons of a type potentially suitable for this purpose and estimate the level of dissipation associated with the surface of the ribbons. We also present measurements of breaking stress which demonstrate that ribbons can have breaking stresses up to 3.7 GPa, giving a significant margin of safety over the proposed 0.76 GPa working load for Advanced LIGO.

The Laser Interferometer Gravitational wave Observatory (LIGO) is a network of first generation interferometric detectors aiming to make the first direct observations of gravitational waves. Progress in the commissioning of the detectors has brought them within a factor of two of their design sensitivity near 150 Hz during the most recent science run of the instruments in March of 2005. Further improvements took place in the instruments since then and operating them at design sensitivity together with high duty cycle is expected by the end of 2005. This Letter surveys the status of the LIGO instruments and discusses results and prospects of direct detections of gravitational waves bursts.

The results of experimental investigation of the mechanical noise produced by fused silica fibers at room temperature is reported. The best achieved resolution is about 0.01 k T for the modes with quality factor from 105 to 107. Over the 90 hours of observation no excess (additional to Brownian) noise was found in fibers loaded at 4%–50% from breaking stress.

We have directly observed broadband thermal noise in silica/tantala coatings in a high-sensitivity Fabry-Perot interferometer. Our result agrees well with the prediction based on indirect, ring-down measurements of coating mechanical loss, validating that method as a tool for the development of advanced interferometric gravitational-wave detectors., Final version synchronized with publication in Phys. Lett. A

We evaluate the parametric phenomenon for the main optical mode coupled to other resonant waves excited by acoustic interaction with the mirrors of a Fabry–Perot. We apply this to the arm cavity of a gravitational wave antenna. Under certain assumptions we find that the amplitude of these parasitic modes is expressed by analytic solutions that are always damped. We analyze both the zero detuning and the detuned case and solve the equations. The form of the solution shows that for equally spaced and excited cavity modes the instability is expressed by a threshold condition, which is well approximated for LIGO arm resonator parameters.

The use of fused-silica ribbons as suspensions in gravitational wave interferometers can result in significant improvements in pendulum mode thermal noise. Surface loss sets a lower bound to the level of noise achievable, at what level depends on the dissipation depth and other physical parameters. For LIGO II, the high breaking strength of pristine fused silica filaments, the correct choice of ribbon aspect ratio (to minimize thermoelastic damping), and low dissipation depth combined with the other achievable parameters can reduce the pendulum mode thermal noise in a ribbon suspension well below the radiation pressure noise. Despite producing higher levels of pendulum mode thermal noise, cylindrical fiber suspensions provide an acceptable alternative for LIGO II, should unforeseen problems with ribbon suspensions arise., Comment: Submitted to Physics Letters A (Dec. 14, 1999). Resubmitted to Physics Letters A (Apr. 3, 2000) after internal (LSC) review process. PACS - 04.80.Nn, 95.55.Ym, 05.40.Ca

Coupling between asymmetry in absorption and laser power fluctuations may be a source of noise in gravitational-wave interferometric detectors. This effect is negligible for the first generation of detectors such as LIGO/VIRGO, but attention should be paid to the reproducibility of the thermal parameters in the next generation, where the noise we consider could be comparable to the shot noise.

Sensitivity enhancements in the laser interferometer gravitational wave observatory (LIGO) project's 40 m interferometer have been achieved through two major instrumental improvements. Improved vibration isolation has reduced the noise due to ground motion. New test masses with less mechanical dissipation were installed to lower the thermal noise associated with mirror vibrations. The minimum interferometer noise (square root of the spectral density of apparent differential displacement) reached 3 x 10^(-19) m/Hz^(1/2) near 450 Hz.

In interferometric gravitational wave detectors like VIRGO and LIGO, the relative distances of the optical elements must be controlled with extreme precision. We develop two schemes which, based on phase modulation of the incident laser beam, give error signals for all necessary degrees of freedom. These schemes are compatible with the required sensitivity to gravitational waves.

The results of measurement of optical mirror coating are presented. These results indicate that Standard Quantum Limit of sensitivity can be reached in the second stage of LIGO project if it is limited by thermoelastic noise in the coating only., 5 pages