Effects of mode degeneracy in the LIGO Livingston Observatory recycling cavity

We analyze the electromagnetic fields in a Pound-Drever-Hall locked, marginally unstable, Fabry-Perot cavity as a function of small changes in the cavity length during resonance. More specifically, we compare the results of a detailed numerical model with the behavior of the recycling cavity of the Laser Interferometer Gravitational-wave Observatory (LIGO) detector that is located in Livingston, Louisiana. In the interferometer's normal mode of operation, the recycling cavity is stabilized by inducing a thermal lens in the cavity mirrors with an external CO2 laser. During the study described here, this thermal compensation system was not operating, causing the cavity to be marginally optically unstable and cavity modes to become degenerate. In contrast to stable optical cavities, the modal content of the resonating beam in the uncompensated recycling cavity is significantly altered by very small cavity length changes. This modifies the error signals used to control the cavity length in such a way that the zero crossing point is no longer the point of maximum power in the cavity nor is it the point where the input beam mode in the cavity is maximized.Comment: Eight pages in two-column format. Six color figures. To be published JOSA

A General Approach to Optomechanical Parametric Instabilities

We present a simple feedback description of parametric instabilities which can be applied to a variety of optical systems. Parametric instabilities are of particular interest to the field of gravitational-wave interferometry where high mechanical quality factors and a large amount of stored optical power have the potential for instability. In our use of Advanced LIGO as an example application, we find that parametric instabilities, if left unaddressed, present a potential threat to the stability of high-power operation

Resonant Dampers for Parametric Instabilities in Gravitational Wave Detectors

Advanced gravitational wave interferometric detectors will operate at their design sensitivity with nearly 1MW of laser power stored in the arm cavities. Such large power may lead to the uncontrolled growth of acoustic modes in the test masses due to the transfer of optical energy to the mechanical modes of the arm cavity mirrors. These parametric instabilities have the potential of significantly compromising the detector performance and control. Here we present the design of "acoustic mode dampers" that use the piezoelectric effect to reduce the coupling of optical to mechanical energy. Experimental measurements carried on an Advanced LIGO-like test mass shown a 10-fold reduction in the amplitude of several mechanical modes, thus suggesting that this technique can greatly mitigate the impact of parametric instabilities in advanced detectors

Thermo-optic noise in coated mirrors for high-precision optical measurements

Thermal fluctuations in the coatings used to make high-reflectors are becoming significant noise sources in precision optical measurements and are particularly relevant to advanced gravitational wave detectors. There are two recognized sources of coating thermal noise, mechanical loss and thermal dissipation. Thermal dissipation causes thermal fluctuations in the coating which produce noise via the thermo-elastic and thermo-refractive mechanisms. We treat these mechanisms coherently, give a correction for finite coating thickness, and evaluate the implications for Advanced LIGO

Second generation instruments for the Laser Interferometer Gravitational Wave Observatory (LIGO)

The interferometers being planned for second generation LIGO promise and order of magnitude increase in broadband strain sensitivity--with the corresponding cubic increase in detection volume--and an extension of the observation band to lower frequencies. In addition, one of the interferometers may be designed for narrowband performance, giving further improved sensitivity over roughly an octave band above a few hundred Hertz. This article discusses the physics and technology of these new interferometer designs, and presents their projected sensitivity spectra.Comment: Proceedings of the SPIE conference on Astronomical Telescopes and Instrumentations, 22-28 Aug 2002, Waikoloa, HI, US

Laser interferometry for the Big Bang Observer

The Big Bang Observer is a proposed space-based gravitational-wave detector intended as a follow on mission to the Laser Interferometer Space Antenna (LISA). It is designed to detect the stochastic background of gravitational waves from the early universe. We discuss how the interferometry can be arranged between three spacecraft for this mission and what research and development on key technologies are necessary to realize this scheme

Optimal configurations of filter cavity in future gravitational-wave detectors

Sensitivity of future laser interferometric gravitational-wave detectors can be improved using squeezed light with frequency-dependent squeeze angle and/or amplitude, which can be created using additional so-called filter cavities. Here we compare performances of several variants of this scheme, proposed during last years, assuming the case of a single relatively short (tens of meters) filter cavity suitable for implementation already during the life cycle of the second generation detectors, like Advanced LIGO. Using numerical optimization, we show that the phase filtering scheme proposed by Kimble et al [Phys.Rev.D 65, 022002 (2001)] looks as the best candidate for this scenario.Comment: 17 pages, 5 figure

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\,ppm 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$^\circ$--80$^\circ$ 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.Comment: 9 pages, 10 figure

Self-cooling of a movable mirror to the ground state using radiation pressure

We show that one can cool a micro-mechanical oscillator to its quantum ground state using radiation pressure in an appropriately detuned cavity (self-cooling). From a simple theory based on Heisenberg-Langevin equations we find that optimal self-cooling occurs in the good cavity regime, when the cavity bandwidth is smaller than the mechanical frequency, but still larger than the effective mechanical damping. In this case the intracavity field and the vibrational mechanical mode coherently exchange their fluctuations. We also present dynamical calculations which show how to access the mirror final temperature from the fluctuations of the field reflected by the cavity.Comment: 4 pages, 3 figure