K. Kokeyama

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.

The advanced LIGO input optics

The advanced LIGO gravitational wave detectors are nearing their design sensitivity and should begin taking meaningful astrophysical data in the fall of 2015. These resonant optical interferometers will have unprecedented sensitivity to the strains caused by passing gravitational waves. The input optics play a significant part in allowing these devices to reach such sensitivities. Residing between the pre-stabilized laser and the main interferometer, the input optics subsystem is tasked with preparing the laser beam for interferometry at the sub-attometer level while operating at continuous wave input power levels ranging from 100 mW to 150 W. These extreme operating conditions required every major component to be custom designed. These designs draw heavily on the experience and understanding gained during the operation of Initial LIGO and Enhanced LIGO. In this article, we report on how the components of the input optics were designed to meet their stringent requirements and present measurements showing how well they have lived up to their design.

Achieving resonance in the Advanced LIGO gravitational-wave interferometer

Interferometric gravitational-wave detectors are complex instruments comprised of a Michelson interferometer enhanced by multiple coupled cavities. Active feedback control is required to operate these instruments and keep the cavities locked on resonance. The optical response is highly nonlinear until a good operating point is reached. The linear operating range is between 0.01% and 1% of a fringe for each degree of freedom. The resonance lock has to be achieved in all five degrees of freedom simultaneously, making the acquisition difficult. Furthermore, the cavity linewidth seen by the laser is only _(~1) Hz, which is four orders of magnitude smaller than the linewidth of the free running laser. The arm length stabilization system is a new technique used for arm cavity locking in Advanced LIGO. Together with a modulation technique utilizing third harmonics to lock the central Michelson interferometer, the Advanced LIGO detector has been successfully locked and brought to an operating point where detecting gravitational-waves becomes feasible.

Higher order Laguerre-Gauss mode degeneracy in realistic, high finesse cavities

Higher order Laguerre-Gauss (LG) beams have been proposed for use in future gravitational wave detectors, such as upgrades to the Advanced LIGO detectors and the Einstein Telescope, for their potential to reduce the effects of the thermal noise of the test masses. This paper details the theoretical analysis and simulation work carried out to investigate the behaviour of LG beams in realistic optical setups, in particular the coupling between different LG modes in a linear cavity. We present a new analytical approximation to compute the coupling between modes, using Zernike polynomials to describe mirror surface distortions. We apply this method in a study of the behaviour of the LG33 mode within realistic arm cavities, using measured mirror surface maps from the Advanced LIGO project. We show mode distortions that can be expected to arise due to the degeneracy of higher order spatial modes within such cavities and relate this to the theoretical analysis. Finally we identify the mirror distortions which cause significant coupling from the LG33 mode into other order 9 modes and derive requirements for the mirror surfaces.

Residual amplitude modulation in interferometric gravitational wave detectors

The effects of residual amplitude modulation (RAM) in laser interferometers using heterodyne sensing can be substantial and difficult to mitigate. In this work, we analyze the effects of RAM on a complex laser interferometer used for gravitational wave detection. The RAM introduces unwanted offsets in the cavity length signals and thereby shifts the operating point of the optical cavities from the nominal point via feedback control. This shift causes variations in the sensing matrix, and leads to degradation in the performance of the precision noise subtraction scheme of the multiple-degree-of-freedom control system. In addition, such detuned optical cavities produce an optomechanical spring, which also perturbs the sensing matrix. We use our simulations to derive requirements on RAM for the Advanced LIGO (aLIGO) detectors, and show that the RAM expected in aLIGO will not limit its sensitivity.

Interferometers for Displacement-Noise-Free Gravitational-Wave Detection

We propose a class of displacement- and laser-noise-free gravitational-wave-interferometer configurations, which does not sense nongeodesic mirror motion and laser noise, but provides a nonvanishing gravitational-wave signal. Our interferometers consist of four mirrors and two beam splitters, which form four Mach-Zehnder interferometers. By contrast to previous works, no composite mirrors with multiple reflective surfaces are required. Each mirror in our configuration is sensed redundantly, by at least two pairs of incident and reflected beams. Displacement- and laser-noise-free detection is achieved when output signals from these four interferometers are combined appropriately. Our 3-dimensional interferometer configuration has a low-frequency response proportional to f2, which is better than the f3 achievable by previous 2-dimensional configurations.

The Experimental plan of the 4m Resonant Sideband Extraction Prototype for The LCGT

The 4m Resonant Sideband Extraction (RSE) interferometer is a planned prototype of the LCGT interferometer. The aim of the experiment is to operate a powerrecycled Broadband RSE interferometer with suspended optics and to achieve diagonalization of length signals of the central part of the interferometer directly through the optical setup. Details of the 4m RSE interferometer control method as well as the design of the experimental setup will be presented.

Interferometer phase noise due to beam misalignment on diffraction gratings

All-reflective interferometer configurations have been proposed for the next generation of gravitational wave detectors, with diffractive elements replacing transmissive optics. However, an additional phase noise creates more stringent conditions for alignment stability. A framework for alignment stability with the use of diffractive elements was required using a Gaussian model. We successfully create such a framework involving modal decomposition to replicate small displacements of the beam (or grating) and show that the modal model does not contain the phase changes seen in an otherwise geometric planewave approach. The modal decomposition description is justified by verifying experimentally that the phase of a diffracted Gaussian beam is independent of the beam shape, achieved by comparing the phase change between a zero-order and first-order mode beam. To interpret our findings we employ a rigorous time-domain simulation to demonstrate that the phase changes resulting from a modal decomposition are correct, provided that the coordinate system which measures the phase is moved simultaneously with the effective beam displacement. This indeed corresponds to the phase change observed in the geometric planewave model. The change in the coordinate system does not instinctively occur within the analytical framework, and therefore requires either a manual change in the coordinate system or an addition of the geometric planewave phase factor.

Phase effects in Gaussian beams on diffraction gratings

Diffraction gratings have been proposed as replacements for transmissive optical elements in the next generation of gravitational wave detectors. However, they couple additional alignment noise to phase noise, and current models are based on unrealistic plane-wave expansion theories. There is a need for a description of grating-related phase noise which is compatible with standard interferometer tools. In this paper we investigate the grating-related phase shift by presenting a fully analytical Gaussian model for the phase accumulation of a displaced beam when diffracted from a grating. We consider a first-order modal decomposition as the method employed by simulation tools for off-axis beams. We show that the phase distribution of a typical displaced beam and a decomposed beam is accurate to within 3.9 × 10−8 radians. However, we find that the grating-related phase noise is not present, and this is further validated experimentally by the absence of a phase shift in beams with different modes. The phase noise must therefore be implemented manually into existing interferometer simulation tools.

Development of a signal-extraction scheme for resonant sideband extraction

As a future plan, an advanced gravitational-wave detector will employ an optical configuration of resonant sideband extraction (RSE), achieved with an additional mirror at the signal-detection port of the power-recycled Fabry–Perot Michelson interferometer. To control the complex coupled cavity system, one of the most important design issues is how to extract the longitudinal control signals of the cavities. We have developed a new signal-extraction scheme which provides an appropriate sensing matrix. The new method uses two sets of sidebands: one of the sideband components satisfies the critical coupling condition for the RSE interferometer and reaches the signal-extraction port, and the other sideband is completely reflected by the Michelson interferometer. They provide a diagonalized sensing matrix and enable the RSE control to be robust.