Experimental Demonstrations of Alignment and Mode Matching in Optical Cavities with Higher-Order Hermite-Gauss Modes.

Higher-order spatial laser modes have recently been investigated as candidates for reducing test-mass thermal noise in ground-based gravitational-wave detectors such as advanced LIGO. In particular, higher-order Hermite-Gauss (HG) modes have gained attention within the community for their more robust behaviors against random test-mass surface deformations and stronger sensing and control capacities. In this Letter we offer experimental investigations on various aspects of HG mode interferometry. We have generated purified HG modes up to the twelfth order HG_{6,6} mode, with a power conversion efficiency of 38.8% and 27.7% for the HG_{3,3} and HG_{6,6} modes respectively. We demonstrate for the first time the misalignment and mode mismatch-induced power coupling loss measurements for HG modes up to the HG_{6,6}. We report an excellent agreement with the extended numerical power loss factors that in the "small power loss" region converge to 2n+1 or n^{2}+n+1 for a misaligned or mode mismatched HG_{n,n} mode. We also demonstrate the wavefront sensing (WFS) signal measurement for HG modes up to the HG_{6,6}. The measurement result is accurately in accordance with theoretical WFS gain ß_{n,n-1}sqrt[n]+ß_{n,n+1}sqrt[n+1] for an HG_{n,n} mode, with ß_{n,n-1} being the beat coefficient of the adjacent HG_{n,n} and HG_{n-1,n} modes on a split photodetector.

Power coupling losses for misaligned and mode-mismatched higher-order Hermite-Gauss modes.

This paper analytically and numerically investigates misalignment and mode-mismatch-induced power coupling coefficients and losses as a function of Hermite-Gauss (HG) mode order. We show that higher-order HG modes are more susceptible to beam perturbations when, for example, coupling into optical cavities: the misalignment and mode-mismatch-induced power coupling losses scale linearly and quadratically with respect to the mode indices, respectively. As a result, the mode-mismatch tolerance for the ${{\rm HG}_{3,3}}$ mode is reduced to a factor of 0.28 relative to the currently used ${{\rm HG}_{0,0}}$ mode. This is a potential hurdle to using higher-order modes to reduce thermal noise in future gravitational-wave detectors.

Ultrastable optical components using adjustable commercial mirror mounts anchored in a ULE spacer.

This paper describes a novel, to the best of our knowledge, approach to build ultrastable interferometers using commercial mirror mounts anchored in an ultralow expansion (ULE) base. These components will play a critical role in any light particle search (ALPS) and will also be included in ground testing equipment for the upcoming laser interferometer space antenna (LISA) mission. Contrary to the standard ultrastable designs where mirrors are bonded to the spacers, ruling out any later modifications and alignments, our design remains flexible and allows the alignment of optical components at all stages to be optimized and changed. Here we present the dimensional stability and angular stability of two commercial mirror mounts characterized in a cavity setup. The long-term length change in the cavity did not exceed 30 nm and the relative angular stability was within 2 µrad, which meet the requirements for ALPS. We were also able to demonstrate 1pm/Hz length noise stability, which is a critical requirement for various subsystems in LISA. These results have led us to design similar opto-mechanical structures, which will be used in ground verification to test the LISA telescope.

Prospects for Detecting Gravitational Waves at 5 Hz with Ground-Based Detectors.

We propose an upgrade to Advanced LIGO (aLIGO), named LIGO-LF, that focuses on improving the sensitivity in the 5-30 Hz low-frequency band, and we explore the upgrade's astrophysical applications. We present a comprehensive study of the detector's technical noises and show that with technologies currently under development, such as interferometrically sensed seismometers and balanced-homodyne readout, LIGO-LF can reach the fundamental limits set by quantum and thermal noises down to 5 Hz. These technologies are also directly applicable to the future generation of detectors. We go on to consider this upgrade's implications for the astrophysical output of an aLIGO-like detector. A single LIGO-LF can detect mergers of stellar-mass black holes (BHs) out to a redshift of z≃6 and would be sensitive to intermediate-mass black holes up to 2000 M_{⊙}. The detection rate of merging BHs will increase by a factor of 18 compared to aLIGO. Additionally, for a given source the chirp mass and total mass can be constrained 2 times better than aLIGO and the effective spin 3-5 times better than aLIGO. Furthermore, LIGO-LF enables the localization of coalescing binary neutron stars with an uncertainty solid angle 10 times smaller than that of aLIGO at 30 Hz and 4 times smaller when the entire signal is used. LIGO-LF also significantly enhances the probability of detecting other astrophysical phenomena including the tidal excitation of neutron star r modes and the gravitational memory effects.

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.

Feedback control of optical beam spatial profiles using thermal lensing.

A method for active control of the spatial profile of a laser beam using adaptive thermal lensing is described. A segmented electrical heater was used to generate thermal gradients across a transmissive optical element, resulting in a controllable thermal lens. The segmented heater also allows the generation of cylindrical lenses, and provides the capability to steer the beam in both horizontal and vertical planes. Using this device as an actuator, a feedback control loop was developed to stabilize the beam size and position.

The generation of higher-order Laguerre-Gauss optical beams for high-precision interferometry.

Thermal noise in high-reflectivity mirrors is a major impediment for several types of high-precision interferometric experiments that aim to reach the standard quantum limit or to cool mechanical systems to their quantum ground state. This is for example the case of future gravitational wave observatories, whose sensitivity to gravitational wave signals is expected to be limited in the most sensitive frequency band, by atomic vibration of their mirror masses. One promising approach being pursued to overcome this limitation is to employ higher-order Laguerre-Gauss (LG) optical beams in place of the conventionally used fundamental mode. Owing to their more homogeneous light intensity distribution these beams average more effectively over the thermally driven fluctuations of the mirror surface, which in turn reduces the uncertainty in the mirror position sensed by the laser light. We demonstrate a promising method to generate higher-order LG beams by shaping a fundamental Gaussian beam with the help of diffractive optical elements. We show that with conventional sensing and control techniques that are known for stabilizing fundamental laser beams, higher-order LG modes can be purified and stabilized just as well at a comparably high level. A set of diagnostic tools allows us to control and tailor the properties of generated LG beams. This enabled us to produce an LG beam with the highest purity reported to date. The demonstrated compatibility of higher-order LG modes with standard interferometry techniques and with the use of standard spherical optics makes them an ideal candidate for application in a future generation of high-precision interferometry.

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.