Experimental demonstration of higher-order Laguerre-Gauss mode interferometry

The compatibility of higher-order Laguerre-Gauss (LG) modes with interferometric technologies commonly used in gravitational wave detectors is investigated. In this paper we present the first experimental results concerning the performance of the LG33 mode in optical resonators. We show that the Pound-Drever-Hall error signal for a LG33 mode in a linear optical resonator is identical to that of the more commonly used LG00 mode, and demonstrate the feedback control of the resonator with a LG33 mode. We succeeded to increase the mode purity of a LG33 mode generated using a spatial-light modulator from 51% to 99% upon transmission through a linear optical resonator. We further report the experimental verification that a triangular optical resonator does not transmit helical LG modes

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.Comment: 7 Pages, 7 figure

Phase effects 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.Comment: 14 pages, 8 figures, submitted to Optics Expres

Astro2020 White Paper: A Direct Measure of Cosmic Acceleration

Nearly a century after the discovery that we live in an expanding Universe, and two decades after the discovery of accelerating cosmic expansion, there remains no direct detection of this acceleration via redshift drift - a change in the cosmological expansion velocity versus time. Because cosmological redshift drift directly determines the Hubble parameter H(z), it is arguably the cleanest possible measurement of the expansion history, and has the potential to constrain dark energy models (e.g. Kim et al. 2015). The challenge is that the signal is small - the best observational constraint presently has an uncertainty several orders of magnitude larger than the expected signal (Darling 2012). Nonetheless, direct detection of redshift drift is becoming feasible, with upcoming facilities such as the ESO-ELT and SKA projecting possible detection within two to three decades. This timescale is uncomfortably long given the potential of this cosmological test. With dedicated experiments it should be possible to rapidly accelerate progress and detect redshift drift with only a five-year observational baseline. Such a facility would also be ideal for precision radial velocity measurements of exoplanets, which could be obtained as a byproduct of the ongoing calibration measurements for the experiment.Comment: White paper submitted to the Astro2020 Decadal Survey. 6 page

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.Comment: 12 pages Submitted to PRD 19/07/201

In-situ characterization of the thermal state of resonant optical interferometers via tracking of their higher-order mode resonances

Thermal lensing in resonant optical interferometers such as those used for gravitational wave detection is a concern due to the negative impact on control signals and instrument sensitivity. In this paper we describe a method for monitoring the thermal state of such interferometers by probing the higher-order spatial mode resonances of the cavities within them. We demonstrate the use of this technique to measure changes in the Advanced LIGO input mode cleaner cavity geometry as a function of input power, and subsequently infer the optical absorption at the mirror surfaces at the level of 1 ppm per mirror. We also demonstrate the generation of a useful error signal for thermal state of the Advanced LIGO power recycling cavity by continuously tracking the first order spatial mode resonance frequency. Such an error signal could be used as an input to thermal compensation systems to maintain the interferometer cavity geometries in the presence of transients in circulating light power levels, thereby maintaining optimal sensitivity and maximizing the duty-cycle of the detectors

Astro2020 Project White Paper: The Cosmic Accelerometer

We propose an experiment, the Cosmic Accelerometer, designed to yield velocity precision of $\leq 1$ cm/s with measurement stability over years to decades. The first-phase Cosmic Accelerometer, which is at the scale of the Astro2020 Small programs, will be ideal for precision radial velocity measurements of terrestrial exoplanets in the Habitable Zone of Sun-like stars. At the same time, this experiment will serve as the technical pathfinder and facility core for a second-phase larger facility at the Medium scale, which can provide a significant detection of cosmological redshift drift on a 6-year timescale. This larger facility will naturally provide further detection/study of Earth twin planet systems as part of its external calibration process. This experiment is fundamentally enabled by a novel low-cost telescope technology called PolyOculus, which harnesses recent advances in commercial off the shelf equipment (telescopes, CCD cameras, and control computers) combined with a novel optical architecture to produce telescope collecting areas equivalent to standard telescopes with large mirror diameters. Combining a PolyOculus array with an actively-stabilized high-precision radial velocity spectrograph provides a unique facility with novel calibration features to achieve the performance requirements for the Cosmic Accelerometer