P. Fulda

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.

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.

Generation of high-purity higher-order Laguerre-Gauss beams at high laser power

We have investigated the generation of highly pure higher-order Laguerre-Gauss (LG) beams at high laser power of order 100 W, the same regime that will be used by second-generation gravitational wave interferometers such as Advanced LIGO. We report on the generation of a helical-type LG33 mode with a purity of order 97% at a power of 83 W, the highest power ever reported in literature for a higher-order LG mode. This is a fundamental step in proving technical readiness for use of LG beams in gravitational wave interferometers of future generations.

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 LG{sub 33} mode in optical resonators. We show that the Pound-Drever-Hall error signal for a LG{sub 33} mode in a linear optical resonator is identical to that of the more commonly used LG{sub 00} mode, and demonstrate the feedback control of the resonator with a LG{sub 33} mode. We succeeded to increase the mode purity of a LG{sub 33} 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.

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.

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 (aLIGO) 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 the thermal state of the aLIGO 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.

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.

Alignment sensing for optical cavities using radio-frequency jitter modulation

Alignment sensing is often required in precision interferometry applications such as Advanced LIGO in order to achieve the optimum performance. Currently favored sensing schemes rely on the use of two separate radio-frequency (RF) quadrant photodetectors and Gouy phase telescopes to determine the alignment of a beam relative to an optical cavity axis. In this paper, we demonstrate an alternative sensing scheme that has potential advantages over the current standard schemes. We show that by using electro-optic beam deflectors to impose RF jitter sidebands on a beam, it is possible to extract full alignment signals for two in-line optical cavities from just one single-element photodetector in reflection of each cavity.