L. Carbone

Update on quadruple suspension design for Advanced LIGO

We describe the design of the suspension systems for the major optics for Advanced LIGO, the upgrade to LIGO—the Laser Interferometric Gravitational-Wave Observatory. The design is based on that used in GEO600—the German/UK interferometric gravitational wave detector, with further development to meet the more stringent noise requirements for Advanced LIGO. The test mass suspensions consist of a four-stage or quadruple pendulum for enhanced seismic isolation. To minimize suspension thermal noise, the final stage consists of a silica mirror, 40 kg in mass, suspended from another silica mass by four silica fibres welded to silica ears attached to the sides of the masses using hydroxide-catalysis bonding. The design is chosen to achieve a displacement noise level for each of the seismic and thermal noise contributions of 10^(−19) m/√Hz at 10 Hz, for each test mass. We discuss features of the design which has been developed as a result of experience with prototypes and associated investigations.

Sensors and actuators for the Advanced LIGO mirror suspensions

We have developed, produced and characterized integrated sensors, actuators and the related read-out and drive electronics that will be used for the control of the Advanced LIGO suspensions. The overall system consists of the BOSEMs (a displacement sensor with an integrated electromagnetic actuator), the satellite boxes (the BOSEM readout and interface electronics) and six different types of coil-driver units. In this paper, we present the design of this read-out and control system, we discuss the related performance relevant for the Advanced LIGO suspensions, and we report on the experimental activity finalized at the production of the instruments for the Advanced LIGO detectors.

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.

Realistic polarizing Sagnac topology with DC readout for the Einstein Telescope

The Einstein Telescope (ET) is a proposed future gravitational wave detector. Its design is original, using a triangular orientation of three detectors and a xylophone configuration, splitting each detector into one high-frequency and one low-frequency system. In other aspects the current design retains the dual-recycled Michelson interferometer typical of current detectors, such as Advanced LIGO. In this paper, we investigate the feasibility of replacing the low-frequency part of the ET detectors with a Sagnac interferometer. We show that a Sagnac interferometer, using realistic optical parameters based on the ET design, could provide a similar level of radiation pressure noise suppression without the need for a signal recycling mirror and the extensive filter cavities. We consider the practical issues of a realistic, power-recycled Sagnac, using linear arm cavities and polarizing optics. In particular, we investigate the effects of nonperfect polarizing optics and propose a new method for the generation of a local oscillator field similar to the DC readout scheme of current detectors.

Invariance of waveguide grating mirrors to lateral displacement phase shifts

We present a method to analyze the coupling of lateral displacements in nanoscale structures, in particular waveguide grating mirrors (WGMs), into the phase of a reflected Gaussian beam using a finite-difference time-domain simulation. Such phase noise is of interest for using WGMs in high-precision interferometry. We show that, to the precision of our simulations (10(-7) rad), waveguide mirrors do not couple lateral displacement into phase noise of a reflected beam and that WGMs are therefore not subject to the same stringent alignment requirements as previously proposed layouts using diffraction gratings.

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.

Design of high-density electron spin-polarized test masses

We present a method of designing test masses with a high density of electron spins for use in mechanical experiments searching for weak spin interactions. Nested arrangements of rare-earth permanent magnets are shown to achieve spin densities of order 1024spins kg−1 together with stray magnetic fields at negligible levels. A full magnetostatic analysis of the proposed designs is presented, the mechanical feasibility is analyzed and the related manufacturing issues are addressed.

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.

Review of the Laguerre-Gauss mode technology research program at Birmingham

Gravitational wave detectors of the advanced generation are expected to be limited in sensitivity by thermal noise of the optics. The reduction of this noise is therefore of high importance for future detectors which aim to surpass the sensitivity of the advanced generation. A proposed method for reducing the impact of this noise is to use higher-order Laguerre-Gauss (LG) modes for the readout beam, as opposed to the currently used fundamental mode. We present here a synopsis of the research program undertaken by the University of Birmingham into the suitability of LG mode technology for future gravitational wave detectors. This will cover our previous and current work on this topic, from initial simulations and table-top LG mode experiments up to implementation in a prototype scale suspended cavity and high-power laser bench.