C. Bond

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.

All-sky search for long-duration gravitational wave transients with LIGO

We present the results of a search for long-duration gravitational wave transients in two sets of data collected by the LIGO Hanford and LIGO Livingston detectors between November 5, 2005 and September 30, 2007, and July 7, 2009 and October 20, 2010, with a total observational time of 283.0 days and 132.9 days, respectively. The search targets gravitational wave transients of duration 10 - 500 seconds in a frequency band of 40 - 1000 Hz, with minimal assumptions about the signal waveform, polarization, source direction, or time of occurrence. All candidate triggers were consistent with the expected background; as a result we set 90% confidence upper limits on the rate of long-duration gravitational wave transients for different types of gravitational wave signals. We also report upper limits on the source rate density per year per Mpc^3 for specific signal models. These are the first results from an all-sky search for unmodeled long-duration transient gravitational waves.

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.

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 study of the KAGRA output mode cleaner

Most second-generation gravitational-wave detectors employ an optical resonator called an output mode cleaner (OMC), which filters out junk light from the signal and the reference light, before it reaches the detection photodiode located at the asymmetric port of the large-scale interferometer. The optical parameters of the OMC should be carefully chosen to satisfy the requirements to filter out unwanted light whilst transmitting the gravitational-wave signal. We use the simulation program FINESSE and realistic mirror phase maps that have the same surface quality as the KAGRA test masses to find out a proper design of the KAGRA OMC.

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.

The effect of mirror surface distortions on higher order Laguerre-Gauss modes

Higher order Laguerre-Gauss (LG) beams have been proposed for use in future generation gravitational wave detectors for their potential to reduce the effects of the thermal noise of the test masses. However, it has been reported that due to the degeneracy of higher order modes using these beams will be extremely challenging. Our aim was to quantify these degeneracy effects. We present a new analytical approximation to compute the coupling between different LG modes, verified with simulation results of realistic arm cavities. This method is applied to Advanced LIGO mirror maps and used to derive requirements for mirrors for the use of the LG33 beam.