J. Agresti

Optimized multilayer dielectric mirror coatings for gravitational wave interferometers

The limit sensitivity of interferometric gravitational wave antennas is set by the thermal noise in the dielectric mirror coatings. These are currently made of alternating quarter-wavelength high/low index material layers with low mechanical losses. The quarter-wavelength design yields the maximum reflectivity for a fixed number of layers, but not the lowest noise for a prescribed reflectivity. This motivated our recent investigation of optimal thickness configurations, which guarantee the lowest thermal noise for a targeted reflectivity. This communication provides a compact overview of our results, involving nonperiodic genetically-engineered and truncated periodically-layered configurations. Possible implications for the advanced Laser Interferometer Gravitational wave Observatory (LIGO) are discussed.

Analytic structure of a family of hyperboloidal beams of potential interest for advanced LIGO

This paper is concerned with a study of the analytic structure of a family of hyperboloidal beams introduced by Bondarescu and Thorne which generalizes the nearly-flat and nearly-concentric mesa beam configurations of interest for advanced LIGO. Capitalizing on certain results from the applied optics literature on flat-top beams, a physically-insightful and computationally-effective representation is derived in terms of rapidly-converging Gauss-Laguerre expansions. A generalization (involving fractional Fourier transform operators of complex order) of some recently discovered duality relations between the nearly-flat and nearly-concentric mesa configurations is obtained. Possible implications for the advanced-LIGO optical cavity design are discussed.

Duality relation between nonspherical mirror optical cavities and its application to gravitational-wave detectors

In this paper, we analytically prove a unique duality relation between the eigenspectra of paraxial optical cavities with nonspherical mirrors: a one-to-one mapping between eigenmodes and eigenvalues of cavities deviating from flat mirrors by h(r) and cavities deviating from concentric mirrors by -h(r), where h need not be a small perturbation. We then illustrate its application to optical cavities, proposed for advanced interferometric gravitational-wave detectors, where the mirrors are designed to support beams with rather flat intensity profiles over the mirror surfaces. This unique mapping might be very useful in future studies of alternative optical designs for advanced gravitational wave interferometers or experiments employing optical cavities with nonstandard mirrors.

Perspectives on beam-shaping optimization for thermal-noise reduction in advanced gravitational-wave interferometric detectors: Bounds, profiles, and critical parameters

Suitable shaping (in particular, flattening and broadening) of the laser beam has recently been proposed as an effective device to reduce internal (mirror) thermal noise in advanced gravitational-wave interferometric detectors. Based on some recently published analytic approximations (valid in the infinite-test-mass limit) for the Brownian and thermoelastic mirror noises in the presence of arbitrary-shaped beams, this paper addresses certain preliminary issues related to the optimal beam-shaping problem. In particular, with specific reference to the Laser Interferometer Gravitational-wave Observatory (LIGO) experiment, absolute and realistic lower bounds for the various thermal-noise constituents are obtained and compared with the current status (Gaussian beams) and trends (mesa beams), indicating fairly ample margins for further reduction. In this framework, the effective dimension of the related optimization problem, and its relationship to the critical design parameters are identified, physical-feasibility and model-consistency issues are considered, and possible additional requirements and/or prior information exploitable to drive the subsequent optimization process are highlighted.

Thermal distortions of non-Gaussian beams in Fabry–Perot cavities

Thermal effects are already important in currently operating interferometric gravitational wave detectors. Planned upgrades of these detectors involve increasing optical power to combat quantum shot noise. We consider the ramifications of this increased power for one particular class of laser beams—wide, flat-topped, mesa beams. In particular we model a single mesa beam Fabry–Perot cavity having thermoelastically deformed mirrors. We calculate the intensity profile of the fundamental cavity eigenmode in the presence of thermal perturbations, and the associated changes in thermal noise. We also outline an idealized method of correcting for such effects. At each stage we contrast our results with those of a comparable Gaussian beam cavity. Although we focus on mesa beams the techniques described are applicable to any azimuthally symmetric system.