Perspectives on Beam-Shaping Optimization for Thermal-Noise Reduction in Advanced Gravitational-Wave Interferometric Detectors: Bounds, Profiles, and Critical Parameters

TL;DR

This paper investigates optimal laser beam shaping to minimize thermal noise in advanced gravitational-wave detectors, providing bounds and analyzing parameters to guide future design improvements.

Contribution

It offers analytic bounds and insights into the beam-shaping optimization problem for thermal noise reduction in gravitational-wave detectors.

Findings

Realistic lower bounds for thermal noise constituents are established.

Ample margins for noise reduction beyond current Gaussian and mesa beams are identified.

The relationship between optimization parameters and detector design is clarified.

Abstract

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.