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Suitable shaping (in particular, flattening and broadening) of the laser beamhas recently been proposed as an effective device to reduce internal (mirror)thermal noise in advanced gravitational wave interferometric detectors. Basedon some recently published analytic approximations (valid in theinfinite-test-mass limit) for the Brownian and thermoelastic mirror noises inthe presence of arbitrary-shaped beams, this paper addresses certainpreliminary issues related to the optimal beam-shaping problem. In particular,with specific reference to the Laser Interferometer Gravitational-waveObservatory (LIGO) experiment, absolute and realistic lower-bounds for thevarious thermal noise constituents are obtained and compared with the currentstatus (Gaussian beams) and trends ("mesa" beams), indicating fairly amplemargins for further reduction. In this framework, the effective dimension ofthe related optimization problem, and its relationship to the critical designparameters are identified, physical-feasibility and model-consistency issuesare considered, and possible additional requirements and/or prior informationexploitable to drive the subsequent optimization process are highlighted.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

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