In addition to the geometric optimization of the coating design, suitable shaping of the laser beam has also been proposed as an effective device to reduce internal (mirror) thermal noise in advanced gravitational-wave interferometric detectors. With specific reference to Advanced LIGO, the use of flat-top (commonly referred to as “mesa”) beams has been explored, intuitively motivated by the potential capability of such a beam to better average the thermally induced mirror surface fluctuations as compared to a standard Gaussian beam. This has been numerically proved to yield significant reductions in the overall thermal noise and has led to the development of a cavity prototype with non-spherical “Mexican hat” profile mirrors.
In [1], we investigated the analytic structure of a family of hyperboloidal beams which generalizes the nearly-flat and nearly-concentric mesa beam configurations. Capitalizing on certain results from the applied optics literature on flat-top beams, we derived a physically-insightful and computationally-effective representation in terms of rapidly-converging Gauss-Laguerre expansions. We also worked out a generalization (involving fractional Fourier transform operators of complex order) of some duality relations between the nearly-flat and nearly-concentric mesa configurations.
In [2], relying on some analytic approximations (valid in the infinite-test-mass limit) for the Brownian and thermoelastic mirror noises in the presence of arbitrary-shaped beams, we explored the optimal beam-shaping problem. The figure top panel shows the assumed cavity geometry, while the bottom panel illustrates the optimal profiles obtained, for the various noise sources. More specifically, \(q=-1,0,1\) refer to the substrate Brownian, the coating (Brownian and thermoelastic), and the substrate thermoelastic noise, respectively. With specific reference to Advanced LIGO, we obtained some absolute and realistic lower bounds for the various thermal-noise constituents, and compared them with the Gaussian- and mesa-beam scenarios. Our result indicate fairly ample margins for further reduction. In this framework, we also identified the effective dimension of the related optimization problem, and its relationship to the critical design parameters. Moreover, we considered the physical-feasibility and model-consistency issues, and highlighted possible additional requirements and/or prior information exploitable to drive the subsequent optimization process.
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.
@article{IJ35_PRD_73_127101_2006, title = {Analytic structure of a family of hyperboloidal beams of potential interest for advanced LIGO}, author = {Galdi, Vincenzo and Castaldi, Giuseppe and Pierro, Vincenzo and Pinto, Innocenzo M. and Agresti, Juri and D'Ambrosio, Erika and DeSalvo, Riccardo}, journal = {Physical Review D}, volume = {73}, issue = {12}, pages = {127101}, numpages = {4}, year = {2006}, month = jun, publisher = {American Physical Society}, doi = {10.1103/PhysRevD.73.127101}, url = {http://link.aps.org/doi/10.1103/PhysRevD.73.127101} }
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.
@article{IJ47_PRD_76_122003_2007, title = {Perspectives on beam-shaping optimization for thermal-noise reduction in advanced gravitational-wave interferometric detectors: Bounds, profiles, and critical parameters}, author = {Pierro, Vincenzo and Galdi, Vincenzo and Castaldi, Giuseppe and Pinto, Innocenzo M. and Agresti, Juri and DeSalvo, Riccardo}, journal = {Physical Review D}, volume = {76}, issue = {12}, pages = {122003}, numpages = {12}, year = {2007}, month = dec, publisher = {American Physical Society}, doi = {10.1103/PhysRevD.76.122003}, url = {http://link.aps.org/doi/10.1103/PhysRevD.76.122003} }