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Analytic structure and generalized duality relations for a family of hyperboloidal beams and supporting mirrors of potential interest for future gravitational wave detection interferometers

Galdi, Vincenzo and Castaldi, Giuseppe and Pierro, Vincenzo and Pinto, Innocenzo M. and Agresti, Juri and D'Ambrosio, Erika and DeSalvo, Riccardo (2006) Analytic structure and generalized duality relations for a family of hyperboloidal beams and supporting mirrors of potential interest for future gravitational wave detection interferometers. In: Laser Beam Shaping VII. Proceedings of SPIE. No.6290. Society of Photo-Optical Instrumentation Engineers (SPIE) , Bellingham, WA, Art. No. 629004. https://resolver.caltech.edu/CaltechAUTHORS:20191106-145502567

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Abstract

For the baseline design of future gravitational wave detection interferometers, use of optical cavities with nonsphericalmirrors supporting flat-top ("mesa") beams, potentially capable of mitigating the thermal noise of the mirrors, has recently drawn a considerable attention. To reduce the severe tilt-instability problems affecting the originally conceived nearly-flat, "Mexican-hat-shaped" mirror configuration, K. S. Thorne proposed a nearly-concentric mirror configuration capable of producing the same mesa beam profile on the mirror surfaces. Subsequently, Bondarescu and Thorne introduced a generalized construction that leads to a one-parameter family of "hyperboloidal" beams which allows continuous spanning from the nearly-flat to the nearly-concentric mesa beam configurations. This paper is concerned with a study of the analytic structure of the above family of hyperboloidal beams. 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. Moreover, the functional relation between two generic hyperboloidal beams is investigated. This leads to 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. Possible implications and perspectives for the advanced Laser Interferometer Gravitational-wave Observatory (LIGO) optical cavity design are discussed.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1117/12.679412DOIArticle
Additional Information:© 2006 Society of Photo-Optical Instrumentation Engineers (SPIE). The work of J.A., E.D’A., and R.DS. was supported by the National Science Foundation under Grant No. PHY-0107417.
Group:LIGO
Funders:
Funding AgencyGrant Number
NSFPHY-0107417
Subject Keywords:Gravitational waves, interferometers, flat-top beams
Series Name:Proceedings of SPIE
Issue or Number:6290
Record Number:CaltechAUTHORS:20191106-145502567
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20191106-145502567
Official Citation:Vincenzo Galdi, Giuseppe Castaldi, Vincenzo Pierro, Innocenzo M. Pinto, Juri Agresti, Erika D'Ambrosio, and Riccardo DeSalvo "Analytic structure and generalized duality relations for a family of hyperboloidal beams and supporting mirrors of potential interest for future gravitational wave detection interferometers", Proc. SPIE 6290, Laser Beam Shaping VII, 629004 (7 September 2006); https://doi.org/10.1117/12.679412
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99707
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:06 Nov 2019 23:06
Last Modified:06 Nov 2019 23:06

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