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Analytic structure of a family of hyperboloidal beams of potential interest for advanced LIGO
- Source :
- Physical Review D. 73
- Publication Year :
- 2006
- Publisher :
- American Physical Society (APS), 2006.
-
Abstract
- For the baseline design of the advanced Laser Interferometer Gravitational-wave Observatory (LIGO), use of optical cavities with non-spherical mirrors 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 LIGO optical cavity design are discussed.<br />9 pages, 6 figures, typos corrected, Eqs. (24) and (26) changed
- Subjects :
- Physics
Nuclear and High Energy Physics
Generalization
Structure (category theory)
FOS: Physical sciences
Duality (optimization)
General Relativity and Quantum Cosmology (gr-qc)
01 natural sciences
General Relativity and Quantum Cosmology
Fractional Fourier transform
LIGO
010309 optics
symbols.namesake
Theoretical physics
Classical mechanics
Fourier transform
0103 physical sciences
symbols
010306 general physics
Representation (mathematics)
Caltech Library Services
Beam (structure)
Subjects
Details
- ISSN :
- 15502368 and 15507998
- Volume :
- 73
- Database :
- OpenAIRE
- Journal :
- Physical Review D
- Accession number :
- edsair.doi.dedup.....82d34d33dbbabc1ab9391efae91b0af6