Duality relation between nonspherical mirror optical cavities and its application to gravitational-wave detectors
Abstract
In this paper, we analytically prove a unique duality relation between the eigenspectra of paraxial optical cavities with nonspherical mirrors: a one-to-one mapping between eigenmodes and eigenvalues of cavities deviating from flat mirrors by h(r⃗) and cavities deviating from concentric mirrors by −h(r⃗), where h need not be a small perturbation. We then illustrate its application to optical cavities, proposed for advanced interferometric gravitational-wave detectors, where the mirrors are designed to support beams with rather flat intensity profiles over the mirror surfaces. This unique mapping might be very useful in future studies of alternative optical designs for advanced gravitational wave interferometers or experiments employing optical cavities with nonstandard mirrors.
Additional Information
© 2012 Optical Society of America. Received May 24, 2012; revised July 6, 2012; accepted July 9, 2012; posted July 10, 2012 (Doc. ID 168898); published August 9, 2012. We thank K.S. Thorne and W. Kells for useful discussions. Research of P.S. and Y.C. was supported by the National Science Foundation under grant No. PHY-0099568. Research of Y.C. was also sponsored by the Alexander von Humboldt Foundation's Sofja Kovalevskaja Award (funded by the German Federal Ministry of Education and Research) and the David and Barbara Groce fund at the San Diego Foundation. Research of J.A. and E.D'A. was supported by National Science Foundation under grant No. PHY-0107417.Attached Files
Published - Agresti_1818.pdf
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Additional details
- Eprint ID
- 35196
- Resolver ID
- CaltechAUTHORS:20121031-084219068
- NSF
- PHY-0099568
- Alexander von Humboldt Foundation Sofja Kovalevskaja Programme
- German Federal Ministry of Education and Research
- San Diego Foundation David and Barbara Groce Fund
- NSF
- PHY-0107417
- Created
-
2012-10-31Created from EPrint's datestamp field
- Updated
-
2023-03-16Created from EPrint's last_modified field
- Caltech groups
- TAPIR