OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 29, Iss. 9 — Sep. 1, 2012
  • pp: 1818–1827

Duality relation between nonspherical mirror optical cavities and its application to gravitational-wave detectors

Juri Agresti, Yanbei Chen, Erika D’Ambrosio, and Pavlin Savov  »View Author Affiliations


JOSA A, Vol. 29, Issue 9, pp. 1818-1827 (2012)
http://dx.doi.org/10.1364/JOSAA.29.001818


View Full Text Article

Enhanced HTML    Acrobat PDF (370 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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.

© 2012 Optical Society of America

OCIS Codes
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(140.0140) Lasers and laser optics : Lasers and laser optics
(230.0230) Optical devices : Optical devices
(260.0260) Physical optics : Physical optics
(080.4228) Geometric optics : Nonspherical mirror surfaces

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: May 24, 2012
Revised Manuscript: July 6, 2012
Manuscript Accepted: July 9, 2012
Published: August 9, 2012

Citation
Juri Agresti, Yanbei Chen, Erika D’Ambrosio, and Pavlin Savov, "Duality relation between nonspherical mirror optical cavities and its application to gravitational-wave detectors," J. Opt. Soc. Am. A 29, 1818-1827 (2012)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-29-9-1818


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. LIGO http://www.ligo.caltech.edu .
  2. Advanced LIGO https://www.advancedligo.mit.edu .
  3. The name mesa beam was invented by P. Willems.
  4. K. S. Thorne, LIGO-G000068-00-D (2000), available at http://admdbsrv.ligo.caltech.edu/dcc/ .
  5. E. D’Ambrosio, R. O’Shaughnessy, S. Strigin, K. S. Thorne, and S. Vyatchanin, “Reducing thermoelastic noise in gravitational-wave interferometers by flattening the light beams,” arXiv:gr-qc/0409075v1.
  6. R. O’Shaughnessy, S. Strigin, and S. Vyatchanin, “The implications of Mexican-hat mirrors: calculations of thermoelastic noise and interferometer sensitivity to perturbation for Mexican-hat mirror proposal for advanced LIGO,” arXiv:gr-qc/0409050v1.
  7. E. D’Ambrosio, “Non-spherical mirrors to reduce thermoelastic noise in advanced gravity wave interferometers,” Phys. Rev. D 67, 102004 (2003). [CrossRef]
  8. M. G. Tarallo, J. Miller, J. Agresti, E. D’Ambrosio, R. DeSalvo, D. Forest, B. Lagrange, J. M. Mackowski, C. Michel, J. L. Montorio, N. Morgado, L. Pinard, A. Remilleux, B. Simoni, and P. Willems, “Generation of a flat-top laser beam for gravitational-wave detectors by means of a non-spherical Fabry–Perot resonator,” Appl. Opt. 46, 6648–6654 (2007). [CrossRef]
  9. M. Bondarescu, O. Kogan, and Y. Chen, “Optimal light beams and mirror shapes for future LIGO interferometers,” Phys. Rev. D 78, 082002 (2008). [CrossRef]
  10. B. Mours, E. Tournefier, and J. Y. Vinet, “Thermal noise reduction in interferometric gravitational wave antennas: using high order TEM modes,” Classical Quantum Gravity 23, 5777–5784 (2006). [CrossRef]
  11. J. Y. Vinet, “On special optical modes and thermal issues in advanced gravitational wave interferometric detectors,” Living Rev. Relativity 12, 5 (2009).
  12. V. Pierro, V. Galdi, G. Castaldi, I. M. Pinto, J. Agresti, and R. DeSalvo, “Perspectives on beam-shaping optimization for thermal-noise reduction in advanced gravitational-wave interferometric detectors: bounds, profiles, and critical parameters,” Phys. Rev. D 76, 122003 (2007). [CrossRef]
  13. J. Agresti and R. DeSalvo, “Thermal noises calculations: Gaussian vs. Mesa beams,” LIGO technical note, LIGO-T050269-00-R available at http://admdbsrv.ligo.caltech.edu/dcc/ .
  14. P. Savov and S. Vyatchanin, “Estimate of tilt instability of Mesa-beam and Gaussian-beam modes for advanced LIGO,” Phys. Rev. D 74, 082002 (2006). [CrossRef]
  15. D. Sigg, “Angular instability in high power FP cavities,” LIGO technical note, LIGO-T030120-00, (2003); available at http://admdbsrv.ligo.caltech.edu/dcc/ .
  16. J. Sidles and D. Sigg, “Optical torques in suspended Fabry–Perot interferometers,” Phys. Lett. A 354, 167–172 (2006). [CrossRef]
  17. M. Bondarescu and K. S. Thorne, “A new family of light beams and mirror shapes for future LIGO interferometers,” Phys. Rev. D 74, 082003 (2006). [CrossRef]
  18. V. Galdi, G. Castaldi, V. Pierro, I. M. Pinto, J. Agresti, E. DAmbrosio, and R. DeSalvo, “Analytic structure of a family of hyperboloidal beams of potential interest for advanced LIGO,” Phys. Rev. D 73, 127101 (2006). [CrossRef]
  19. A. P. Lundgren, R. Bondarescu, D. Tsang, and M. Bondarescu, “Finite mirror effects in advanced interferometric gravitational wavedetectors,” Phys. Rev. D 77, 042003(2008). [CrossRef]
  20. A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
  21. J. P. Gordon and H. Kogelnik, “Equivalence relations among spherical mirror optical resonators,” Bell Syst. Tech. J. 43, 2873–2886 (1964).
  22. H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966). [CrossRef]
  23. G. Herziger and H. Weber, “Equivalent optical resonators,” Appl. Opt. 23, 1450–1452 (1984). [CrossRef]
  24. A. Siegman, Lasers (University Science Books, 1996), Ch. 19.
  25. P. Domokos and H. Ritsch, “Mechanical effects of light in optical resonators,” J. Opt. Soc. Am. B 20, 1098–1130 (2003). [CrossRef]
  26. V. B. Braginsky, S. E. Strigin, and S. P. Vyatchanin, “Parametric oscillatory instability in Fabry–Perot interferometer,” Phys. Lett. A 287, 331–338 (2001). [CrossRef]
  27. S. Gras, D. G. Blair, and L. Ju, “Opto-acoustic interactions in gravitational wave detectors: comparing flat-top beams with Gaussian beams,” Phys. Rev. D 81, 042001 (2010). [CrossRef]
  28. Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10–16-level laser stabilization,” Nat. Photon. 5, 158161 (2011).
  29. R. Grimm, M. Weidenmüller, and Y. B. Ovchinnikov, “Optical dipole traps for neutral atoms,” Adv. Atomic Molec. Opt. Phys. 42, 95–170 (2000).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited