OSA's Digital Library

Optics Letters

Optics Letters

| RAPID, SHORT PUBLICATIONS ON THE LATEST IN OPTICAL DISCOVERIES

  • Vol. 29, Iss. 1 — Jan. 1, 2004
  • pp: 8–10

Whispering-gallery-bottle microcavities: the three-dimensional etalon

M. Sumetsky  »View Author Affiliations


Optics Letters, Vol. 29, Issue 1, pp. 8-10 (2004)
http://dx.doi.org/10.1364/OL.29.000008


View Full Text Article

Acrobat PDF (1042 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

In a tapered optical fiber there exist localized light structures that, in analogy to the magnetic bottles used in plasma fusion, can be called whispering-gallery bottles (WGBs). These essentially three-dimensional structures are formed by the spiral rays that experience total internal reflection at the fiber surface and that also bounce along the fiber axis in response to reflection from the regions of tapering. It is shown that the Wentzel—Kramers—Brillouin quantization rules for the strongly prolate WGBs can be inversed exactly, thus determining the cavity shape from its spectrum. The approximation considered allows one to find the shape of the etalon bottle, which, similar to the one-dimensional Fabry—Perot etalon, contains an unlimited number of equally spaced wave-number eigenvalues. The problem of determining such a non-one-dimensional cavity is not trivial, because such a cavity does not exist among the uniformly filled cavities such as rectangular boxes, cylinders, and spheroids that allow separation of variables. The etalon cavity corresponds to the fiber radius variation ρ(z)=ρ0|cos (Δkz)|, where Δk is the wave-number spacing. The latter result is in excellent agreement with ray-dynamics numerical modeling.

© 2004 Optical Society of America

OCIS Codes
(060.2340) Fiber optics and optical communications : Fiber optics components
(190.0190) Nonlinear optics : Nonlinear optics
(230.5750) Optical devices : Resonators
(230.7370) Optical devices : Waveguides

Citation
M. Sumetsky, "Whispering-gallery-bottle microcavities: the three-dimensional etalon," Opt. Lett. 29, 8-10 (2004)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-29-1-8


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, Opt. Lett. 22, 1129 (1997).
  2. B. E. Little, J.-P. Laine, D. R. Lim, H. A. Haus, L. C. Kimerling, and S. T. Chu, Opt. Lett. 25, 73 (2000).
  3. W. von Klitzing, R. Long, V. S. Ilchenko, J. Hare, and V. Lefèvre-Seguin, New J. Phys. 3, 14.1 (2001).
  4. V. I. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, J. Opt. Soc. Am. A 20, 157 (2003).
  5. S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, Phys. Rev. Lett. 91, 043902 (2003).
  6. V. M. Babich and V. S. Buldyrev, Short-Wavelength Diffraction Theory (Springer-Verlag, Berlin, 1991).
  7. J. U. Nöckel and A. D. Stone, Nature 385, 45 (1997).
  8. P. A. Sturrock, Plasma Physics (Cambridge University, Cambridge, UK, 1994).
  9. G. Kakaranzas, T. E. Dimmick, T. A. Birks, R. Le Roux, and P. St. J. Russell, Opt. Lett. 26, 1137 (2001).
  10. B. Z. Katsenelenbaum, L. Mercader del Rio, M. Pereyaslavets, M. Sorolla Ayza, and M. Thumm, Theory of Nonuniform Waveguides: The Cross-Section Method (Institution of Electrical Engineers, London, 1998).
  11. M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981).
  12. R. Gorenflo and S. Vessella, Abel Integral Equations, Vol. 1461 of Lecture Notes in Mathematics Series, A. Dold, B. Eckmann, and F. Takens, eds. (Springer-Verlag, Berlin, 1991).
  13. L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon, New York, 1958).
  14. A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer-Verlag, New York, 1983).

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