Table of Contents
Physics Research International
Volume 2014, Article ID 615605, 10 pages
http://dx.doi.org/10.1155/2014/615605
Research Article

Analytical Approximations of Whispering Gallery Modes in Anisotropic Ellipsoidal Resonators

1Institute of Applied Physics, Friedrich-Schiller University Jena, Max-Wien-Platz, 07743 Jena, Germany
2Max Planck Institute for the Science of Light, Günther-Scharowsky-Straße 1, Bau 24, 91058 Erlangen, Germany
3Institute for Optics, Information and Photonics, University of Erlangen-Nurmberg, Staudtstraße 7/B2, 91058 Erlangen, Germany

Received 1 May 2014; Accepted 12 November 2014; Published 10 December 2014

Academic Editor: Lorenzo Pavesi

Copyright © 2014 Marco Ornigotti and Andrea Aiello. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Review of applications of whispering-gallery mode resonators in photonics and nonlinear optics,” IPN Progress Report, vol. 42, p. 162, 2005. View at Google Scholar
  2. H. Quan and Z. Guo, “Simulation of whispering-gallery-mode resonance shifts for optical miniature biosensors,” Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 93, no. 1-3, pp. 231–243, 2005. View at Publisher · View at Google Scholar · View at Scopus
  3. D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Fabrication and coupling to planar high-Q silica disk microcavities,” Nature, vol. 422, p. 797, 2003. View at Google Scholar
  4. J. U. Fürst, D. V. Strekalov, D. Elser et al., “Quantum light from a whispering-gallery-mode disk resonator,” Physical Review Letters, vol. 106, Article ID 113901, 2011. View at Publisher · View at Google Scholar · View at Scopus
  5. R. D. Richtmyer, “Dielectric resonators,” Journal of Applied Physics, vol. 10, no. 6, pp. 391–398, 1939. View at Publisher · View at Google Scholar · View at Scopus
  6. V. S. Ilchenko, M. L. Gorodetsky, X. S. Yao, and L. Maleki, “Microtorus: a high-finesse microcavity with whispering-gallery modes,” Optics Letters, vol. 26, no. 5, pp. 256–258, 2001. View at Publisher · View at Google Scholar · View at Scopus
  7. K. J. Vahala, “Optical microcavities,” Nature, vol. 424, no. 6950, pp. 839–846, 2003. View at Publisher · View at Google Scholar · View at Scopus
  8. M. Ornigotti and A. Aiello, “Theory of anisotropic whispering-gallery-mode resonators,” Physical Review A—Atomic, Molecular, and Optical Physics, vol. 84, no. 1, Article ID 013828, 2011. View at Publisher · View at Google Scholar · View at Scopus
  9. COMSOL Multiphysic, Version 3.5, http://www.comsol.com/.
  10. A. E. Formin and M. L. Gorodetsky, “Spheroidal microresonators for optoelectronics,” in Photonic Applications in Industry and Research IV, R. S. Ryszard, S. Romaniuk, S. Simrock, and V. M. Lutkovski, Eds., vol. 5948 of Proceedings of SPIE, pp. 181–188, 2005.
  11. M. L. Gorodetsky and A. E. Fomin, “Geometrical theory of whispering-gallery modes,” IEEE Journal on Selected Topics in Quantum Electronics, vol. 12, no. 1, pp. 33–39, 2006. View at Publisher · View at Google Scholar · View at Scopus
  12. L.-W. Li, X.-K. Kang, and M.-S. Leong, Spheroidal Wave Functions in Electromagnetic Theory, John Wiley & Sons, New York, NY, USA, 2002.
  13. A. N. Oraevsky, “Whispering-gallery waves,” Quantum Electronics, vol. 32, no. 5, pp. 377–400, 2002. View at Publisher · View at Google Scholar · View at Scopus
  14. M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Transactions on Microwave Theory and Techniques, vol. 55, no. 6, pp. 1209–1218, 2007. View at Publisher · View at Google Scholar · View at Scopus
  15. J.-F. Lee, G. M. Wilkins, and R. Mittra, “Finite-element analysis of axisymmetric cavity resonator using a hybrid edge element technique,” IEEE Transactions on Microwave Theory and Techniques, vol. 41, no. 11, pp. 1981–1987, 1993. View at Publisher · View at Google Scholar · View at Scopus
  16. J. D. Jackson, Classical Electrodynamics, Wiley-Interscience, New York, NY, USA, 3rd edition, 1999. View at MathSciNet
  17. R. A. Osegueda, University of Texas, El Paso and JPL, Caltech, Technical Report, http://trs-new.jpl.nasa.gov/dspace/handle/2014/32335.
  18. O. C. Zienkiewicz, R. L. Taylor, and J. Z. Zhu, The Finite Element Method: Its Basis and Fundamentals, Elsevier, 6th edition, 2005.
  19. C. C. Lam, P. T. Leung, and K. Young, “Explicit asymptotic formulas for the positions, widths, and strengths of resonances in Mie scattering,” The Journal of the Optical Society of America B, vol. 9, p. 1585, 1992. View at Google Scholar
  20. M. A. Abramowitz and I. Stegun, Eds., Handbook of Mathematical Functions: With Formulas, Graphs and Mathematical Tables, Dover, New York, NY, USA, 1965.
  21. M. R. Foreman, W.-L. Jin, and F. Vollmer, “Optimizing detection limits in whispering gallery mode biosensing,” Optics Express, vol. 22, no. 5, pp. 5491–5511, 2014. View at Publisher · View at Google Scholar · View at Scopus
  22. M. Förtsch, J. U. Fürst, C. Wittmann et al., “A versatile source of single photons for quantum information processing,” Nature Communications, vol. 4, article 1818, 2013. View at Publisher · View at Google Scholar · View at Scopus
  23. D. V. Strekalov, A. S. Kowligy, Y.-P. Huang, and P. Kumar, “Optical sum-frequency generation in a whispering-gallery-mode resonator,” New Journal of Physics, vol. 16, Article ID 053025, 2014. View at Publisher · View at Google Scholar · View at Scopus
  24. Y. Louyer, D. Meschede, and A. Rauschenbeutel, “Tunable whispering-gallery-mode resonators for cavity quantum electrodynamics,” Physical Review A: Atomic, Molecular, and Optical Physics, vol. 72, no. 3, Article ID 031801, 2005. View at Publisher · View at Google Scholar · View at Scopus
  25. M. C. Collodo, F. Sedlmeir, B. Sprenger, S. Svitlov, L. J. Wang, and H. G. L. Schwefel, “Sub-kHz lasing of a CaF2 whispering gallery mode resonator stabilized fiber ring laser,” Optics Express, vol. 22, no. 16, pp. 19227–19283, 2014. View at Publisher · View at Google Scholar