OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry van Driel
  • Vol. 29, Iss. 11 — Nov. 1, 2012
  • pp: 3010–3014

Finite-element modeling of coupled optical microdisk resonators for displacement sensing

Ivan S. Grudinin and Nan Yu  »View Author Affiliations

JOSA B, Vol. 29, Issue 11, pp. 3010-3014 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (472 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We analyze normal mode splitting in a pair of vertically coupled microdisk resonators. A full vectorial finite-element model is used to find the eigenfrequencies of the symmetric and antisymmetric composite modes as a function of coupling distance. We find that the coupled microdisks can compete with the best Fabry–Perot resonators in displacement sensing. We also show how we configured FreeFem++ for the sphere eigenvalue problem.

© 2012 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(140.4780) Lasers and laser optics : Optical resonators

ToC Category:
Lasers and Laser Optics

Original Manuscript: August 7, 2012
Revised Manuscript: September 11, 2012
Manuscript Accepted: September 17, 2012
Published: October 3, 2012

Ivan S. Grudinin and Nan Yu, "Finite-element modeling of coupled optical microdisk resonators for displacement sensing," J. Opt. Soc. Am. B 29, 3010-3014 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. R. D. Richtmyer, “Dielectric resonators,” J. Appl. Phys. 10, 391–398 (1939). [CrossRef]
  2. A. N. Oraevsky, “Whispering gallery waves,” Quantum Electron. 32, 377–400 (2002). [CrossRef]
  3. M. L. Gorodetsky, Optical Microresonators with Gigantic Quality Factor (in Russian) (Fizmatlit, 2011), http://www.ozon.ru/context/detail/id/6210477/ .
  4. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, and L. Maleki, “Optical resonators with ten million finesse,” Opt. Express 15, 6768–6773 (2007). [CrossRef]
  5. R. T. Wang and G. J. Dick, “Cryocooled sapphire oscillator with ultrahigh stability,” IEEE Trans. Instrum. Meas. 48, 528–531 (1999). [CrossRef]
  6. T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express 15, 17172–12305 (2007). [CrossRef]
  7. A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering–gallery modes—part I: basics,” IEEE J. Sel. Top. Quantum Electron. 12, 3–14 (2006). [CrossRef]
  8. K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003). [CrossRef]
  9. J. Moore, M. Tomes, T. Carmon, and M. Jarrahi, “Continuous-wave ultraviolet emission through fourth-harmonic generation in a whispering-gallery resonator,” Opt. Express 19, 24139–24146 (2011). [CrossRef]
  10. A. B. Matsko, A. A. Savchenkov, N. Yu, and L. Maleki, “Whispering-gallery-mode resonators as frequency references. I. Fundamental limitations,” J. Opt. Soc. Am. B 24, 1324–1335 (2007). [CrossRef]
  11. C. Shi, H. S. Choi, and A. M. Armani, “Optical microcavities with a thiol-functionalized gold nanoparticle polymer thin film coating,” Appl. Phys. Lett. 100, 013305 (2012). [CrossRef]
  12. F. Vollmer, S. Arnold, and D. Keng, “Single virus detection from the reactive shift of a whispering-gallery mode,” Proc. Natl. Acad. Sci. 105, 20701–20704 (2008). [CrossRef]
  13. T. Lu, H. Lee, T. Chen, S. Herchak, J.-H. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. 108, 5976–5979 (2011). [CrossRef]
  14. I. S. Grudinin, L. Baumgartel, and N. Yu, “Frequency comb from a microresonator with engineered spectrum,” Opt. Express 20, 6604–6609 (2012). [CrossRef]
  15. M. Hossein-Zadeh and A. F. J. Levi, “Ring resonator-based photonic microwave receiver modulator with picowatt sensitivity,” IET Optoelectron. 5, 36–39 (2011). [CrossRef]
  16. W. Liang, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Whispering-gallery-mode-resonator-based ultranarrow linewidth external-cavity semiconductor laser,” Opt. Lett. 35, 2822–2824 (2010). [CrossRef]
  17. V. S. Ilchenko, M. L. Gorodetsky, and S. P. Vyatchanin, “Coupling and tunability of optical whispering–gallery modes: a basis for coordinate meter,” Opt. Commun. 107, 41–48 (1994). [CrossRef]
  18. V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, and S. P. Vyatchanin, “On the ultimate sensitivity in coordinate measurements,” Phys. Lett. A 179, 244–248 (1993). [CrossRef]
  19. W. P. Huang, “Coupled–mode theory for optical waveguides: an overview,” J. Opt. Soc. Am. A 11, 963–983 (1994). [CrossRef]
  20. I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two–level system,” Phys. Rev. Lett. 104, 083901 (2010). [CrossRef]
  21. H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012). [CrossRef]
  22. M. L. Gorodetsky and A. E. Fomin, “Geometrical theory of whispering-gallery modes,” IEEE J. Sel. Top. Quantum Electron. 12, 33–39 (2006). [CrossRef]
  23. J. P. Webb, “The finite–element method for finding modes of dielectric–loaded cavities,” IEEE Trans. Microwave Theor. mtt-33, 635–639 (1985). [CrossRef]
  24. M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microwave Theor. 55, 1209–1218 (2007). [CrossRef]
  25. S. H. Wong and Z. J. Cendes, “Combined finite element–modal solution of three-dimensional eddy current problems,” IEEE Trans. Magn. 24, 2685–2687 (1988). [CrossRef]
  26. O. Pironneau, F. Hecht, A. Le Hyaric, and J. Morice, “FreeFem++,” http://www.freefem.org/ .
  27. http://www.caam.rice.edu/software/ARPACK/ .
  28. http://www.cise.ufl.edu/research/sparse/umfpack/ .
  29. M. A. Arain and G. Mueller, “Optical layout and parameters for the advanced LIGO cavities,” LIGO-T0900043-10 (2009).
  30. V. B. Braginsky, V. P. Mitrofanov, and V. I. Panov, Systems with Small Dissipation (Chicago, 1985).
  31. G. Rempe, R. J. Thompson, H. J. Kimble, and R. Lalezari, “Measurement of ultralow losses in an optical interferometer,” Opt. Lett. 17363–365 (1992). [CrossRef]
  32. M. L. Gorodetsky and I. S. Grudinin, “Fundamental thermal fluctuations in microspheres,” J. Opt. Soc. Am. B 21, 697–705 (2004). [CrossRef]
  33. K. Kakihara, N. Kono, K. Saitoh, and M. Koshiba, “Full-vectorical finite element method in a cylindrical coordinate system for loss analysis of photonic wire bends,” Opt. Express 14, 11128–11141 (2006). [CrossRef]
  34. D. B. Thompson, D. A. Keating, E. Guler, K. Ichimura, M. E. Williams, and K. A. Fuller, “Separation-sensitive measurements of morphology dependent resonances in coupled fluorescent microspheres,” Opt. Express 18, 19209–19218 (2010). [CrossRef]
  35. B. Wu, Y. Liu, Z. Dai, and S. Liu, “Stable narrow linewidth Er-doped fiber laser at 1550 nm,” Microw. Opt. Technol. Lett. 49, 1453–1456 (2007). [CrossRef]
  36. M. L. Povinelli, S. G. Johnson, M. Lonar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering gallery-mode resonators,” Opt. Express 13, 8286–8295 (2005). [CrossRef]
  37. FreeFem++ example is available, http://arxiv.org/abs/1208.4320.

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.


Fig. 1. Fig. 2. Fig. 3.
Fig. 4.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited