OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 20 — Oct. 7, 2013
  • pp: 24240–24253

Semiclassical evaluation of frequency splittings in coupled optical microdisks

Jeong-Bo Shim and Jan Wiersig  »View Author Affiliations

Optics Express, Vol. 21, Issue 20, pp. 24240-24253 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (1129 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



When two microdisks are placed close to each other and the evanescent fields of their whispering gallery modes are overlapped, a strong coupling can be induced in the modes and lead to a doublet state. We attempt to evaluate the frequency splittings of the doublets by applying a semiclassical analysis in the regime of small wavelengths. Since a whispering gallery mode in a microdisk is a leaky mode, an established semiclassical method that deals with coupled closed systems is modified. As a result, we attain an analytic formula which can conveniently compute the frequency splittings of coupled whispering gallery modes. The derived formula is verified by demostrating a perfect agreement with numerical solutions of Maxwell’s equations.

© 2013 OSA

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(130.3120) Integrated optics : Integrated optics devices
(140.4780) Lasers and laser optics : Optical resonators
(140.5960) Lasers and laser optics : Semiconductor lasers
(080.1753) Geometric optics : Computation methods
(080.7343) Geometric optics : Wave dressing of rays

ToC Category:
Integrated Optics

Original Manuscript: June 24, 2013
Revised Manuscript: August 16, 2013
Manuscript Accepted: August 28, 2013
Published: October 3, 2013

Jeong-Bo Shim and Jan Wiersig, "Semiclassical evaluation of frequency splittings in coupled optical microdisks," Opt. Express 21, 24240-24253 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. K. Vahala, ed., Optical Microcavities(World Scientific, 2004).
  2. M. Benyoucef, J.-B. Shim, J. Wiersig, and O. G. Schmidt, “Quality-factor enhancement of supermodes in coupled microdisks,” Opt. Lett.36, 1317–1319 (2011). [CrossRef] [PubMed]
  3. M. Witzany, T.-L. Liu, J.-B. Shim, F. Hargart, E. Koroknay, W.-M. Schulz, M. Jetter, E. Hu, J. Wiersig, and P. Michler, “Strong mode coupling in InP quantum dot-based GaInP microdisk cavity dimers,” New J. Phys.15, 013060 (2013). [CrossRef]
  4. S. Preu, H. G. L. Schwefel, S. Malzer, G. H. Döhler, L. J. Wang, M. Hanson, J. D. Zimmerman, and A. C. Gossard, “Coupled whispering gallery mode resonators in the terahertz frequency range.” Opt. Express16, 7336–7343 (2008). [CrossRef] [PubMed]
  5. K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett.98, 213904 (2007). [CrossRef] [PubMed]
  6. U. Kuhl, S. Barkhofen, T. Tudorovskiy, H.-J. Stöckmann, T. Hossain, L. de Forges de Parny, and F. Mortessagne, “Dirac point and edge states in a microwave realization of tight-binding graphene-like structures,” Phys. Rev. B82, 094308 (2010). [CrossRef]
  7. M. Zhang, G. Wiederhecker, S. Manipatruni, A. Barnard, P. McEuen, and M. Lipson, “Synchronization of micromechanical oscillators using light,” Phys. Rev. Lett.109, 233906 (2012). [CrossRef]
  8. J.-M. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (Wiley-IEEE, 2002).
  9. J. Wiersig, “Boundary element method for resonances in dielectric microcavities,” J. Opt. A5, 53–60 (2003). [CrossRef]
  10. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181, 687–702 (2010). [CrossRef]
  11. S. V. Boriskina, “Spectrally engineered photonic molecules as optical sensors with enhanced sensitivity: a proposal and numerical analysis,” J. Opt. Soc. Am. B23, 1565–1573 (2006). [CrossRef]
  12. C. Herring, “Critique of the Heitler-London method of calculating spin couplings at large distances,” Rev. Mod. Phys.34, 631–645 (1962). [CrossRef]
  13. M. Wilkinson, “Tunnelling between tori in phase space,” Physica D21, 341–354 (1986). [CrossRef]
  14. M. Brack and R. K. Bhaduri, Semiclassical Physics (Westview, 2008).
  15. S. C. Creagh and M. D. Finn, “Evanescent coupling between discs: a model for near-integrable tunnelling,” J. Phys. A34, 3791–3801 (2001). [CrossRef]
  16. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
  17. B. R. Johnson, “Theory of morphology-dependent resonances: shape resonances and width formulas,” J. Opt. Soc. Am. A10, 343–352 (1993). [CrossRef]
  18. S.-Y. Lee and K. An, “Directional emission through dynamical tunneling in a deformed microcavity,” Phys. Rev. A83, 023827 (2011). [CrossRef]
  19. G. B. Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic, 1985).
  20. R. Dubertrand, E. Bogomolny, N. Djellali, M. Lebental, and C. Schmit, “Circular dielectric cavity and its deformations,” Phys. Rev. A77, 013804 (2008). [CrossRef]
  21. S. C. Creagh and M. White, “Differences between emission patterns and internal modes of optical resonators,” Phys. Rev. E85, 015201 (2012). [CrossRef]
  22. J.-B. Shim, J. Wiersig, and H. Cao, “Whispering gallery modes formed by partial barriers in ultrasmall deformed microdisks,” Phys. Rev. E84, 035202 (2011). [CrossRef]
  23. F. W. J. Oliver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, eds., NIST Handbook of Mathematical Functions(Cambridge University, 2010).

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