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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 17 — Aug. 15, 2011
  • pp: 15669–15678

Quick root searching method for resonances of dielectric optical microcavities with the boundary element method

Chang-Ling Zou, Harald G. L. Schwefel, Fang-Wen Sun, Zheng-Fu Han, and Guang-Can Guo  »View Author Affiliations


Optics Express, Vol. 19, Issue 17, pp. 15669-15678 (2011)
http://dx.doi.org/10.1364/OE.19.015669


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Abstract

In this paper, we developed an efficient method for searching the resonant eigenfrequency of dielectric optical microcavities by the boundary element method. By transforming the boundary integral equation to a general eigenvalue problem for arbitrary, symmetric, and multi-domain shaped optical microcavities, we analyzed the regular motion of the eigenvalues against the frequency. The new strategy can predict multiple resonances, increase the speed of convergence, and avoid non-physical spurious solutions. These advantages greatly reduce the computation time in the search process of the resonances. Moreover, this method is not only valuable for dielectric microcavities, but is also suitable for other photonic systems with dissipations, whose resonant eigenfrequencies are complex numbers.

© 2011 OSA

OCIS Codes
(000.3860) General : Mathematical methods in physics
(230.5750) Optical devices : Resonators
(140.3945) Lasers and laser optics : Microcavities

ToC Category:
Physical Optics

History
Original Manuscript: May 3, 2011
Revised Manuscript: June 21, 2011
Manuscript Accepted: July 15, 2011
Published: August 1, 2011

Citation
Chang-Ling Zou, Harald G. L. Schwefel, Fang-Wen Sun, Zheng-Fu Han, and Guang-Can Guo, "Quick root searching method for resonances of dielectric optical microcavities with the boundary element method," Opt. Express 19, 15669-15678 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-17-15669


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References

  1. K. Vahala, “Optical Microavities,” Nature 424, 839–845 (2004). [CrossRef]
  2. J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385, 45–47 (1997). [CrossRef]
  3. J. Wiersig, “Boundary element method for resonances in dielectric microcavities,” J. Opt. A: Pure Appl. Opt. 5, 53–60 (2003). [CrossRef]
  4. C.-L. Zou, Y. Yang, Y.-F. Xiao, C.-H. Dong, Z.-F. Han, and G.-C. Guo, “Accurately calculating high quality factor of whispering-gallery modes with boundary element method,” J. Opt. Soc. Am. B 26, 2050–2053 (2009). [CrossRef]
  5. S.-Y. Lee, M. S. Kurdoglyan, S. Rim, and C.-M. Kim, “Resonance patterns in a stadium-shaped microcavity,” Phys. Rev. A 70, 023809 (2004). [CrossRef]
  6. J. Wiersig and M. Hentschel, “Combining directional light output and ultralow loss in deformed microdisks,” Phys. Rev. Lett. 100, 033901 (2008). [CrossRef] [PubMed]
  7. C.-L. Zou, F.-W. Sun, C.-H. Dong, X.-W. Wu, J.-M. Cui, Y. Yang, G.-C. Guo, and Z.-F. Han, “Mechanism of unidirectional emission of ultrahigh Q whispering gallery mode in microcavities,” http://arxiv.org/abs/0908.3531 .
  8. H. Cheng, W. Crutchfield, M. Doery, and L. Greengard, “Fast, accurate integral equation methods for the analysis of photonic crystal fibers I: theory,” Opt. Express 12, 3791–3805 (2004). [CrossRef] [PubMed]
  9. E. Pone, A. Hassani, S. Lacroix, A. Kabashin, and M. Skorobogatiy, “Boundary integral method for the challenging problems in bandgap guiding, plasmonics and sensing,” Opt. Express 15, 10231–10246 (2007). [CrossRef] [PubMed]
  10. L.-M. Zhou, C.-L. Zou, Z.-F. Han, G.-C. Guo, and F.-W. Sun, “Negative Goos-Hänchen shift on a concave dielectric interface,” Opt. Lett. 36, 624–626 (2011). [CrossRef] [PubMed]
  11. H. E. Türeci, H. G. L. Schwefel, P. Jacquod, and A. D. Stone, “Modes of wave-chaotic dielectric resonators,” Prog. Opt. 47, 75–137 (2005). [CrossRef]
  12. H. E. Türeci and H. G. L. Schwefel, “An efficient Fredholm method for the calculation of highly excited states of billiards,” J. Phys. A: Math. Theor. 40, 13869–13882 (2007). [CrossRef]
  13. H. G. L. Schwefel and C. G. Poulton, “An improved method for calculating resonances of multiple dielectric disks arbitrarily positioned in the plane,” Opt. Express 17, 13178–13186 (2009). [CrossRef] [PubMed]
  14. H. E. Türeci, A. D. Stone, and B. Collier, “Self-consistent multimode lasing theory for complex or random lasing media,” Phys. Rev. A 74, 043822 (2006). [CrossRef]
  15. H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320, 643–646 (2008). [CrossRef] [PubMed]
  16. A. Bäcker, “Numerical aspects of eigenvalue and eigenfunction computations for chaotic quantum systems,” in Lecture Notes in Physics Vol. 618, S. Graffi and M. Degli Esposti, eds. (Spinger, 2003), pp. 91–144. [CrossRef]
  17. J. H. Graf, “Über die Addition und Subtraction der Argumente bei Bessel’schen Functionen nebst einer Anwendung,” Math. Ann. 43, 136–144 (1893). [CrossRef]
  18. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Applied Mathematics Series 55) , (National Bureau of Standards1966), Chapter 9, pp. 360, Eq. (9.1.16).
  19. H. E. Türeci, “Wave Chaos in Dielectric Resonators: Asymptotic and Numerical Approaches,” Ph.D. thesis (Yale University, New Haven, Connecticut, 2003).
  20. J.-W. Ryu, S. Rin, Y.-J. Park, C.-M. Kim, and S. -Y. Lee, “Resonances in a circular dielectric cavity,” Phys. Lett. A 372, 3531–3536 (2008). [CrossRef]

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