OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry Van Driel
  • Vol. 26, Iss. 9 — Sep. 1, 2009
  • pp: 1664–1674

Q-factor instability and its explanation in the staircased FDTD simulation of high-Q circular cavity

Shan-Liang Qiu and Yong-Ping Li  »View Author Affiliations


JOSA B, Vol. 26, Issue 9, pp. 1664-1674 (2009)
http://dx.doi.org/10.1364/JOSAB.26.001664


View Full Text Article

Enhanced HTML    Acrobat PDF (628 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The loss of high-Q whispering-gallery modes (WGMs) with lower azimuthal mode number [ m ( 9 12 ) ] in a circular cavity have been analyzed by using a two-dimensional finite-difference time domain method (2D FDTD) method employing Cartesian gridding and staircase approximation. The FDTD simulated Q-factors of these WGMs are generally lower than those of theoretical expectations. The variations of FDTD simulated Q-factors with spatial-calculation step size indicate that the FDTD results do not simply approximate to their theoretical expectation but jump unstably under the expectation. A loss estimation method similar to volume current method (VCM) is developed to explain the FDTD results and instability. This method calculates the “incoherent” scattering field of a scattering source under influence of cavity. Theoretical results coincident with the FDTD simulation are obtained, especially for transverse magnetic modes. As based on the developed method, the energy loss is affected by only a few harmonics of boundary fluctuation that cause the FDTD loss instability.

© 2009 Optical Society of America

OCIS Codes
(240.5770) Optics at surfaces : Roughness
(290.5880) Scattering : Scattering, rough surfaces
(140.3945) Lasers and laser optics : Microcavities

ToC Category:
Optics at Surfaces

History
Original Manuscript: April 6, 2009
Revised Manuscript: June 24, 2009
Manuscript Accepted: June 24, 2009
Published: August 4, 2009

Citation
Shan-Liang Qiu and Yong-Ping Li, "Q-factor instability and its explanation in the staircased FDTD simulation of high-Q circular cavity," J. Opt. Soc. Am. B 26, 1664-1674 (2009)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-26-9-1664


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289-291 (1992). [CrossRef]
  2. M. K. Chin, D. Y. Chu, and S. T. Ho, “Estimation of the spontaneous emission factor for microdisk lasers via the approximation of whispering gallery modes,” J. Appl. Phys. 75, 3302-3307 (1994). [CrossRef]
  3. R. E. Slusher, A. F. J. Levi, S. L. McCall, S. J. Pearton, and R. A. Logan, “Threshold characteristics of semiconductor microdisk lasers,” Appl. Phys. Lett. 63, 1310-1312 (1993). [CrossRef]
  4. S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range and mode Q-factors in 2D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175-1182 (2006). [CrossRef]
  5. J. Yang and L. J. Guo, “Optical sensors based on active microcavities,” IEEE J. Sel. Top. Quantum Electron. 12, 143-147 (2006). [CrossRef]
  6. R. W. Boyd and J. E. Heebner, “Sensitive disk resonator photonic biosensor,” Appl. Opt. 40, 5742-5447 (2001). [CrossRef]
  7. K. J. Vahala, “Optical microcavities,” Nature 424, 839-846 (2003). [CrossRef] [PubMed]
  8. M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, “Fiber-coupled microsphere laser,” Opt. Lett. 25, 1430-1432 (2000). [CrossRef]
  9. M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, “Ultimate Q of optical microspherere resonators,” Opt. Lett. 21, 453-455 (1996). [CrossRef] [PubMed]
  10. M. L. M. Balistreri, D. J. W. Klunder, F. C. Blom, A. Driessen, H. W. J. M. Hoekstra, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Visualizing the whispering gallery modes in a cylindrical optical microcavity,” Opt. Lett. 24, 1929-1831 (1999). [CrossRef]
  11. M. Borselli, K. Srinivasan, P. E. Barclay, and O. Painter, “Rayleigh scattering, mode coupling, and optical loss in silicon microdisks,” Appl. Phys. Lett. 85, 3693-3695 (2004). [CrossRef]
  12. A. W. Poon, F. Courvoisier, and R. K. Chang, “Multimode resonances in square-shaped optical microcavities,” Opt. Lett. 26, 632-634 (2001). [CrossRef]
  13. W. H. Guo, Y. Z. Huang, Q. Y. Li, and L. J. Yu, “Modes in square resonators,” IEEE J. Quantum Electron. 39, 1563-1566 (2003). [CrossRef]
  14. T. Nobis and M. Grundmann, “Low-order optical whispering-gallery modes in hexagonal nanocavities,” Phys. Rev. A 72, 063806 (2005). [CrossRef]
  15. Y. Z. Huang, W. H. Guo, and Q. M. Wang, “Analysis and numerical simulation of eigenmode characteristics for semiconductor lasers with an equilateral triangle micro-resonator,” IEEE J. Quantum Electron. 37, 100-107 (2001). [CrossRef]
  16. J. U. Nockel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optial cavities,” Nature 385, 45-47 (1997). [CrossRef]
  17. J. U. Nöckel, A. D. Stone, G. Chen, H. L. Grossman, and R. K. Chang, “Directional emission from asymmetric resonant cavities,” Opt. Lett. 21, 1609-1611 (1996). [CrossRef]
  18. S. Y. Lee, S. Rim, J. W. Ryu, T. Y. Kwon, M. Choi, and C. M. Kim, “Quasi-scarred resonances in a spiral-shaped microcavity,” Phys. Rev. Lett. 93, 164102 (2004). [CrossRef] [PubMed]
  19. T. Ling, L. Y. Liu, Q. H. Song, L. Xu, and W. C. Wang, “Intense directional lasing from a deformed square-shaped organic-inorganic hybrid glass microring cavity,” Opt. Lett. 28, 1784-1786 (2003). [CrossRef] [PubMed]
  20. M. S. Kurdoglyan, S. Y. Lee, S. Rim, and C. M. Kim, “Unidirectional lasing from a microcavity with a rounded isosceles triangle shape,” Opt. Lett. 29, 2758-2760 (2004). [CrossRef] [PubMed]
  21. M. Fujita and T. Baba, “Proposal and finite-difference time-domain simulation of whispering gallery mode microgear cavity,” IEEE J. Quantum Electron. 37, 1253-1258 (2001). [CrossRef]
  22. S. L. Qiu, J. X. Cai, Y. P. Li, and X. F. Han, “Mode frequency shifts and Q-factor changes in microflower cavity and its deformed cavity,” Opt. Commun. 277, 406-410 (2007). [CrossRef]
  23. J. Wiersig and M. Hentschel, “Unidirectional light emission from high-Q modes in optical microcavities,” Phys. Rev. A 73, 031802 (2006). [CrossRef]
  24. S. A. Backes, J. R. A. Cleaver, A. P. Heberle, J. J. Baumberg, and K. Köhler, “Threshold reduction in pierced microdisk lasers,” Appl. Phys. Lett. 74, 176-178 (1999). [CrossRef]
  25. S. V. Boriskina, P. Sewell, T. M. Benson, and A. I. Nosich, “Accurate simulation of two-dimensional optical microcavities with uniquely solvable boundary integral equations and trigonometric Galerkin discretization,” J. Opt. Soc. Am. A 21, 393-402 (2004). [CrossRef]
  26. J. Wiersig, “Boundary element method for resonances in dielectric microcavities,” J. Opt. A, Pure Appl. Opt. 5, 53-60 (2003). [CrossRef]
  27. M. Hentschel1 and K. Richter, “Quantum chaos in optical systems: the annular billiard,” Phys. Rev. E 66, 056207 (2002). [CrossRef]
  28. A. I. Nosich, E. I. Smotrova, S. V. Boriskina, T. M. Benson, and P. Sewell, “Trends in microdisk laser research and linear optical modelling,” Opt. Quantum Electron. 39, 1253-1272 (2007). [CrossRef]
  29. W.-H. Guo, W.-J. Li, and Y.-Z. Huang, “Computation of resonant frequencies and quality factors of cavities by FDTD technique and Padé approximation,” IEEE Microw. Wirel. Compon. Lett. 11, 223-225 (2001). [CrossRef]
  30. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).
  31. A. Mohammadi, H. Nadgaran, and M. Agio, “Contour-path effective permittivities for the two-dimensional finite-difference time-domain method,” Opt. Express 13, 10367-10381 (2005). [CrossRef] [PubMed]
  32. G. L. Hower, R. G. Olsen, J. D. Earls, and J. B. Schneider, “Inaccuracies in numerical calculation of scattering near natural frequencies of penetrable object,” IEEE Trans. Antennas Propag. 41, 982-986 (1993). [CrossRef]
  33. B. E. Little and S. T. Chu, “Estimating surface-roughness loss and output coupling in microdisk resonators,” Opt. Lett. 21, 1390-1392 (1996). [CrossRef] [PubMed]
  34. A. V. Boriskin, S. V. Boriskina, A. Rolland, R. Sauleau, and A. I. Nosich, “Test of the FDTD accuracy in the analysis of the scattering resonances associated with high-Q whispering-gallery modes of a circular cylinder,” J. Opt. Soc. Am. A 25, 1169-1173 (2008). [CrossRef]
  35. M. Kuznetsov and H. A. Haus, “Radiation loss in dielectric waveguide structures by the volume current method,” IEEE J. Quantum Electron. 19, 1505-1514 (1983). [CrossRef]
  36. M. L. Gorodetsky, A. D. Pryamikov, and V. S. Ilchenko, “Rayleigh scattering in high-Q microspheres,” J. Opt. Soc. Am. B 17, 1051-1057 (2000). [CrossRef]
  37. H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187-5198 (1990). [CrossRef] [PubMed]

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.


Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited