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. 29, Iss. 9 — Sep. 1, 2012
  • pp: 2510–2515

Calculation of quasi dispersion curves and quality factors of coupled resonator optical waveguides in photonic-crystal slabs

Chih-Hsien Huang, Wei-Shuo Li, Jing-Nuo Wu, Wen-Feng Hsieh, and Yia-Chung Chang  »View Author Affiliations


JOSA B, Vol. 29, Issue 9, pp. 2510-2515 (2012)
http://dx.doi.org/10.1364/JOSAB.29.002510


View Full Text Article

Enhanced HTML    Acrobat PDF (653 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We propose a stabilization method to numerically calculate the dispersion relations and quality factors of optically confined finite structures. For the coupled resonator optical waveguide (CROW) made in a photonic-crystal slab (PCS) used as an example, the dispersion curve is normally not well defined due to the appearance of discontinuities, which do not occur in a two-dimensional CROW with infinite slab height. Therefore, there is less effort devoted to the calculation of quasi dispersion curves of the CROW in a slab. The dispersion relation of the PCS CROW can only be obtained by theoretical fitting to the experimental data under the tight-binding approximation. Here, we demonstrate the use of a stabilization method to calculate the quasi dispersion relation of a PCS CROW accurately. From the stabilization graph, we can calculate the quality factor for an eigenfrequency and properly choose the size of the simulation cell to avoid coupling the CROW modes with the unconfined modes and to accurately calculate the dispersion curve of the PCS CROW using the plane-wave expansion method. The proposed method and results not only provide important information for designing practical photonic devices such as slow-light optical waveguides and nonlinear photonic devices for the PCS CROWs but also can be applied to compute the quality factors and resonance frequencies of microcavities or nanocavities.

© 2012 Optical Society of America

OCIS Codes
(200.4490) Optics in computing : Optical buffers
(230.1150) Optical devices : All-optical devices
(230.7400) Optical devices : Waveguides, slab
(230.5298) Optical devices : Photonic crystals

ToC Category:
Optical Devices

History
Original Manuscript: March 7, 2012
Revised Manuscript: June 7, 2012
Manuscript Accepted: July 31, 2012
Published: August 28, 2012

Citation
Chih-Hsien Huang, Wei-Shuo Li, Jing-Nuo Wu, Wen-Feng Hsieh, and Yia-Chung Chang, "Calculation of quasi dispersion curves and quality factors of coupled resonator optical waveguides in photonic-crystal slabs," J. Opt. Soc. Am. B 29, 2510-2515 (2012)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-29-9-2510


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. E. Yablonovitch, “Inhibited spontaneous emission on solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987). [CrossRef]
  2. S. Y. Lin, E. Chow, J. Bur, S. G. Johnson, and J. D. Joannopoulos, “Low-loss, wide-angle Y splitter ∼1.6  μm wavelengths built with a two-dimensional photonic crystal,” Opt. Lett. 27, 1400–1402 (2002). [CrossRef]
  3. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999). [CrossRef]
  4. D. N. Christodoulides and N. K. Efremidis, “Discrete temporal solitons along a chain of nonlinear coupled microcavities embedded in photonic crystals,” Opt. Lett. 27, 568–570 (2002). [CrossRef]
  5. C. F. Ouyang, Z. Q. Xiong, F. Y. Zhao, B. Q. Dong, X. H. Hu, X. H. Liu, and J. Zi, “Slow light with low group-velocity dispersion at the edge of photonic graphene,” Phys. Rev. A 84, 015801 (2011). [CrossRef]
  6. K. H. Tian, W. Arora, S. Takahashi, J. Hong, and G. Barbastathis, “Dynamic group velocity control in a mechanically tunable photonic-crystal coupled-resonator optical waveguide,” Phys. Rev. B 80, 134305 (2009). [CrossRef]
  7. M. Bayindir and E. Ozbay, “Heavy photons at coupled-cavity waveguide band edges in a three-dimensional photonic crystal,” Phys. Rev. B 62, R2247–R2250 (2000). [CrossRef]
  8. M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000). [CrossRef]
  9. M. L. Cooper, G. Gupta, M. A. Schneider, W. M. J. Green, S. Assefa, F. N. A. Xia, D. K. Gifford, and S. Mookherjea, “Waveguide dispersion effects in silicon-on-insulator coupled-resonator optical waveguides,” Opt. Lett. 35, 3030–3032 (2010). [CrossRef]
  10. S. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt. 12, 104004 (2010). [CrossRef]
  11. A. Talneau, “Slow light modes for optical delay lines: 2D photonic crystal-based design structures, performances and challenges,” J. Opt. 12, 104005 (2010). [CrossRef]
  12. C. H. Huang, Y. H. Lai, S. C. Cheng, and W. F. Hsieh, “Modulation instability in nonlinear coupled resonator optical waveguides and photonic crystal waveguides,” Opt. Express 17, 1299–1307 (2009). [CrossRef]
  13. C. H. Huang, J. N. Wu, S. C. Cheng, and W. F. Hsieh, “The evolution of solitons in coupled resonator optical waveguides and photonic-crystal waveguides,” Comput. Phys. Commun. 182, 232–236 (2011). [CrossRef]
  14. D. P. Fussell and M. M. Dignam, “Quantum-dot photon dynamics in a coupled-cavity waveguide: observing band-edge quantum optics,” Phys. Rev. A 76, 053801 (2007). [CrossRef]
  15. M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photon. 2, 741–747 (2008). [CrossRef]
  16. C. Agger, T. S. Skovgard, N. Gregersen, and J. Mork, “Modeling of mode-locked coupled-resonator optical waveguide lasers,” IEEE J. Quantum Electron. 46, 1804–1812 (2010). [CrossRef]
  17. H. C. Liu and A. Yariv, “Synthesis of high-order bandpass filters based on coupled-resonator optical waveguides (CROWs),” Opt. Express 19, 17653–17668 (2011). [CrossRef]
  18. J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express 12, 90–103 (2004). [CrossRef]
  19. S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999). [CrossRef]
  20. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Modeling the Flow of Light (Princeton University, 2008).
  21. S. G. Johnson, and J. D. Joannopoulos, Photonic Crystals: the Road from Theory to Practice (Kluwer Academic, 2002), pp. 99–112.
  22. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001). [CrossRef]
  23. V. A. Mandelshtam, T. R. Ravuri, and H. S. Taylor, “Calculation of the density of resonance states using the stabilization method,” Phys. Rev. Lett. 70, 1932–1935 (1993). [CrossRef]
  24. D. M. T. Kuo and Y. C. Chang, “Electron tunneling rate in quantum dots under a uniform electric field,” Phys. Rev. B 61, 11051–11056 (2000). [CrossRef]
  25. E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000). [CrossRef]
  26. C. H. Huang, J. N. Wu, P. Y. Lee, W. F. Hsieh, and S. C. Cheng, “The properties and design concepts of photonic directional couplers made of photonic crystal slabs,” J. Phys. D 43, 465103 (2010). [CrossRef]

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.

Figures

Fig. 1. Fig. 2. Fig. 3.
 
Fig. 4.
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited