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Optics Express

Optics Express

  • Vol. 17, Iss. 7 — Mar. 30, 2009
  • pp: 5176–5192

The effects of periodic and quasi-periodic orders on the photonic bandgap structures of microring coupled-resonator optical waveguides

Thomas Y. L. Ang and Mee-Koy Chin  »View Author Affiliations


Optics Express, Vol. 17, Issue 7, pp. 5176-5192 (2009)
http://dx.doi.org/10.1364/OE.17.005176


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Abstract

We present a coupling matrix formalism to investigate the effects of periodic and quasi-periodic orders on the photonic bandgap (PBG) structures of coupled-resonator optical waveguides (CROWs) based on microring resonators. For the periodic order case, size-tuned defects are introduced at periodic locations among the regular rings, which are size-untuned, to form a periodic ordered CROW system. The periodic coupled defects result in multiple localization states that lead to the formation of mini-defect bands and mini-PBGs within the PBG of a defect-free CROW. The position and number of such mini-defect bands depend on the size tuning of the defects. For the quasi-periodic order case, the arrangement of the defects and the regular rings in the ring cascade is an intermediate between periodic order and randomness, thus forming a quasi-periodic ordered CROW system. The effects of quasi-periodicity on the PBG structures are illustrated using the Fibonacci sequences, which result in a single high-Q localized state to appear that gradually transits to a mini-band within a wide photonic stop band as the number of lattice cells increases.

© 2009 Optical Society of America

OCIS Codes
(130.2790) Integrated optics : Guided waves
(230.3120) Optical devices : Integrated optics devices
(230.5750) Optical devices : Resonators

ToC Category:
Nonlinear Optics

History
Original Manuscript: October 13, 2008
Revised Manuscript: November 22, 2008
Manuscript Accepted: November 22, 2008
Published: March 18, 2009

Citation
Thomas Y. L. Ang and Mee-Koy Chin, "The effects of periodic and quasi-periodic orders on the photonic bandgap structures of microring coupled-resonator optical waveguides," Opt. Express 17, 5176-5192 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-7-5176


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References

  1. 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]
  2. D. D.  Smith, H.  Chang, K. A.  Fuller, A. T.  Rosenberger, and R. W.  Boyd, "Coupled-resonator-induced transparency," Phys. Rev. A  69, 063804 (2004). [CrossRef]
  3. Y.  Xu, Y.  Li, R. K.  Lee, and A.  Yariv, "Scattering-theory analysis of waveguide-resonator coupling," Phys. Rev. E  62,7389-7404 (2000). [CrossRef]
  4. B. E.  Little, S. T.  Chu, H. A.  Haus, J.  Foresi, and J.-P.  Laine, "Microring resonator channel dropping filters," J. Lightwave Technol.  15, 998-1005 (1997). [CrossRef]
  5. Y. M.  Landobasa, S.  Darmawan, and M. K.  Chin, "Matrix analysis of 2-D micro-resonator lattice optical filters," IEEE J. Quantum Electron.  41, 1410-1418 (2005). [CrossRef]
  6. F. Xia, M. Rooks, L. Sekaric, and Y. Vlasov, "Ultra-compact high order ring resonator filters using submicron silicon photonic wires for on-chip optical interconnects," Opt. Express 15, 11934-11941 (2007). [CrossRef]
  7. W.-Y. Chen, V. Van, W. N. Herman, and P.-T. Ho, "Periodic Microring Lattice as a Bandstop Filter," IEEE Photon. Technol. Lett. 18, 2041-2043 (2006). [CrossRef]
  8. J. K. S. Poon, J. Scheuer, Y. Xu, and A. Yariv, "Designing coupled-resonator optical waveguide delay lines," J. Opt. Soc. Am. B. 21, 1665-1673 (2004). [CrossRef]
  9. F. Xia, L. Sekaric, and Y. Vlasov, "Ultracompact optical buffers on a silicon chip," Nature Photonics 1, 65 (2007). [CrossRef]
  10. Y. Landobasa and M. Chin, "Defect modes in micro-ring resonator arrays," Opt. Express 13, 7800-7815 (2005). [CrossRef]
  11. J. E. Heebner, R. W. Boyd, and Q. Park, "SCISSOR solitons and other novel propagation effects in microresonator-modified waveguides," J. Opt. Soc. Am. B 19, 722-731 (2002). [CrossRef]
  12. M. M. Sigalas, C. M. Soukoulis, C. T. Chan and D. Turner, "Localization of electromagnetic waves in two-dimensional disordered systems," Phys. Rev. B. 53, 8340 (1996). [CrossRef]
  13. J. S.  Foresi, P. R.  Villeneuve, J.  Ferrera, E. R.  Thoen, G.  Steinmeyer, S.  Fan, J. D.  Joannopoulos, L. C.  Kimerling, H. I.  Smith, and E. P.  Ippen, "Photonic-bandgap microcavities in optical waveguides," Nature  390, 143-145 (1997). [CrossRef]
  14. J. Poon, J. Scheuer, S. Mookherjea, G. Paloczi, Y. Huang, and A. Yariv, "Matrix analysis of microring coupled-resonator optical waveguides," Opt. Express 12, 90-103 (2004). [CrossRef]
  15. H. Hiramoto and M. Kohmoto, "Electronic spectral and wave function properties of one-dimensional quasi-periodic systems: A scaling approach," Int. J. Mod. Phys. B. 6, 281 (1992). [CrossRef]
  16. X. Huang, Y. Wang, and C. Gong, "Numerical investigation of light-wave localization in optical Fibonacci superlattices with symmetric internal structure, " J. Phys. Condens. Matter. 11, 7645 (1999). [CrossRef]
  17. L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc, and J. Haavisto, "Photon bandgap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals," Appl. Phys. Lett. 84, 5186 (2004). [CrossRef]
  18. L. Moretti and V. Mocella, "Two-dimensional photonic aperiodic crystals based on Thue-Morse sequence," Opt. Express 15, 15314-15323 (2007). [CrossRef]
  19. K. Mnaymneh and R. C. Gauthier, "Mode localization and band-gap formation in defect-free photonic quasicrystals," Opt. Express 15, 5089-5099 (2007). [CrossRef]
  20. S. V. Boriskina, A. Gopinath, and L. Dal Negro, "Optical gap formation and localization properties of optical modes in deterministic aperiodic photonic structures," Opt. Express 16, 18813-18826 (2008). [CrossRef]
  21. E. Maciá, "The role of aperiodic order in science and technology," Rep. Prog. Phys. 69, 397 (2006). [CrossRef]
  22. J.-B. Suck, M. Schreiber, and P. Häussler, Quasicrystals: An Introduction to Structure, Physical Properties and Applications (Springer-Verlag Berlin Heidelberg, 2002), Chap. 2.
  23. H. A. Haus, Waves and fields in optoelectronics (New York: Prentice-Hall, 1984).
  24. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 2001), Chap.1.
  25. T.  Kalamakis and T. Sphicopoulos, "Analytical expressions for the resonant frequencies and modal fields of finite coupled optical cavity chains," IEEE J. Quantum Electron.  41, 1419-1425 (2007). [CrossRef]
  26. Y.  Chen and S.  Blair, "Nonlinearity enhancement in finite coupled-resonator slow-light waveguides," Opt. Express  12, 3353-3366 (2004). [CrossRef]
  27. L. Y. M. Tobing, P. Dumon, R. Baets, and M. Chin, "Boxlike filter response based on complementary photonic bandgaps in two-dimensional microresonator arrays," Opt. Lett. 33, 2512-2514 (2008). [CrossRef]
  28. FullWAVE, Rsoft Design Group, Inc., Ossining, NY.
  29. J. Capmany, P. Muñoz, J. D. Domenech, and M. A. Muriel, "Apodized coupled resonator waveguides," Opt. Express 15, 10196-10206 (2007). [CrossRef]
  30. C. E. Png, G. H. Park, S. T. Lim, E. P. Li, A. J. Danner, K. Ogawa, and Y. T. Tan, "Electrically controlled silicon-based photonic crystal chromatic dispersion compensator with ultralow power consumption," Appl. Phys. Lett. 93, 061111 (2008). [CrossRef]

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