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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: G. I. Stegeman
  • Vol. 23, Iss. 6 — Jun. 1, 2006
  • pp: 1137–1145

Spectral characteristics of coupled resonators

Shayan Mookherjea  »View Author Affiliations

JOSA B, Vol. 23, Issue 6, pp. 1137-1145 (2006)

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In devices consisting of a large number of coupled resonators, the coupling coefficients are unlikely to be identical throughout the ensemble, owing to statistical fluctuations in the fabrication process, the surrounding environment, or the device operation process. We describe how the frequency spectrum of such a disordered device differs from that of earlier models that assume a perfectly ordered lattice of resonant elements. Based on simulations for a large number of nominally identical resonators perturbed by disorder in the coupling coefficients, we describe the change in the density of modes (resonances) using both Hermitian and non-Hermitian coupling pathways, following recent experimental demonstrations. The band-edge zero-group-velocity state is highly sensitive to disorder, and applications that rely on band-edge effects, such as ultraslow light and group-velocity dispersion compensation, may be strongly impacted.

© 2006 Optical Society of America

OCIS Codes
(140.4780) Lasers and laser optics : Optical resonators
(230.7370) Optical devices : Waveguides

ToC Category:
Optical Devices

Original Manuscript: November 11, 2005
Manuscript Accepted: December 9, 2005

Shayan Mookherjea, "Spectral characteristics of coupled resonators," J. Opt. Soc. Am. B 23, 1137-1145 (2006)

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  1. J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, "Higher order filter response in coupled microring resonators," IEEE Photon. Technol. Lett. 12, 320-322 (2000). [CrossRef]
  2. B. Liu, A. Shakouri, and J. E. Bowers, "Wide tunable double ring coupled lasers," IEEE Photon. Technol. Lett. 14, 600-602 (2002). [CrossRef]
  3. D. Rabus, M. Hamacher, H. Heidrich, and U. Troppenz, "High-Q channel dropping filters using ring resonators with integrated SOAs," IEEE Photon. Technol. Lett. 14, 1442-1444 (2002). [CrossRef]
  4. R. Iliew, U. Peschel, C. Etrich, and F. Lederer, "Light propagation via coupled defects in photonic crystals," in Conference on Lasers and Electro-Optics, Vol. 73 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), postconference edition, 191-192
  5. A. Melloni, F. Morichetti, and M. Martinelli, "Optical slow wave structures," Opt. Photonics News 14, 44-48 (2003). [CrossRef]
  6. 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]
  7. Y. Chen, G. Pasrija, B. Farhang-Boroujeny, and S. Blair, "Engineering the nonlinear phase shift with multistage autoregressive moving-average optical filters," Appl. Opt. 44, 2564-2574 (2005). [CrossRef] [PubMed]
  8. J. B. Khurgin, "Optical buffers based on slow light in electromagnetically induced transparent media and coupled resonator structures: comparative analysis," J. Opt. Soc. Am. B 22, 1062-1074 (2005). [CrossRef]
  9. J. B. Pendry and A. MacKinnon, "Calculation of photon dispersion relations," Phys. Rev. Lett. 69, 2772-2775 (1992). [CrossRef] [PubMed]
  10. C. Barnes, T. Wei-chao, and J. B. Pendry, "The localization length and density of states of 1D disordered systems," J. Phys. Condens. Matter 3, 5297-5305 (1991). [CrossRef]
  11. H. Matsuoka and R. Grobe, "Effect of eigenmodes on the optical transmission through one-dimensional random media," Phys. Rev. E 71, 046606 (2005). [CrossRef]
  12. D. J. Thouless, "A relation between the density of states and range of localization for one dimensional random systems," J. Phys. C 5, 77-81 (1972). [CrossRef]
  13. J. M. Ziman, Models of Disorder (Cambridge U. Press, 1979).
  14. A. Gonis, Green Functions for Ordered and Disordered Systems (North-Holland, 1992).
  15. W. H. Louisell, Coupled Mode and Parametric Electronics (Wiley, 1960).
  16. H. A. Haus, Electromagnetic Noise and Quantum Optical Measurements (Springer, 2000).
  17. C. Cohen-Tannoudji, B. Diu, and F. Laloë, Quantum Mechanics (Wiley, 1977).
  18. R. J. C. Spreeuw and J. P. Woerdman, "Optical atoms," in Progress in Optics, Vol. XXXI, E.Wolf, ed., pp. 263-319 (North-Holland, 1993).
  19. T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, "Tight-binding photonic molecule modes of resonant bispheres," Phys. Rev. Lett. 82, 4623-4626 (1999). [CrossRef]
  20. A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford, 1997).
  21. T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Mode coupling in traveling-wave resonators," Opt. Lett. 27, 1669-1671 (2002). [CrossRef]
  22. D. S. Weiss, V. Sandoghdar, J. Hare, V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, "Splitting of high-Q Mie modes induced by light backscattering in silica microspheres," Opt. Lett. 20, 1835-1837 (1995). [CrossRef] [PubMed]
  23. 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]
  24. M. Bayer, I. Gutbrod, A. Forchel, T. Reinecke, P. Knipp, R. Werner, and J. Reithmaier, "Optical demonstration of a crystal band structure formation," Phys. Rev. Lett. 83, 5374 (1999). [CrossRef]
  25. 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] [PubMed]
  26. Y. Xu, R. K. Lee, and A. Yariv, "Propagation and second-harmonic generation of electromagnetic waves in a coupled-resonator optical waveguide," J. Opt. Soc. Am. B 17, 387-400 (2000). [CrossRef]
  27. S. Olivier, C. Smith, M. Rattier, H. Benisty, C. Weisbuch, T. Krauss, R. Houdré, and U. Oesterlé, "Miniband transmission in a photonic crystal coupled-resonator optical waveguide," Opt. Lett. 26, 1019-1021 (2001). [CrossRef]
  28. S. Mookherjea, "Coupled-resonator optical waveguides and multiplexed solitons," Ph.D. thesis (California Institute of Technology, 2003).
  29. H. Altug and J. Vuckovic, "Two dimensional coupled photonic crystal resonator arrays," Appl. Phys. Lett. 84, 161-163 (2004). [CrossRef]
  30. S. Mookherjea and A. Yariv, "Optical pulse propagation in the tight-binding approximation," Opt. Express 9, 91-96 (2001). [CrossRef] [PubMed]
  31. D. N. Christodoulides and R. I. Joseph, "Discrete self-focusing in nonlinear arrays of coupled waveguides," Opt. Lett. 13, 794-796 (1988). [CrossRef] [PubMed]
  32. 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]
  33. S. Mookherjea and A. Yariv, "Kerr-stabilized super-resonant modes in coupled-resonator optical waveguides," Phys. Rev. E 66, 046610 (2002). [CrossRef]
  34. A. Yariv, "Coupled-mode theory for guided-wave optics," IEEE J. Quantum Electron. QE-9, 919-933 (1973). [CrossRef]
  35. J. N. Franklin, Matrix Theory (Dover, 2000).
  36. J. E. Heebner, R. W. Boyd, and Q.-H. Park, "SCISSOR solitons and other novel propagation effects in microresonator-modified waveguides," J. Opt. Soc. Am. B 19, 722-731 (2004).
  37. J. E. Heebner, P. Chak, S. Pereira, J. E. Sipe, and R. W. Boyd, "Distributed and localized feedback in microresonator sequences for linear and nonlinear optics," J. Opt. Soc. Am. B 21, 1818-1832 (2004). [CrossRef]
  38. S. Mookherjea, "Mode cycling in microring optical resonators," Opt. Lett. 30, 2751-2753 (2005). [CrossRef] [PubMed]
  39. M. Kulishov, J. M. Laniel, N. Bélanger, and D. V. Plant, "Trapping light in a ring resonator using a grating-assisted coupler with asymmetric transmission," Opt. Express 13, 3567-3578 (2005). [CrossRef] [PubMed]
  40. M. Greenberg and M. Orenstein, "Unidirectional complex grating assisted couplers," Opt. Express 12, 4013-4018 (2004). [CrossRef] [PubMed]
  41. S. Mookherjea, "Principles and applications of coupled microring optical resonators," in Workshop on Fibres and Optical Passive Components 2005: 4th IEEE/LEOS Workshop on Fibers and Optical Passive Components (IEEE, Piscataway, NJ, 2005), pp. 51-57 .
  42. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77 (Cambridge U. Press, 1996).
  43. N. Hatano and D. R. Nelson, "Localized transitions in non-Hermitian quantum mechanics," Phys. Rev. Lett. 77, 570-573 (1996). [CrossRef] [PubMed]
  44. I. Y. Goldsheid and B. A. Khoruzhenko, "Distribution of eigenvalues in non-Hermitian Anderson models," Phys. Rev. Lett. 80, 2897-2900 (1998). [CrossRef]
  45. J. Feinberg and A. Zee, "Spectral curves of non-hermitian hamiltonians," Nucl. Phys. B 552, 599 (1999). [CrossRef]
  46. R. M. Martin, Electronic Structure (Cambridge U. Press, 2004).
  47. E. R. Smith, "One-dimensional X−Y model with random coupling constants I. Thermodynamics," J. Phys. C 3, 1419-1432 (1970). [CrossRef]
  48. I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, 1988).
  49. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Harcourt, 1976).
  50. S. Mookherjea, "Dispersion characteristics of coupled-resonator optical waveguides," Opt. Lett. 30, 2406-2408 (2005). [CrossRef] [PubMed]

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