OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 21, Iss. 10 — Oct. 1, 2004
  • pp: 1818–1832

Distributed and localized feedback in microresonator sequences for linear and nonlinear optics

John E. Heebner, Philip Chak, Suresh Pereira, John E. Sipe, and Robert W. Boyd  »View Author Affiliations

JOSA B, Vol. 21, Issue 10, pp. 1818-1832 (2004)

View Full Text Article

Acrobat PDF (1105 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Sequences of optical microresonators can be used to construct densely integrated structures that display slow group velocity, ultrahigh or low dispersion of controllable sign, enhanced self-phase modulation, and nonlinear optical switching. We consider four archetypal geometries consisting of effectively one-dimensional sequences of coupled microresonators. Two of these cases exhibit distributed feedback such as is found in a traditional multilayered structure supporting photonic bandgaps. The other two exhibit localized feedback and resonant enhancement but are free from photonic bandgaps. All of these structures offer unique properties useful for controlling the propagation of light pulses on a chip.

© 2004 Optical Society of America

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(190.4360) Nonlinear optics : Nonlinear optics, devices
(190.4390) Nonlinear optics : Nonlinear optics, integrated optics
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
(230.5750) Optical devices : Resonators
(250.5300) Optoelectronics : Photonic integrated circuits

John E. Heebner, Philip Chak, Suresh Pereira, John E. Sipe, and Robert W. Boyd, "Distributed and localized feedback in microresonator sequences for linear and nonlinear optics," J. Opt. Soc. Am. B 21, 1818-1832 (2004)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, Calif., 2001).
  2. B. E. Little and S. T. Chu, “Toward very large-scale integrated photonics,” Opt. Photonics News 11 (11), 24–29 (2000).
  3. G. I. Stegeman and C. Seaton, “Nonlinear integrated optics,” J. Appl. Phys. 58, 57 (1985).
  4. V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
  5. J. E. Heebner and R. W. Boyd, “Enhanced all-optical switching by use of a nonlinear fiber ring resonator,” Opt. Lett. 24, 847–849 (1999).
  6. Strictly speaking, the first configuration is constructed from two-port resonators and is a special case.
  7. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999).
  8. Y. Xu, R. K. Lee, and A. Yariv, “Scattering theory analysis of waveguide-resonator coupling,” Phys. Rev. E 62, 7389–7404 (2000).
  9. J. E. Heebner, R. W. Boyd, and Q. Park, “Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonator-array waveguide,” Phys. Rev. E 65, 036619 (2002).
  10. D. Rafizadeh, J. P. Zhang, S. C. Hagness, A. Taflove, K. A. Stair, S. T. Ho, and R. C. Tiberio, “Waveguide-coupled AlGaAs/GaAs microcavity ring and disk resonators with high finesse and 21.6-nm free-spectral range,” Opt. Lett. 22, 1244–1246 (1997).
  11. K. Djordjev, S. Choi, and P. D. Dapkus, “High-Q vertically coupled InP microdisk resonators,” IEEE Photon. Technol. Lett. 14, 331–333 (2002).
  12. P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single-photon turnstile device,” Science 290, 2282–2285 (2000).
  13. We define the finesse as the free spectral range (FSR) divided by the full width at half-depth (FWHD) of the resonance peak. Applying this definition to either the normalized group delay or the intensity buildup of an all-pass resonator, the finesse is calculated as F =FSR FWHD =2π 2 arccos 2r 1+r2 r≈1 π 1−r. In the case of the add–drop resonator, r is replaced with r1 r2.
  14. C. K. Madsen and G. Lenz, “Optical all-pass filters for phase response design with applications for dispersion compensation,” IEEE Photon. Technol. Lett. 10, 994–996 (1998).
  15. 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).
  16. B. E. Little, S. T. Chu, J. V. Hryniewicz, and P. P. Absil, “Filter synthesis for periodically coupled microring resonators,” Opt. Lett. 25, 344–346 (2000).
  17. C. K. Madsen, “Efficient architectures for exactly realizing optical filters with optimum bandpass designs,” IEEE Photon. Technol. Lett. 10, 1136–1138 (1998).
  18. R. Orta, P. Savi, R. Tascone, and D. Trinchero, “Synthesis of multiple ring resonator filters for optical systems,” IEEE Photon. Technol. Lett. 7, 1447–1449 (1995).
  19. B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
  20. S. Mookherjea, D. S. Cohen, and A. Yariv, “Nonlinear dispersion in a coupled-resonator optical waveguide,” Opt. Lett. 27, 933–935 (2002).
  21. R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, San Diego, Calif., 2003).
  22. J. E. Heebner, R. W. Boyd, and Q. Park, “SCISSOR solitons and other propagation effects in microresonator modified waveguides,” J. Opt. Soc. Am. B 19, 722–731 (2002).
  23. 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).
  24. 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).
  25. W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett. 58, 160–163 (1987).
  26. S. Pereira, J. E. Sipe, J. E. Heebner, and R. W. Boyd, “Gap solitons in a two-channel SCISSOR structure,” Opt. Lett. 27, 536–538 (2002).
  27. S. T. Chu, B. E. Little, W. Pan, T. Kaneko, and Y. Kokubun, “Second-order filter response from parallel coupled glass microring resonators,” IEEE Photon. Technol. Lett. 11, 1426–1428 (1999).
  28. 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).
  29. G. Griffel, “Synthesis of optical filters using ring resonator arrays,” IEEE Photon. Technol. Lett. 12, 810–812 (2000).
  30. A. Melloni, “Synthesis of a parallel-coupled ring-resonator filter,” Opt. Lett. 26, 917–919 (2001).
  31. R. Grover, V. Van, T. A. Ibrahim, P. P. Absil, L. C. Calhoun, F. G. Johnson, J. V. Hryniewicz, and P.-T. Ho, “Parallel-cascaded semiconductor microring resonators for high-order and wide-FSR Filters,” J. Lightwave Technol. 20, 900–905 (2002).
  32. A. Melloni, F. Morichetti, and M. Martinelli, “Optical slow wave structures,” Opt. Photon. News 14, 44–48 (2003).
  33. R. W. Boyd and D. J. Gauthier, “Slow and fast light,” Prog. Opt. 33, 497–530 (2002).
  34. G. Lenz, B. J. Eggleton, C. K. Madsen, and R. E. Slusher, “Optical delay lines based on optical filters,” IEEE J. Quantum Electron. 37, 525–532 (2001).
  35. C. K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez, and R. E. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” IEEE Photon. Technol. Lett. 11, 1623–1625 (1999).
  36. K. Djordjev, S. Choi, and P. D. Dapkus, “Microdisk tunable resonant filters and switches,” IEEE Photon. Technol. Lett. 14, 828–830 (2002).
  37. J. E. Heebner and R. W. Boyd, “Slow and fast light in resonator-coupled waveguides,” J. Mod. Opt. 49, 2629–2636 (2002).
  38. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
  39. G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, and R. E. Slusher, “Dispersive properties of optical filters for WDM Systems,” IEEE J. Quantum Electron. 34, 1390–1402 (1998).
  40. 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).
  41. Y. Yamamoto and R. E. Slusher, “Optical processes in microcavities,” Phys. Today 46 (6), 66–74 (1993).
  42. S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415, 621–623 (2002).
  43. J. Popp, M. H. Fields, and R. K. Chang, “Q-switching by saturable absorption in microdroplets: elastic scattering and laser emission,” Opt. Lett. 22, 1296–1298 (1997).
  44. F. C. Blom, D. R. van Dijk, H. J. Hoekstra, A. Driessen, and Th. J. A. Popma, “Experimental study of integrated-optics microcavity resonators: toward an all-optical switching device,” Appl. Phys. Lett. 71, 747–749 (1997).
  45. V. Van, T. A. Ibrahim, K. Ritter, P. P. Absil, F. G. Johnson, R. Grover, J. Goldhar, and P.-T. Ho, “All-optical nonlinear switching in GaAs–AlGaAs microring resonators,” IEEE Photon. Technol. Lett. 14, 74–77 (2002).
  46. T. A. Ibrahim, V. Van, and P.-T. Ho, “All-optical time-division demultiplexing and spatial pulse routing with a GaAs/AlGaAs microring resonator,” Opt. Lett. 27, 803–805 (2002).
  47. J. E. Heebner, N. N. Lepeshkin, A. Schweinsberg, G. W. Wicks, R. W. Boyd, R. Grover, and P.-T. Ho, “Enhanced linear and nonlinear optical phase response of AlGaAs microring resonators,” Opt. Lett. 29, 769–771 (2004).
  48. P. Chak, J. E. Sipe, and S. Pereira, “Depositing light in a photonic stop gap by use of Kerr nonlinear microresonators,” Opt. Lett. 28, 1966–1968 (2003).
  49. S. Pereira, P. Chak, and J. E. Sipe, “Gap-soliton switching in short microresonator structures,” J. Opt. Soc. Am. B 19, 2191–2202 (2002).
  50. S. Blair, “Nonlinear sensitivity enhancement with one-dimensional photonic bandgap microcavity arrays,” Opt. Lett. 27, 613–615 (2002).
  51. M. Soljacic, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B 19, 2052–2059 (2002).
  52. P. Absil, J. V. Hryniewicz, B. E. Little, P. S. Cho, R. A. Wilson, L. G. Jonekis, and P.-T. Ho, “Wavelength conversion in GaAs micro-ring resonators,” Opt. Lett. 25, 554–556 (2000).
  53. S. T. Ho, C. E. Soccolich, M. N. Islam, W. S. Hobson, A. F. J. Levi, and R. E. Slusher, “Large nonlinear phase shifts in low-loss AlGaAs waveguides near half-gap,” Appl. Phys. Lett. 59, 2558–2560 (1991).
  54. G. I. Stegeman, A. Villeneuve, J. Kang, J. S. Aitchison, C. N. Ironside, K. Al-Hemyari, C. C. Yang, C. H. Lin, H. H. Lin, G. T. Kennedy, R. S. Grant, and W. Sibbett, “AlGaAs below the half-gap: the silicon of nonlinear optical materials,” Int. J. Nonlinear Opt. Phys. 3, 347–371 (1994).
  55. G. Lenz, J. Zimmermann, T. Katsufuji, M. E. Lines, H. Y. Hwang, S. Spalter, R. E. Slusher, S.-W. Cheong, J. S. Sanghera, and I. D. Aggarwal, “Large Kerr effect in bulk Se-based chalcogenide glasses,” Opt. Lett. 25, 254–256 (2000).
  56. S. Spalter, H. Y. Wang, J. Zimmermann, G. Lenz, T. Katsufuji, S.-W. Cheong, and R. E. Slusher, “Strong self-phase modulation in planar chalcogenide glass waveguides,” Opt. Lett. 27, 363–365 (2002).
  57. J. M. Harbold, F. O. Ilday, F. W. Wise, J. S. Sanghera, V. Q. Nguyen, L. B. Shaw, and I. D. Aggarwal, “Highly nonlinear As–S–Se glasses for all-optical switching,” Opt. Lett. 27, 119–121 (2002).
  58. P. Chak, J. E. Sipe, and S. Pereira, “Lorentzian model for nonlinear switching in a microresonator structure,” Opt. Commun. 213, 163–171 (2002).
  59. S. Pereira, P. Chak, and J. E. Sipe, “All-optical AND gate by use of a Kerr nonlinear microresonator structure,” Opt. Lett. 28, 444–446 (2003).
  60. B. E. Little and S. T. Chu, “Estimating surface roughness loss and output coupling in microdisk resonators,” Opt. Lett. 21, 1390–1392 (1996).
  61. V. B. Braginsky and V. S. Ilchenko, “Properties of optical dielectric microresonators,” Sov. Phys. Dokl. 32, 306–307 (1987).
  62. S. Arnold, C. T. Liu, W. B. Whitten, and J. M. Ramsey, “Room-temperature microparticle-based persistent spectral hole burning memory,” Opt. Lett. 16, 420–422 (1991).
  63. N. Dubreuil, J. C. Knight, D. K. Leventhal, V. Sandoghdar, J. Hare, and V. Lefevre, “Eroded monomode optical fiber for whispering-gallery mode excitation in fused-silica microspheres,” Opt. Lett. 20, 813–815 (1995).
  64. M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, “Ultimate Q of optical microsphere resonators,” Opt. Lett. 21, 453–455 (1996).
  65. D. W. Vernooy, V. S. Ilchenko, H. Mabuchi, E. W. Streed, and H. J. Kimble, “High-Q measurements of fused-silica microspheres in the near infrared,” Opt. Lett. 23, 247–249 (1998).
  66. J.-P. Laine, B. E. Little, and H. A. Haus, “Etch-eroded fiber coupler for whispering-gallery-mode excitation in high-Q silica microspheres,” IEEE Photon. Technol. Lett. 11, 1429–1430 (1999).
  67. M. Cai, O. Painter, and K. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-galley mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
  68. S. Blair, J. E. Heebner, and R. W. Boyd, “Beyond the absorption-limited nonlinear phase shift with microring resonators,” Opt. Lett. 27, 357–359 (2002).
  69. J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, and R. C. Tiberio, “Photonic-wire laser,” Phys. Rev. Lett. 75, 2678–2681 (1995).
  70. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3 (7), 4–11 (1998).
  71. M. D. Rahn, A. M. Fox, M. S. Skolnick, and T. F. Krauss, “Propagation of ultrashort nonlinear pulses through two-dimensional AlGaAs high-contrast photonic crystal waveguides,” J. Opt. Soc. Am. B 19, 716–721 (2002).
  72. S. Mingaleev and Y. Kivshar, “Nonlinear transmission and light localization in photonic-crystal waveguides,” J. Opt. Soc. Am. B 19, 2241–2249 (2002).
  73. C. V. Bennett and B. H. Kolner, “Upconversion time microscope demonstrating 103× magnification of femtosecond waveforms,” Opt. Lett. 24, 783–785 (1999).

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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited