Abstract

We use the coupling matrix formalism to investigate continuous wave and pulse propagation through microring coupled-resonator optical waveguides (CROWs). The dispersion relation agrees with that derived using the tight-binding model in the limit of weak inter-resonator coupling. We obtain an analytical expression for pulse propagation through a semi-infinite CROW in the case of weak coupling which fully accounts for the nonlinear dispersive characteristics. We also show that intensity of a pulse in a CROW is enhanced by a factor inversely proportional to the inter-resonator coupling. In finite CROWs, anomalous dispersions allows for a pulse to propagate with a negative group velocity such that the output pulse appears to emerge before the input as in �??superluminal�?? propagation. The matrix formalism is a powerful approach for microring CROWs since it can be applied to structures and geometries for which analyses with the commonly used tight-binding approach are not applicable.

© 2004 Optical Society of America

PDF Article

References

  • View by:
  • |

  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).
  2. 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 77, 387�??400 (2000).
  3. N. Stefanou and A. Modinos, �??Impurity bands in photonic insulators,�?? Phys. Rev. B 57, 12 127�??12 133 (1998).
    [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).
  5. S. Mookherjea and A. Yariv, �??Kerr-stabilized super-resonant modes in coupled-resonator optical waveguides,�?? Phys. Rev. E 66, 046 610 (2002).
    [CrossRef]
  6. J. E. Heebner and R. W. Boyd, �??�??Slow�?? and �??fast�?? light in resonator-coupled waveguides,�?? J. Mod. Opt. 49, 2629�??2636 (2002).
  7. C. K. Madsen, �??General IIR optical filter design for WDM applications using all-pass filters,�?? IEEE J. Lightwave Technol. 18, 860�??868 (2000).
    [CrossRef]
  8. 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).
    [CrossRef]
  9. B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, �??Vertically coupled glass microring resonator channel dropping filters,�?? IEEE Photon. Technol. Lett. 11, 215�??217 (1999).
    [CrossRef]
  10. 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]
  11. A. Yariv and P. Yeh, Optical waves in crystals: Propagation and control of laser radiation (Wiley, New York, 1984).
  12. K. Oda, N. Takato, and H. Toba, �??A wide-FSR waveguide double-ring resonator for optical FDM transmission systems,�?? IEEE J. of Lightwave Technol. 9, 728�??736 (1991).
  13. 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).
    [CrossRef]
  14. 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]
  15. A. Melloni, R. Costa, P. Monguzzi, and M. Martinelli, �??Ring-resonator filters in silicon oxynitride technology for dense wavelength-division multiplexing systems,�?? Opt. Lett. 28, 1567�??1569 (2003).
  16. A. Yariv, �??Universal relations for coupling of optical power between microresonators and dielectric waveguides,�?? Electron. Lett. 36, 321�??322 (2000).
    [CrossRef]
  17. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, �??Microring resonator channel dropping filter,�?? IEEE J. Lightwave Technol. 15, 998�??1005 (1997).
    [CrossRef]
  18. A. Melloni and F. Morichetti, �??Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,�?? Opt. Quantum Electron. 35, 365�??379 (2003).
    [CrossRef]
  19. J. E. Heeber, 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 (2002).
  20. S. Mookherjea and A. Yariv, �??Pulse propagation in a coupled-resonator optical waveguide to all orders of dispersion,�?? Phys. Rev. E 65, 056 601 (2002).
    [CrossRef]
  21. A. D. Poularikas, The handbook af formulas and tables for signal processing (IEEE Press, New York, 1998).
  22. G. T. Paloczi, Y. Huang, A. Yariv, and S. Mookherjea, �??Polymeric Mach-Zehnder interferometer using serially coupled microresonators,�?? Opt. Express 11, 2666�??2671 (2003).
  23. S. Longhi, M. Marano, M. Belmonte, and P. Laporta, �??Superluminal pulse propagation in linear and nonlinear photonic grating structures,�?? IEEE. J. Sel. Top. Quantum Electron. 9, 4�??16 (2003).
  24. M. Bayindir, S. Tanriseven, and E. Ozbay, �??Propagation of light through localized coupled-cavity modes in one-dimensional photonic band-gap structures,�?? Appl. Phys. A 72, 117�??119 (2001).
  25. W. Chen and D. L. Mills, �??Gap solitons and the nonlinear optical-response of superlattices,�?? Phys. Rev. Lett. 58, 160�??163 (1987).
    [CrossRef]
  26. C. M. de Sterke and J. E. Sipe, �??Envelope-function approach for the electrodynamics of nonlinear periodic structures,�?? Phys. Rev. A 38, 5149�??5165 (1988).
    [CrossRef]
  27. C. M. de Sterke, D. G. Salinas, and J. E. Sipe, �??Coupled-mode theory for light propagation through deep nonlinear gratings,�?? Phys. Rev. E 54, 1969�??1989 (1996).
    [CrossRef]
  28. 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).
    [CrossRef]
  29. D. N. Christodoulides and R. I. Joseph, �??Slow Bragg solitons in nonlinear periodic structures,�?? Phys. Rev. Lett. 62, 1746�??1749 (1989).
    [CrossRef]
  30. Little Optics press release, �??Higher order optical filters using microring resonators�?? (Little Optics, 2003), <a href="http://www.littleoptics.com/hofilter.pdf.">http://www.littleoptics.com/hofilter.pdf.</a>

Appl. Phys. A (1)

M. Bayindir, S. Tanriseven, and E. Ozbay, �??Propagation of light through localized coupled-cavity modes in one-dimensional photonic band-gap structures,�?? Appl. Phys. A 72, 117�??119 (2001).

Electron. Lett. (1)

A. Yariv, �??Universal relations for coupling of optical power between microresonators and dielectric waveguides,�?? Electron. Lett. 36, 321�??322 (2000).
[CrossRef]

IEEE J. Lightwave Technol. (2)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, �??Microring resonator channel dropping filter,�?? IEEE J. Lightwave Technol. 15, 998�??1005 (1997).
[CrossRef]

C. K. Madsen, �??General IIR optical filter design for WDM applications using all-pass filters,�?? IEEE J. Lightwave Technol. 18, 860�??868 (2000).
[CrossRef]

IEEE J. of Lightwave Technol. (1)

K. Oda, N. Takato, and H. Toba, �??A wide-FSR waveguide double-ring resonator for optical FDM transmission systems,�?? IEEE J. of Lightwave Technol. 9, 728�??736 (1991).

IEEE J. Quantum Electron. (1)

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).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, �??Vertically coupled glass microring resonator channel dropping filters,�?? IEEE Photon. Technol. Lett. 11, 215�??217 (1999).
[CrossRef]

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).
[CrossRef]

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]

IEEE. J. Sel. Top. Quantum Electron. (1)

S. Longhi, M. Marano, M. Belmonte, and P. Laporta, �??Superluminal pulse propagation in linear and nonlinear photonic grating structures,�?? IEEE. J. Sel. Top. Quantum Electron. 9, 4�??16 (2003).

J. Mod. Opt. (1)

J. E. Heebner and R. W. Boyd, �??�??Slow�?? and �??fast�?? light in resonator-coupled waveguides,�?? J. Mod. Opt. 49, 2629�??2636 (2002).

J. Opt. Soc. Am. B (2)

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 77, 387�??400 (2000).

J. E. Heeber, 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 (2002).

Opt. Express (1)

Opt. Lett. (3)

Opt. Quantum Electron. (1)

A. Melloni and F. Morichetti, �??Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,�?? Opt. Quantum Electron. 35, 365�??379 (2003).
[CrossRef]

Phys. Rev. A (1)

C. M. de Sterke and J. E. Sipe, �??Envelope-function approach for the electrodynamics of nonlinear periodic structures,�?? Phys. Rev. A 38, 5149�??5165 (1988).
[CrossRef]

Phys. Rev. B (1)

N. Stefanou and A. Modinos, �??Impurity bands in photonic insulators,�?? Phys. Rev. B 57, 12 127�??12 133 (1998).
[CrossRef]

Phys. Rev. E (3)

S. Mookherjea and A. Yariv, �??Pulse propagation in a coupled-resonator optical waveguide to all orders of dispersion,�?? Phys. Rev. E 65, 056 601 (2002).
[CrossRef]

S. Mookherjea and A. Yariv, �??Kerr-stabilized super-resonant modes in coupled-resonator optical waveguides,�?? Phys. Rev. E 66, 046 610 (2002).
[CrossRef]

C. M. de Sterke, D. G. Salinas, and J. E. Sipe, �??Coupled-mode theory for light propagation through deep nonlinear gratings,�?? Phys. Rev. E 54, 1969�??1989 (1996).
[CrossRef]

Phys. Rev. Lett. (4)

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).
[CrossRef]

D. N. Christodoulides and R. I. Joseph, �??Slow Bragg solitons in nonlinear periodic structures,�?? Phys. Rev. Lett. 62, 1746�??1749 (1989).
[CrossRef]

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]

W. Chen and D. L. Mills, �??Gap solitons and the nonlinear optical-response of superlattices,�?? Phys. Rev. Lett. 58, 160�??163 (1987).
[CrossRef]

Other (3)

A. D. Poularikas, The handbook af formulas and tables for signal processing (IEEE Press, New York, 1998).

A. Yariv and P. Yeh, Optical waves in crystals: Propagation and control of laser radiation (Wiley, New York, 1984).

Little Optics press release, �??Higher order optical filters using microring resonators�?? (Little Optics, 2003), <a href="http://www.littleoptics.com/hofilter.pdf.">http://www.littleoptics.com/hofilter.pdf.</a>

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Metrics