Abstract

Using coupled-mode theory we examine the linear and Kerr nonlinear behavior of multiple consecutive photonic-crystal switches. Two types of resonators are considered, those with the cavity inside and those adjacent to the waveguide. We observe gap solitons in both structures and examine a nonlinear mode with energy localized near the boundaries of the finite system. Finally, we propose a device with two side-coupled resonators and a judiciously chosen intercavity distance that demonstrates switching at low powers. In addition to coupled-mode theory, rigorous simulations are performed for this structure.

© 2005 Optical Society of America

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  1. S. D. Gupta and G. S. Agarwal, "Dispersive bistability in coupled nonlinear Fabry-Perot resonators," J. Opt. Soc. Am. B 4, 691-695 (1987).
    [CrossRef]
  2. H. A. Haus and Y. Lai, "Theory of cascaded quarter wave shifted distributed feedback resonators," IEEE J. Quantum Electron. 28, 205-213 (1992).
    [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. 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]
  5. 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 (2002).
    [CrossRef]
  6. W. Bogaerts, D. Taillaert, B. Luyssaert, P. Dumon, J. Van Campenhout, P. Bienstman, D. Van Thourhout, R. Baets, V. Wiaux, and S. Beckx, "Basic structures for photonic integrated circuits in silicon-on-insulator," Opt. Express 12, 1583-1591 (2004).
    [CrossRef] [PubMed]
  7. P. Sanchis, J. Garcia, J. Marti, W. Bogaerts, P. Dumon, D. Taillaert, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, "Experimental demonstration of high coupling efficiency between wide ridge waveguides and single-mode photonic crystal waveguides," IEEE Photonics Technol. Lett. 16, 2272-2274 (2004).
    [CrossRef]
  8. S. Fan, W. Suh, and J. D. Joannopoulos, "Temporal coupled-mode theory for the Fano resonance in optical resonators," J. Opt. Soc. Am. A 20, 569-572 (2003).
    [CrossRef]
  9. C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, "Coupling of modes analysis of resonant channel add-drop filters," IEEE J. Quantum Electron. 35, 1322-1331 (1999).
    [CrossRef]
  10. M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystals," Phys. Rev. E 66, 055601 (2002).
    [CrossRef]
  11. M. F. Yanik, S. Fan, and M. Soljacic, "High-contrast all-optical bistable switching in photonic crystal microcavities," Appl. Phys. Lett. 83, 2739-2741 (2003).
    [CrossRef]
  12. W. Chen and D. L. Mills, "Gap solitons and the nonlinear optical-response of superlattices," Phys. Rev. Lett. 58, 160-163 (1987).
    [CrossRef] [PubMed]
  13. S. F. Mingaleev, Y. S. Kivshar, and R. A. Sammut, "Long-range interaction and nonlinear localized modes in photonic crystal waveguides," Phys. Rev. E 62, 5777-5782 (2000).
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  14. S. Mookherjea and A. Yariv, "Kerr-stabilized super-resonant modes in coupled-resonator optical waveguides," Phys. Rev. E 66, 046610 (2002).
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  15. S. Pereira, P. Chak, and J. E. Sipe, "Gap-soliton switching in short microresonator structures," J. Opt. Soc. Am. B 19, 2191-2202 (2002).
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  17. A. R. McGurn and G. Birkok, "Transmission anomalies in Kerr media photonic crystal circuits: intrinsic localized modes," Phys. Rev. B 69, 235105 (2004).
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  18. P. Bienstman and R. Baets, "Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers," Opt. Quantum Electron. 33, 327-341 (2001).
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    [CrossRef]
  21. D. Pissoort, B. Denecker, P. Bienstman, F. Olyslager, and D. De Zutter, "Comparative study of three methods for the simulation of two-dimensional photonic crystals," J. Opt. Soc. Am. A 21, 2186-2195 (2004).
    [CrossRef]
  22. B. Maes, P. Bienstman, and R. Baets, "Modeling of Kerr nonlinear photonic components with mode expansion," Opt. Quantum Electron. 36, 15-24 (2004).
    [CrossRef]
  23. M. Soljacic, C. Luo, J. D. Joannopoulos, and S. Fan, "Nonlinear photonic crystal microdevices for optical integration," Opt. Lett. 28, 637-639 (2003).
    [CrossRef] [PubMed]
  24. P. Chak, J. E. Sipe, and S. Pereira, "Lorentzian model for nonlinear switching in a microresonator structure," Opt. Commun. 213, 163-171 (2002).
    [CrossRef]
  25. J. E. Sipe, L. Poladian, and C. M. de Sterke, "Propagation through nonuniform grating structures," J. Opt. Soc. Am. A 11, 1307-1320 (1994).
    [CrossRef]

2004 (6)

W. Bogaerts, D. Taillaert, B. Luyssaert, P. Dumon, J. Van Campenhout, P. Bienstman, D. Van Thourhout, R. Baets, V. Wiaux, and S. Beckx, "Basic structures for photonic integrated circuits in silicon-on-insulator," Opt. Express 12, 1583-1591 (2004).
[CrossRef] [PubMed]

P. Sanchis, J. Garcia, J. Marti, W. Bogaerts, P. Dumon, D. Taillaert, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, "Experimental demonstration of high coupling efficiency between wide ridge waveguides and single-mode photonic crystal waveguides," IEEE Photonics Technol. Lett. 16, 2272-2274 (2004).
[CrossRef]

P. Xie and Z. Q. Zhang, "Excitation of gap solitons, soliton trains, and soliton sets in finite-sized two-dimensional photonic crystals," Phys. Rev. E 69, 036601 (2004).
[CrossRef]

A. R. McGurn and G. Birkok, "Transmission anomalies in Kerr media photonic crystal circuits: intrinsic localized modes," Phys. Rev. B 69, 235105 (2004).
[CrossRef]

D. Pissoort, B. Denecker, P. Bienstman, F. Olyslager, and D. De Zutter, "Comparative study of three methods for the simulation of two-dimensional photonic crystals," J. Opt. Soc. Am. A 21, 2186-2195 (2004).
[CrossRef]

B. Maes, P. Bienstman, and R. Baets, "Modeling of Kerr nonlinear photonic components with mode expansion," Opt. Quantum Electron. 36, 15-24 (2004).
[CrossRef]

2003 (4)

M. Soljacic, C. Luo, J. D. Joannopoulos, and S. Fan, "Nonlinear photonic crystal microdevices for optical integration," Opt. Lett. 28, 637-639 (2003).
[CrossRef] [PubMed]

K. C. Huang, P. Bienstman, J. D. Joannopoulos, K. A. Nelson, and S. Fan, "Phonon-polariton excitations in photonic crystals," Phys. Rev. B 68, 075209 (2003).
[CrossRef]

M. F. Yanik, S. Fan, and M. Soljacic, "High-contrast all-optical bistable switching in photonic crystal microcavities," Appl. Phys. Lett. 83, 2739-2741 (2003).
[CrossRef]

S. Fan, W. Suh, and J. D. Joannopoulos, "Temporal coupled-mode theory for the Fano resonance in optical resonators," J. Opt. Soc. Am. A 20, 569-572 (2003).
[CrossRef]

2002 (5)

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 (2002).
[CrossRef]

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystals," Phys. Rev. E 66, 055601 (2002).
[CrossRef]

S. Mookherjea and A. Yariv, "Kerr-stabilized super-resonant modes in coupled-resonator optical waveguides," Phys. Rev. E 66, 046610 (2002).
[CrossRef]

S. Pereira, P. Chak, and J. E. Sipe, "Gap-soliton switching in short microresonator structures," J. Opt. Soc. Am. B 19, 2191-2202 (2002).
[CrossRef]

P. Chak, J. E. Sipe, and S. Pereira, "Lorentzian model for nonlinear switching in a microresonator structure," Opt. Commun. 213, 163-171 (2002).
[CrossRef]

2001 (1)

P. Bienstman and R. Baets, "Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers," Opt. Quantum Electron. 33, 327-341 (2001).
[CrossRef]

2000 (2)

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]

S. F. Mingaleev, Y. S. Kivshar, and R. A. Sammut, "Long-range interaction and nonlinear localized modes in photonic crystal waveguides," Phys. Rev. E 62, 5777-5782 (2000).
[CrossRef]

1999 (2)

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]

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, "Coupling of modes analysis of resonant channel add-drop filters," IEEE J. Quantum Electron. 35, 1322-1331 (1999).
[CrossRef]

1994 (1)

1992 (1)

H. A. Haus and Y. Lai, "Theory of cascaded quarter wave shifted distributed feedback resonators," IEEE J. Quantum Electron. 28, 205-213 (1992).
[CrossRef]

1987 (2)

S. D. Gupta and G. S. Agarwal, "Dispersive bistability in coupled nonlinear Fabry-Perot resonators," J. Opt. Soc. Am. B 4, 691-695 (1987).
[CrossRef]

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

Agarwal, G. S.

Baets, R.

P. Sanchis, J. Garcia, J. Marti, W. Bogaerts, P. Dumon, D. Taillaert, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, "Experimental demonstration of high coupling efficiency between wide ridge waveguides and single-mode photonic crystal waveguides," IEEE Photonics Technol. Lett. 16, 2272-2274 (2004).
[CrossRef]

B. Maes, P. Bienstman, and R. Baets, "Modeling of Kerr nonlinear photonic components with mode expansion," Opt. Quantum Electron. 36, 15-24 (2004).
[CrossRef]

W. Bogaerts, D. Taillaert, B. Luyssaert, P. Dumon, J. Van Campenhout, P. Bienstman, D. Van Thourhout, R. Baets, V. Wiaux, and S. Beckx, "Basic structures for photonic integrated circuits in silicon-on-insulator," Opt. Express 12, 1583-1591 (2004).
[CrossRef] [PubMed]

P. Bienstman and R. Baets, "Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers," Opt. Quantum Electron. 33, 327-341 (2001).
[CrossRef]

Beckx, S.

P. Sanchis, J. Garcia, J. Marti, W. Bogaerts, P. Dumon, D. Taillaert, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, "Experimental demonstration of high coupling efficiency between wide ridge waveguides and single-mode photonic crystal waveguides," IEEE Photonics Technol. Lett. 16, 2272-2274 (2004).
[CrossRef]

W. Bogaerts, D. Taillaert, B. Luyssaert, P. Dumon, J. Van Campenhout, P. Bienstman, D. Van Thourhout, R. Baets, V. Wiaux, and S. Beckx, "Basic structures for photonic integrated circuits in silicon-on-insulator," Opt. Express 12, 1583-1591 (2004).
[CrossRef] [PubMed]

Bienstman, P.

W. Bogaerts, D. Taillaert, B. Luyssaert, P. Dumon, J. Van Campenhout, P. Bienstman, D. Van Thourhout, R. Baets, V. Wiaux, and S. Beckx, "Basic structures for photonic integrated circuits in silicon-on-insulator," Opt. Express 12, 1583-1591 (2004).
[CrossRef] [PubMed]

D. Pissoort, B. Denecker, P. Bienstman, F. Olyslager, and D. De Zutter, "Comparative study of three methods for the simulation of two-dimensional photonic crystals," J. Opt. Soc. Am. A 21, 2186-2195 (2004).
[CrossRef]

B. Maes, P. Bienstman, and R. Baets, "Modeling of Kerr nonlinear photonic components with mode expansion," Opt. Quantum Electron. 36, 15-24 (2004).
[CrossRef]

K. C. Huang, P. Bienstman, J. D. Joannopoulos, K. A. Nelson, and S. Fan, "Phonon-polariton excitations in photonic crystals," Phys. Rev. B 68, 075209 (2003).
[CrossRef]

P. Bienstman and R. Baets, "Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers," Opt. Quantum Electron. 33, 327-341 (2001).
[CrossRef]

Birkok, G.

A. R. McGurn and G. Birkok, "Transmission anomalies in Kerr media photonic crystal circuits: intrinsic localized modes," Phys. Rev. B 69, 235105 (2004).
[CrossRef]

Bogaerts, W.

P. Sanchis, J. Garcia, J. Marti, W. Bogaerts, P. Dumon, D. Taillaert, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, "Experimental demonstration of high coupling efficiency between wide ridge waveguides and single-mode photonic crystal waveguides," IEEE Photonics Technol. Lett. 16, 2272-2274 (2004).
[CrossRef]

W. Bogaerts, D. Taillaert, B. Luyssaert, P. Dumon, J. Van Campenhout, P. Bienstman, D. Van Thourhout, R. Baets, V. Wiaux, and S. Beckx, "Basic structures for photonic integrated circuits in silicon-on-insulator," Opt. Express 12, 1583-1591 (2004).
[CrossRef] [PubMed]

Boyd, R. W.

Chak, P.

S. Pereira, P. Chak, and J. E. Sipe, "Gap-soliton switching in short microresonator structures," J. Opt. Soc. Am. B 19, 2191-2202 (2002).
[CrossRef]

P. Chak, J. E. Sipe, and S. Pereira, "Lorentzian model for nonlinear switching in a microresonator structure," Opt. Commun. 213, 163-171 (2002).
[CrossRef]

Chen, W.

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

de Sterke, C. M.

De Zutter, D.

Denecker, B.

Dumon, P.

W. Bogaerts, D. Taillaert, B. Luyssaert, P. Dumon, J. Van Campenhout, P. Bienstman, D. Van Thourhout, R. Baets, V. Wiaux, and S. Beckx, "Basic structures for photonic integrated circuits in silicon-on-insulator," Opt. Express 12, 1583-1591 (2004).
[CrossRef] [PubMed]

P. Sanchis, J. Garcia, J. Marti, W. Bogaerts, P. Dumon, D. Taillaert, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, "Experimental demonstration of high coupling efficiency between wide ridge waveguides and single-mode photonic crystal waveguides," IEEE Photonics Technol. Lett. 16, 2272-2274 (2004).
[CrossRef]

Fan, S.

S. Fan, W. Suh, and J. D. Joannopoulos, "Temporal coupled-mode theory for the Fano resonance in optical resonators," J. Opt. Soc. Am. A 20, 569-572 (2003).
[CrossRef]

K. C. Huang, P. Bienstman, J. D. Joannopoulos, K. A. Nelson, and S. Fan, "Phonon-polariton excitations in photonic crystals," Phys. Rev. B 68, 075209 (2003).
[CrossRef]

M. F. Yanik, S. Fan, and M. Soljacic, "High-contrast all-optical bistable switching in photonic crystal microcavities," Appl. Phys. Lett. 83, 2739-2741 (2003).
[CrossRef]

M. Soljacic, C. Luo, J. D. Joannopoulos, and S. Fan, "Nonlinear photonic crystal microdevices for optical integration," Opt. Lett. 28, 637-639 (2003).
[CrossRef] [PubMed]

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, "Coupling of modes analysis of resonant channel add-drop filters," IEEE J. Quantum Electron. 35, 1322-1331 (1999).
[CrossRef]

Fink, Y.

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystals," Phys. Rev. E 66, 055601 (2002).
[CrossRef]

Garcia, J.

P. Sanchis, J. Garcia, J. Marti, W. Bogaerts, P. Dumon, D. Taillaert, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, "Experimental demonstration of high coupling efficiency between wide ridge waveguides and single-mode photonic crystal waveguides," IEEE Photonics Technol. Lett. 16, 2272-2274 (2004).
[CrossRef]

Gupta, S. D.

Haus, H. A.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, "Coupling of modes analysis of resonant channel add-drop filters," IEEE J. Quantum Electron. 35, 1322-1331 (1999).
[CrossRef]

H. A. Haus and Y. Lai, "Theory of cascaded quarter wave shifted distributed feedback resonators," IEEE J. Quantum Electron. 28, 205-213 (1992).
[CrossRef]

Heebner, J. E.

Huang, K. C.

K. C. Huang, P. Bienstman, J. D. Joannopoulos, K. A. Nelson, and S. Fan, "Phonon-polariton excitations in photonic crystals," Phys. Rev. B 68, 075209 (2003).
[CrossRef]

Ibanescu, M.

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystals," Phys. Rev. E 66, 055601 (2002).
[CrossRef]

Joannopoulos, J. D.

K. C. Huang, P. Bienstman, J. D. Joannopoulos, K. A. Nelson, and S. Fan, "Phonon-polariton excitations in photonic crystals," Phys. Rev. B 68, 075209 (2003).
[CrossRef]

S. Fan, W. Suh, and J. D. Joannopoulos, "Temporal coupled-mode theory for the Fano resonance in optical resonators," J. Opt. Soc. Am. A 20, 569-572 (2003).
[CrossRef]

M. Soljacic, C. Luo, J. D. Joannopoulos, and S. Fan, "Nonlinear photonic crystal microdevices for optical integration," Opt. Lett. 28, 637-639 (2003).
[CrossRef] [PubMed]

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystals," Phys. Rev. E 66, 055601 (2002).
[CrossRef]

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, "Coupling of modes analysis of resonant channel add-drop filters," IEEE J. Quantum Electron. 35, 1322-1331 (1999).
[CrossRef]

Johnson, S. G.

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystals," Phys. Rev. E 66, 055601 (2002).
[CrossRef]

Khan, M. J.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, "Coupling of modes analysis of resonant channel add-drop filters," IEEE J. Quantum Electron. 35, 1322-1331 (1999).
[CrossRef]

Kivshar, Y. S.

S. F. Mingaleev, Y. S. Kivshar, and R. A. Sammut, "Long-range interaction and nonlinear localized modes in photonic crystal waveguides," Phys. Rev. E 62, 5777-5782 (2000).
[CrossRef]

Lai, Y.

H. A. Haus and Y. Lai, "Theory of cascaded quarter wave shifted distributed feedback resonators," IEEE J. Quantum Electron. 28, 205-213 (1992).
[CrossRef]

Lee, R. K.

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]

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]

Li, Y.

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]

Luo, C.

Luyssaert, B.

Maes, B.

B. Maes, P. Bienstman, and R. Baets, "Modeling of Kerr nonlinear photonic components with mode expansion," Opt. Quantum Electron. 36, 15-24 (2004).
[CrossRef]

Manolatou, C.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, "Coupling of modes analysis of resonant channel add-drop filters," IEEE J. Quantum Electron. 35, 1322-1331 (1999).
[CrossRef]

Marti, J.

P. Sanchis, J. Garcia, J. Marti, W. Bogaerts, P. Dumon, D. Taillaert, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, "Experimental demonstration of high coupling efficiency between wide ridge waveguides and single-mode photonic crystal waveguides," IEEE Photonics Technol. Lett. 16, 2272-2274 (2004).
[CrossRef]

McGurn, A. R.

A. R. McGurn and G. Birkok, "Transmission anomalies in Kerr media photonic crystal circuits: intrinsic localized modes," Phys. Rev. B 69, 235105 (2004).
[CrossRef]

Mills, D. L.

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

Mingaleev, S. F.

S. F. Mingaleev, Y. S. Kivshar, and R. A. Sammut, "Long-range interaction and nonlinear localized modes in photonic crystal waveguides," Phys. Rev. E 62, 5777-5782 (2000).
[CrossRef]

Mookherjea, S.

S. Mookherjea and A. Yariv, "Kerr-stabilized super-resonant modes in coupled-resonator optical waveguides," Phys. Rev. E 66, 046610 (2002).
[CrossRef]

Nelson, K. A.

K. C. Huang, P. Bienstman, J. D. Joannopoulos, K. A. Nelson, and S. Fan, "Phonon-polariton excitations in photonic crystals," Phys. Rev. B 68, 075209 (2003).
[CrossRef]

Olyslager, F.

Park, Q. H.

Pereira, S.

S. Pereira, P. Chak, and J. E. Sipe, "Gap-soliton switching in short microresonator structures," J. Opt. Soc. Am. B 19, 2191-2202 (2002).
[CrossRef]

P. Chak, J. E. Sipe, and S. Pereira, "Lorentzian model for nonlinear switching in a microresonator structure," Opt. Commun. 213, 163-171 (2002).
[CrossRef]

Pissoort, D.

Poladian, L.

Sammut, R. A.

S. F. Mingaleev, Y. S. Kivshar, and R. A. Sammut, "Long-range interaction and nonlinear localized modes in photonic crystal waveguides," Phys. Rev. E 62, 5777-5782 (2000).
[CrossRef]

Sanchis, P.

P. Sanchis, J. Garcia, J. Marti, W. Bogaerts, P. Dumon, D. Taillaert, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, "Experimental demonstration of high coupling efficiency between wide ridge waveguides and single-mode photonic crystal waveguides," IEEE Photonics Technol. Lett. 16, 2272-2274 (2004).
[CrossRef]

Scherer, A.

Sipe, J. E.

Soljacic, M.

M. Soljacic, C. Luo, J. D. Joannopoulos, and S. Fan, "Nonlinear photonic crystal microdevices for optical integration," Opt. Lett. 28, 637-639 (2003).
[CrossRef] [PubMed]

M. F. Yanik, S. Fan, and M. Soljacic, "High-contrast all-optical bistable switching in photonic crystal microcavities," Appl. Phys. Lett. 83, 2739-2741 (2003).
[CrossRef]

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystals," Phys. Rev. E 66, 055601 (2002).
[CrossRef]

Suh, W.

Taillaert, D.

P. Sanchis, J. Garcia, J. Marti, W. Bogaerts, P. Dumon, D. Taillaert, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, "Experimental demonstration of high coupling efficiency between wide ridge waveguides and single-mode photonic crystal waveguides," IEEE Photonics Technol. Lett. 16, 2272-2274 (2004).
[CrossRef]

W. Bogaerts, D. Taillaert, B. Luyssaert, P. Dumon, J. Van Campenhout, P. Bienstman, D. Van Thourhout, R. Baets, V. Wiaux, and S. Beckx, "Basic structures for photonic integrated circuits in silicon-on-insulator," Opt. Express 12, 1583-1591 (2004).
[CrossRef] [PubMed]

Van Campenhout, J.

Van Thourhout, D.

Villeneuve, P. R.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, "Coupling of modes analysis of resonant channel add-drop filters," IEEE J. Quantum Electron. 35, 1322-1331 (1999).
[CrossRef]

Wiaux, V.

P. Sanchis, J. Garcia, J. Marti, W. Bogaerts, P. Dumon, D. Taillaert, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, "Experimental demonstration of high coupling efficiency between wide ridge waveguides and single-mode photonic crystal waveguides," IEEE Photonics Technol. Lett. 16, 2272-2274 (2004).
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W. Bogaerts, D. Taillaert, B. Luyssaert, P. Dumon, J. Van Campenhout, P. Bienstman, D. Van Thourhout, R. Baets, V. Wiaux, and S. Beckx, "Basic structures for photonic integrated circuits in silicon-on-insulator," Opt. Express 12, 1583-1591 (2004).
[CrossRef] [PubMed]

Wouters, J.

P. Sanchis, J. Garcia, J. Marti, W. Bogaerts, P. Dumon, D. Taillaert, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, "Experimental demonstration of high coupling efficiency between wide ridge waveguides and single-mode photonic crystal waveguides," IEEE Photonics Technol. Lett. 16, 2272-2274 (2004).
[CrossRef]

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P. Xie and Z. Q. Zhang, "Excitation of gap solitons, soliton trains, and soliton sets in finite-sized two-dimensional photonic crystals," Phys. Rev. E 69, 036601 (2004).
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M. F. Yanik, S. Fan, and M. Soljacic, "High-contrast all-optical bistable switching in photonic crystal microcavities," Appl. Phys. Lett. 83, 2739-2741 (2003).
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S. Mookherjea and A. Yariv, "Kerr-stabilized super-resonant modes in coupled-resonator optical waveguides," Phys. Rev. E 66, 046610 (2002).
[CrossRef]

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[CrossRef]

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]

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P. Xie and Z. Q. Zhang, "Excitation of gap solitons, soliton trains, and soliton sets in finite-sized two-dimensional photonic crystals," Phys. Rev. E 69, 036601 (2004).
[CrossRef]

Appl. Phys. Lett. (1)

M. F. Yanik, S. Fan, and M. Soljacic, "High-contrast all-optical bistable switching in photonic crystal microcavities," Appl. Phys. Lett. 83, 2739-2741 (2003).
[CrossRef]

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IEEE Photonics Technol. Lett. (1)

P. Sanchis, J. Garcia, J. Marti, W. Bogaerts, P. Dumon, D. Taillaert, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, "Experimental demonstration of high coupling efficiency between wide ridge waveguides and single-mode photonic crystal waveguides," IEEE Photonics Technol. Lett. 16, 2272-2274 (2004).
[CrossRef]

J. Opt. Soc. Am. A (3)

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B. Maes, P. Bienstman, and R. Baets, "Modeling of Kerr nonlinear photonic components with mode expansion," Opt. Quantum Electron. 36, 15-24 (2004).
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P. Xie and Z. Q. Zhang, "Excitation of gap solitons, soliton trains, and soliton sets in finite-sized two-dimensional photonic crystals," Phys. Rev. E 69, 036601 (2004).
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S. Mookherjea and A. Yariv, "Kerr-stabilized super-resonant modes in coupled-resonator optical waveguides," Phys. Rev. E 66, 046610 (2002).
[CrossRef]

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, "Scattering-theory analysis of waveguide-resonator coupling," Phys. Rev. E 62, 7389-7404 (2000).
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Other (1)

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Figures (14)

Fig. 1
Fig. 1

Two geometries with resonator and waveguide amplitudes. (a) Resonant-coupled structure, (b) Side-coupled structure.

Fig. 2
Fig. 2

Transmission spectra for resonant coupled geometry with ϕ = π 2 and N = 1 , 2, and 5.

Fig. 3
Fig. 3

Transmission for resonant coupling. N = 1 is indicated, whereas curves (a) and (b) correspond to N = 2 but with ϕ = 0 and ϕ = 0.15 π , respectively.

Fig. 4
Fig. 4

Bloch mode results. For the resonant-coupled structure the shaded region indicates the transmission band; for the side-coupled geometry it represents the resonator gap.

Fig. 5
Fig. 5

Transmission spectra for side-coupled geometry with ϕ = π 2 and N = 1 , 2, and 5.

Fig. 6
Fig. 6

Transmission for side coupling with ϕ = 0.1 π and N = 4 .

Fig. 7
Fig. 7

Transmission for side coupling with ϕ = 0.025 π and N = 2 .

Fig. 8
Fig. 8

Fundamental gap solitons for resonant-coupling (solid curve) and side-coupling (dashed curve) geometry, with necessary input powers 0.94 × 10 4 P 0 and 1.08 × 10 4 P 0 , respectively. a i is the amplitude of resonator number i. The energy profiles follow a square hyperbolic secant curve.

Fig. 9
Fig. 9

Resonator energy profile of the nonlinear switching mode for 20 side-coupled cavities. The dashed curve shows the corresponding linear resonance profile at δ = 1.3 , normalized according to the maximum nonlinear value. The solid curve shows the nonlinearly adjusted resonance with δ = 1.6 and input power 0.6 P 0 .

Fig. 10
Fig. 10

Transmission versus δ for a resonant coupled system with N = 5 at fixed input power 0.02 P 0 . The gap soliton originating from a nonlinear resonance is indicated by (a), and the energy profile a i 2 is shown in the inset.

Fig. 11
Fig. 11

Transmission versus δ for a side-coupled system with N = 5 at fixed-input powers P 1 = 0.08 P 0 (circles) and P 2 = 0.09 P 0 (crosses). The linear transmission is also shown with a solid curve.

Fig. 12
Fig. 12

Structure of the PC switching device. The electric field at the transmission maximum is superimposed. Because of high Q the waveguide field is very small compared with the resonator fields.

Fig. 13
Fig. 13

Linear transmission for one and two resonators. The dashed (solid) curve represents the CMT calculations, whereas the circles (dots) show the rigorous simulations for one (two) resonator(s), respectively.

Fig. 14
Fig. 14

Output power versus input power for the two-resonator device at ω = 0.366883 ( 2 π c p ) . The CMT calculation is shown with a solid curve, the dots represent rigorous simulations.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

d a d t = [ j ( ω r + δ ω ) 1 τ ] a + d f 1 + d b 2 ,
b 1 = exp ( j ϕ ) f 1 + d a ,
f 2 = exp ( j ϕ ) b 2 + d a .
δ ω = a 2 P 0 τ 2 ,
d a d t = [ j ( ω r + δ ω ) 1 τ ] a + d f 1 + d b 2 ,
f 2 = exp ( j ϕ ) f 1 + d a ,
b 1 = exp ( j ϕ ) b 2 + d a .
[ f 2 b 2 ] = exp ( j β Λ ) [ f 1 b 1 ] = T [ f 1 b 1 ] ,
T = δ 4 ( 4 cos 2 ϕ ) δ 4 ( 4 cos 2 ϕ ) + ( δ tan ϕ ) 2 .

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