Abstract

We investigate the unidirectional transmission behavior of coupled photonic crystal defects with nonlinearity by using the coupled mode theory, focusing on how to enhance the transmission contrast. Although the unidirectional transmission originates from the asymmetric configuration and nonlinear property of the structure, it is revealed that the maximum transmission contrast depends mainly on two linear factors. For two coupled defects, they are the highest order of the frequency detuning appearing in the transmission formula and the frequency splitting due to the coupling. Our analyses are supported by the numerical simulations based on the finite-difference time-domain technique. An enhancement of the maximum transmission contrast by an order of magnitude is achieved in the structure consisting of two coupled defects.

© 2006 Optical Society of America

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  1. E. Centeno and D. Felbacq, "Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity," Phys. Rev. B 62,7683-7686 (2000).
    [CrossRef]
  2. 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]
  3. S. Mingaleev and Y. Kivshar, "Nonlinear transmission and light localization in photonic crystal waveguides," J. Opt. Soc. Am. B 19,2241-2249 (2002).
    [CrossRef]
  4. M. Soljacic, C. Luo, and J. D. Joannopoulos, "Nonlinear photonic crystal microdevices for optical integration," Opt. Lett. 28,637-639 (2003).
    [CrossRef] [PubMed]
  5. 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]
  6. M. F. Yanik, H. Altug, J. Vuckovic, and S. Fan, "Submicrometer all-optical digital memory and integration of nanoscale photonic devices without isolators," J. Lightwave Technol. 22,2316-2322 (2004).
    [CrossRef]
  7. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, NJ, 1984).
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    [CrossRef]
  9. K. Gallo and G. Assanto, "All-optical diode in a periodically poled lithium niobate waveguide," Appl. Phys. Lett. 79,314-316 (2001).
    [CrossRef]
  10. S. Pereira, P. Chak, J. E. Sipe, L. Tkeshelashvili, and K. Busch, "All-optical diode in an asymmetrically apodized Kerr nonlinear microresonator system," Photonics and Nanostructure-Fundamentals and Applications 2,181-190 (2004).
    [CrossRef]
  11. M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, "Bistable diode action in left-handed periodic structures," Phys. Rev. E 71,037602 (2005).
    [CrossRef]
  12. J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, "Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions," Nature Materials 4,383-387 (2005).
    [CrossRef] [PubMed]
  13. X. S. Lin and S. Lan, "Unidirectional transmission in asymmetrically confined photonic crystal defects with Kerr nonlinearity," Chin. Phys. Lett. 22, 2847-2850 (2005).
    [CrossRef]
  14. S. Lan, X. W. Chen, J. D. Chen, and X. S. Lin, "Physical origin of the ultrafast response of nonlinear photonic crystal atoms to the excitation of ultrashort pulses," Phys. Rev. B 71,125122 (2005).
    [CrossRef]
  15. S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, "Theoretical analysis of channel drop tunneling processes," Phys. Rev. B 59,15882-15892 (1999).
    [CrossRef]
  16. 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]
  17. Y. Akahane, T. Asano, H. Takano, B.-S. Song, Y. Takana, and S. Noda, "Two-dimensional photonic-crystal-slab channel-drop filter with flat-top response," Opt. Express 13,2512-2530 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-7-2512.
    [CrossRef] [PubMed]
  18. C. Jin, S. Fan, S. Han, and D. Zhang, "Reflectionless multichannel wavelength demultiplexer in a transmission resonator configuration," IEEE J. Quantum Electron. 39,160-165 (2003).
    [CrossRef]
  19. B. Maes, P. Bienstman, and R. Baets, "Switching in coupled nonlinear photonic-crystal resonators," J. Opt. Soc. Am. B 22,1778-1784 (2005).
    [CrossRef]
  20. X. S. Lin, X. W. Chen, and S. Lan, "Investigation and modification of coupling of photonic crystal defects," Chin. Phys. Lett. 22, 1698-1701 (2005).
    [CrossRef]
  21. M. Qiu, "Effective index method for heterostructure-slab-waveguide-based two-dimensional photonic crystals," Appl. Phys. Lett. 81,1163-1165 (2002).
    [CrossRef]
  22. A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, Norwood, MA, 2000). In this paper, a commercial software developed by Rsoft Design Group (http://www.rsoftdesign.com) is used for nonlinear FDTD simulation.

2005 (7)

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, "Bistable diode action in left-handed periodic structures," Phys. Rev. E 71,037602 (2005).
[CrossRef]

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, "Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions," Nature Materials 4,383-387 (2005).
[CrossRef] [PubMed]

X. S. Lin and S. Lan, "Unidirectional transmission in asymmetrically confined photonic crystal defects with Kerr nonlinearity," Chin. Phys. Lett. 22, 2847-2850 (2005).
[CrossRef]

S. Lan, X. W. Chen, J. D. Chen, and X. S. Lin, "Physical origin of the ultrafast response of nonlinear photonic crystal atoms to the excitation of ultrashort pulses," Phys. Rev. B 71,125122 (2005).
[CrossRef]

X. S. Lin, X. W. Chen, and S. Lan, "Investigation and modification of coupling of photonic crystal defects," Chin. Phys. Lett. 22, 1698-1701 (2005).
[CrossRef]

Y. Akahane, T. Asano, H. Takano, B.-S. Song, Y. Takana, and S. Noda, "Two-dimensional photonic-crystal-slab channel-drop filter with flat-top response," Opt. Express 13,2512-2530 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-7-2512.
[CrossRef] [PubMed]

B. Maes, P. Bienstman, and R. Baets, "Switching in coupled nonlinear photonic-crystal resonators," J. Opt. Soc. Am. B 22,1778-1784 (2005).
[CrossRef]

2004 (2)

M. F. Yanik, H. Altug, J. Vuckovic, and S. Fan, "Submicrometer all-optical digital memory and integration of nanoscale photonic devices without isolators," J. Lightwave Technol. 22,2316-2322 (2004).
[CrossRef]

S. Pereira, P. Chak, J. E. Sipe, L. Tkeshelashvili, and K. Busch, "All-optical diode in an asymmetrically apodized Kerr nonlinear microresonator system," Photonics and Nanostructure-Fundamentals and Applications 2,181-190 (2004).
[CrossRef]

2003 (3)

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]

C. Jin, S. Fan, S. Han, and D. Zhang, "Reflectionless multichannel wavelength demultiplexer in a transmission resonator configuration," IEEE J. Quantum Electron. 39,160-165 (2003).
[CrossRef]

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

2002 (3)

M. Qiu, "Effective index method for heterostructure-slab-waveguide-based two-dimensional photonic crystals," Appl. Phys. Lett. 81,1163-1165 (2002).
[CrossRef]

S. Mingaleev and Y. Kivshar, "Nonlinear transmission and light localization in photonic crystal waveguides," J. Opt. Soc. Am. B 19,2241-2249 (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]

2001 (1)

K. Gallo and G. Assanto, "All-optical diode in a periodically poled lithium niobate waveguide," Appl. Phys. Lett. 79,314-316 (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]

E. Centeno and D. Felbacq, "Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity," Phys. Rev. B 62,7683-7686 (2000).
[CrossRef]

1999 (1)

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, "Theoretical analysis of channel drop tunneling processes," Phys. Rev. B 59,15882-15892 (1999).
[CrossRef]

1994 (1)

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, "The photonic band edge optical diode," J. Appl. Phys. 76,2023-2026 (1994).
[CrossRef]

Akahane, Y.

Altug, H.

Asano, T.

Assanto, G.

K. Gallo and G. Assanto, "All-optical diode in a periodically poled lithium niobate waveguide," Appl. Phys. Lett. 79,314-316 (2001).
[CrossRef]

Baets, R.

Bienstman, P.

Bloemer, M. J.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, "The photonic band edge optical diode," J. Appl. Phys. 76,2023-2026 (1994).
[CrossRef]

Bowden, C. M.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, "The photonic band edge optical diode," J. Appl. Phys. 76,2023-2026 (1994).
[CrossRef]

Busch, K.

S. Pereira, P. Chak, J. E. Sipe, L. Tkeshelashvili, and K. Busch, "All-optical diode in an asymmetrically apodized Kerr nonlinear microresonator system," Photonics and Nanostructure-Fundamentals and Applications 2,181-190 (2004).
[CrossRef]

Centeno, E.

E. Centeno and D. Felbacq, "Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity," Phys. Rev. B 62,7683-7686 (2000).
[CrossRef]

Chak, P.

S. Pereira, P. Chak, J. E. Sipe, L. Tkeshelashvili, and K. Busch, "All-optical diode in an asymmetrically apodized Kerr nonlinear microresonator system," Photonics and Nanostructure-Fundamentals and Applications 2,181-190 (2004).
[CrossRef]

Chen, J. D.

S. Lan, X. W. Chen, J. D. Chen, and X. S. Lin, "Physical origin of the ultrafast response of nonlinear photonic crystal atoms to the excitation of ultrashort pulses," Phys. Rev. B 71,125122 (2005).
[CrossRef]

Chen, X. W.

S. Lan, X. W. Chen, J. D. Chen, and X. S. Lin, "Physical origin of the ultrafast response of nonlinear photonic crystal atoms to the excitation of ultrashort pulses," Phys. Rev. B 71,125122 (2005).
[CrossRef]

X. S. Lin, X. W. Chen, and S. Lan, "Investigation and modification of coupling of photonic crystal defects," Chin. Phys. Lett. 22, 1698-1701 (2005).
[CrossRef]

Dowling, J. P.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, "The photonic band edge optical diode," J. Appl. Phys. 76,2023-2026 (1994).
[CrossRef]

Fan, S.

M. F. Yanik, H. Altug, J. Vuckovic, and S. Fan, "Submicrometer all-optical digital memory and integration of nanoscale photonic devices without isolators," J. Lightwave Technol. 22,2316-2322 (2004).
[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]

C. Jin, S. Fan, S. Han, and D. Zhang, "Reflectionless multichannel wavelength demultiplexer in a transmission resonator configuration," IEEE J. Quantum Electron. 39,160-165 (2003).
[CrossRef]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, "Theoretical analysis of channel drop tunneling processes," Phys. Rev. B 59,15882-15892 (1999).
[CrossRef]

Feise, M. W.

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, "Bistable diode action in left-handed periodic structures," Phys. Rev. E 71,037602 (2005).
[CrossRef]

Felbacq, D.

E. Centeno and D. Felbacq, "Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity," Phys. Rev. B 62,7683-7686 (2000).
[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]

Gallo, K.

K. Gallo and G. Assanto, "All-optical diode in a periodically poled lithium niobate waveguide," Appl. Phys. Lett. 79,314-316 (2001).
[CrossRef]

Han, S.

C. Jin, S. Fan, S. Han, and D. Zhang, "Reflectionless multichannel wavelength demultiplexer in a transmission resonator configuration," IEEE J. Quantum Electron. 39,160-165 (2003).
[CrossRef]

Haus, H. A.

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, "Theoretical analysis of channel drop tunneling processes," Phys. Rev. B 59,15882-15892 (1999).
[CrossRef]

Hwang, J.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, "Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions," Nature Materials 4,383-387 (2005).
[CrossRef] [PubMed]

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]

Ishikawa, K.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, "Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions," Nature Materials 4,383-387 (2005).
[CrossRef] [PubMed]

Jin, C.

C. Jin, S. Fan, S. Han, and D. Zhang, "Reflectionless multichannel wavelength demultiplexer in a transmission resonator configuration," IEEE J. Quantum Electron. 39,160-165 (2003).
[CrossRef]

Joannopoulos, J. D.

M. Soljacic, C. Luo, and J. D. Joannopoulos, "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]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, "Theoretical analysis of channel drop tunneling processes," Phys. Rev. B 59,15882-15892 (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.

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, "Theoretical analysis of channel drop tunneling processes," Phys. Rev. B 59,15882-15892 (1999).
[CrossRef]

Kivshar, Y.

Kivshar, Y. S.

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, "Bistable diode action in left-handed periodic structures," Phys. Rev. E 71,037602 (2005).
[CrossRef]

Lan, S.

S. Lan, X. W. Chen, J. D. Chen, and X. S. Lin, "Physical origin of the ultrafast response of nonlinear photonic crystal atoms to the excitation of ultrashort pulses," Phys. Rev. B 71,125122 (2005).
[CrossRef]

X. S. Lin, X. W. Chen, and S. Lan, "Investigation and modification of coupling of photonic crystal defects," Chin. Phys. Lett. 22, 1698-1701 (2005).
[CrossRef]

X. S. Lin and S. Lan, "Unidirectional transmission in asymmetrically confined photonic crystal defects with Kerr nonlinearity," Chin. Phys. Lett. 22, 2847-2850 (2005).
[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]

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]

Lin, X. S.

X. S. Lin and S. Lan, "Unidirectional transmission in asymmetrically confined photonic crystal defects with Kerr nonlinearity," Chin. Phys. Lett. 22, 2847-2850 (2005).
[CrossRef]

X. S. Lin, X. W. Chen, and S. Lan, "Investigation and modification of coupling of photonic crystal defects," Chin. Phys. Lett. 22, 1698-1701 (2005).
[CrossRef]

S. Lan, X. W. Chen, J. D. Chen, and X. S. Lin, "Physical origin of the ultrafast response of nonlinear photonic crystal atoms to the excitation of ultrashort pulses," Phys. Rev. B 71,125122 (2005).
[CrossRef]

Luo, C.

Maes, B.

Manolatou, C.

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, "Theoretical analysis of channel drop tunneling processes," Phys. Rev. B 59,15882-15892 (1999).
[CrossRef]

Mingaleev, S.

Nishimura, S.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, "Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions," Nature Materials 4,383-387 (2005).
[CrossRef] [PubMed]

Noda, S.

Park, B.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, "Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions," Nature Materials 4,383-387 (2005).
[CrossRef] [PubMed]

Pereira, S.

S. Pereira, P. Chak, J. E. Sipe, L. Tkeshelashvili, and K. Busch, "All-optical diode in an asymmetrically apodized Kerr nonlinear microresonator system," Photonics and Nanostructure-Fundamentals and Applications 2,181-190 (2004).
[CrossRef]

Qiu, M.

M. Qiu, "Effective index method for heterostructure-slab-waveguide-based two-dimensional photonic crystals," Appl. Phys. Lett. 81,1163-1165 (2002).
[CrossRef]

Scalora, M.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, "The photonic band edge optical diode," J. Appl. Phys. 76,2023-2026 (1994).
[CrossRef]

Shadrivov, I. V.

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, "Bistable diode action in left-handed periodic structures," Phys. Rev. E 71,037602 (2005).
[CrossRef]

Sipe, J. E.

S. Pereira, P. Chak, J. E. Sipe, L. Tkeshelashvili, and K. Busch, "All-optical diode in an asymmetrically apodized Kerr nonlinear microresonator system," Photonics and Nanostructure-Fundamentals and Applications 2,181-190 (2004).
[CrossRef]

Soljacic, M.

M. Soljacic, C. Luo, and J. D. Joannopoulos, "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]

Song, B.-S.

Song, M. H.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, "Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions," Nature Materials 4,383-387 (2005).
[CrossRef] [PubMed]

Takana, Y.

Takanishi, Y.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, "Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions," Nature Materials 4,383-387 (2005).
[CrossRef] [PubMed]

Takano, H.

Takezoe, H.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, "Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions," Nature Materials 4,383-387 (2005).
[CrossRef] [PubMed]

Tkeshelashvili, L.

S. Pereira, P. Chak, J. E. Sipe, L. Tkeshelashvili, and K. Busch, "All-optical diode in an asymmetrically apodized Kerr nonlinear microresonator system," Photonics and Nanostructure-Fundamentals and Applications 2,181-190 (2004).
[CrossRef]

Toyooka, T.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, "Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions," Nature Materials 4,383-387 (2005).
[CrossRef] [PubMed]

Villeneuve, P. R.

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, "Theoretical analysis of channel drop tunneling processes," Phys. Rev. B 59,15882-15892 (1999).
[CrossRef]

Vuckovic, J.

Wu, J. W.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, "Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions," Nature Materials 4,383-387 (2005).
[CrossRef] [PubMed]

Xu, 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]

Yanik, M. F.

M. F. Yanik, H. Altug, J. Vuckovic, and S. Fan, "Submicrometer all-optical digital memory and integration of nanoscale photonic devices without isolators," J. Lightwave Technol. 22,2316-2322 (2004).
[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]

Yariv, A.

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Figures (6)

Fig. 1.
Fig. 1.

Schematic structures for the nonlinear PC defects studied in this paper. (a) a single asymmetrically confined PC defect; (b) two coupled PC defects.

Fig. 2.
Fig. 2.

Theoretical transmission spectrum of the single asymmetrically confined PC defect for the two launch directions and their evolutions with increasing input power. In the calculation, (p 02/p 01) and η are set as 3 and 0.6 respectively.

Fig. 3.
Fig. 3.

Linear lineshapes of (a) the single asymmetrically confined PC defect and (b) two coupled PC defects calculated by the CMT (solid curves) and simulated by the FDTD (empty circles).

Fig. 4.
Fig. 4.

Evolution of the transmission spectrum of the single asymmetrically confined PC defect with increasing input power. The solid and empty circles represent the rightward and leftward launch cases respectively.

Fig. 5.
Fig. 5.

Evolution of the transmission spectrum of the two coupled PC defects with increasing input power. The solid and empty circles represent the rightward and leftward launch cases respectively.

Fig. 6.
Fig. 6.

Unidirectional transmission behavior of the two coupled PC defects for a Gaussian pulse of 3 ps under two different launch conditions. (a) δ = 2.0, pin = 16W/μm and (b) δ = 2.5, pin = 21W/μm.

Equations (7)

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{ d A d t = [ j ( ω 0 γ s out 2 p 0 ) γ ] A + 2 γ 1 s in , s out = 2 γ 2 A
d s out d t = [ j ( ω 0 γ s out 2 p 0 ) γ ] s out + 4 γ 1 γ 2 s in .
T = s out s in 2 = p out p in = η 1 + ( p out p 0 δ ) 2 ,
p 0 ~ [ Defect F ( x , z ) 2 d x d z ] 2 [ Defect F ( x , z ) 4 d x d z ] ,
T = η 1 + [ ( p in p 0 ) T δ ] 2 ,
T = 1 P 1 + P 2 ( δ + P 3 ) 2 + P 4 ( δ + P 3 ) 4 ,
{ P 1 = sin 2 φ 4 γ 1 3 γ 2 [ ( γ 1 + γ 01 ) ( γ 2 + γ 02 ) + γ 1 2 sin 2 φ ] 2 , P 2 = γ 2 sin 2 φ 4 γ 1 3 γ 2 [ ( γ 1 + γ 01 ) 2 + ( γ 2 + γ 02 ) 2 2 γ 1 2 sin 2 φ ] , P 3 = γ 1 γ tan φ , and P 4 = γ 4 sin 2 φ 4 γ 1 3 γ 2 .

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