Abstract

We demonstrate how slow group velocities of light, which are readily achievable in photonic-crystal systems, can dramatically increase the induced phase shifts caused by small changes in the index of refraction. Such increased phase sensitivity may be used to decrease the sizes of many devices, including switches, routers, all-optical logical gates, wavelength converters, and others. At the same time a low group velocity greatly decreases the power requirements needed to operate these devices. We show how these advantages can be used to design switches smaller than 20 µm×200 µm in size by using readily available materials and at modest levels of power. With this approach, one could have 105 such devices on a surface that is 2 cm×2 cm, making it an important step towards large-scale all-optical integration.

© 2002 Optical Society of America

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  1. W. E. Martin, “A new waveguide switch/modulator for integrated optics,” Appl. Phys. Lett. 26, 562–564 (1975).
    [CrossRef]
  2. K. Kawano, S. Sekine, H. Takeuchi, M. Wada, M. Kohtoku, N. Yoshimoto, T. Ito, M. Yanagibashi, S. Kondo, and Y. Noguchi, “4×4 InGaAlAs/InAlAs MQW directional coupler waveguide switch modules integrated with spot-size converters and their 10-Gbit/s operation,” Electron. Lett. 31, 96–97 (1995).
    [CrossRef]
  3. A. Sneh, J. E. Zucker, and B. I. Miller, “Compact, low-cross-talk, and low-propagation-loss quantum-well Y-branch switches,” IEEE Photonics Technol. Lett. 8, 1644–1646 (1996).
    [CrossRef]
  4. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50, 36–42 (1997).
    [CrossRef]
  5. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature (London) 397, 594–598 (1999).
    [CrossRef]
  6. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, Cambridge, UK, 1997).
  7. M. D. Lukin and A. Imamoglu, “Controlling photons using electromagnetically induced transparency,” Nature (London) 413, 273–276 (2001).
    [CrossRef]
  8. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [CrossRef] [PubMed]
  9. J. Sajeev, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
    [CrossRef]
  10. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).
  11. 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, 235902(1–4) (2001).
    [CrossRef]
  12. 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]
  13. S. Mookherjea and A. Yariv, “Second-harmonic generation with pulses in a coupled-resonator optical waveguide,” Phys. Rev. E 65, 026607(1–8) (2002).
    [CrossRef]
  14. S. Mookherjea and A. Yariv, “Coupled resonator optical waveguides,” IEEE J. Sel. Top. Quantum Electron. 8, 448–456 (2002).
    [CrossRef]
  15. 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]
  16. See, for example, N. W. Ashcroft and N. D. Mermin, Solid-State Physics (Saunders, Philadelphia, Pa., 1976).
  17. E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Tight-binding parameterization for photonic band gap materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
    [CrossRef]
  18. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a plane-wave basis,” Opt. Express 8, 173–190 (2001).
    [CrossRef] [PubMed]
  19. For a review, see A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech, Norwood, Mass., 1995).
  20. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
    [CrossRef]
  21. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
    [CrossRef] [PubMed]
  22. S. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B 18, 960–963 (1998).
  23. In accord with the frequency-domain prediction, the active region therefore needs to be approximately 16 coupled cavities long if δn/nH=0.002; we find that we actually need δn/nH=0.00166 in the time-domain calculation. We attribute most of the discrepancy to the inadequacy of the tight-binding approximation, the finite bandwidth of the beam, and the numerical inaccuracies of the simulations.
  24. One might wonder about the practicality of applying a large positive field in one arm and a large negative field in the other arm of such a tiny device. All that is required, however, is to establish a strong gradient of the field between the two arms.
  25. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960–963 (1998).
    [CrossRef]
  26. S. G. Johnson and J. D. Joannopoulos, “Three-dimensionally periodic dielectric layered structure with omnidirectional photonic band gap,” Appl. Phys. Lett. 77, 3490–3492 (2000).
    [CrossRef]
  27. M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, “Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap,” Phys. Rev. B 64, 0753131(1–8) (2001).
    [CrossRef]

2002 (2)

S. Mookherjea and A. Yariv, “Second-harmonic generation with pulses in a coupled-resonator optical waveguide,” Phys. Rev. E 65, 026607(1–8) (2002).
[CrossRef]

S. Mookherjea and A. Yariv, “Coupled resonator optical waveguides,” IEEE J. Sel. Top. Quantum Electron. 8, 448–456 (2002).
[CrossRef]

2001 (4)

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a plane-wave basis,” Opt. Express 8, 173–190 (2001).
[CrossRef] [PubMed]

M. D. Lukin and A. Imamoglu, “Controlling photons using electromagnetically induced transparency,” Nature (London) 413, 273–276 (2001).
[CrossRef]

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, 235902(1–4) (2001).
[CrossRef]

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, “Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap,” Phys. Rev. B 64, 0753131(1–8) (2001).
[CrossRef]

2000 (2)

S. G. Johnson and J. D. Joannopoulos, “Three-dimensionally periodic dielectric layered structure with omnidirectional photonic band gap,” Appl. Phys. Lett. 77, 3490–3492 (2000).
[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] [PubMed]

1999 (2)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature (London) 397, 594–598 (1999).
[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]

1998 (3)

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Tight-binding parameterization for photonic band gap materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[CrossRef]

S. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B 18, 960–963 (1998).

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960–963 (1998).
[CrossRef]

1997 (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50, 36–42 (1997).
[CrossRef]

1996 (2)

A. Sneh, J. E. Zucker, and B. I. Miller, “Compact, low-cross-talk, and low-propagation-loss quantum-well Y-branch switches,” IEEE Photonics Technol. Lett. 8, 1644–1646 (1996).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

1995 (1)

K. Kawano, S. Sekine, H. Takeuchi, M. Wada, M. Kohtoku, N. Yoshimoto, T. Ito, M. Yanagibashi, S. Kondo, and Y. Noguchi, “4×4 InGaAlAs/InAlAs MQW directional coupler waveguide switch modules integrated with spot-size converters and their 10-Gbit/s operation,” Electron. Lett. 31, 96–97 (1995).
[CrossRef]

1994 (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

1987 (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

J. Sajeev, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef]

1975 (1)

W. E. Martin, “A new waveguide switch/modulator for integrated optics,” Appl. Phys. Lett. 26, 562–564 (1975).
[CrossRef]

Bayindir, M.

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]

Behroozi, C. H.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature (London) 397, 594–598 (1999).
[CrossRef]

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Dutton, Z.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature (London) 397, 594–598 (1999).
[CrossRef]

Economou, E. N.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Tight-binding parameterization for photonic band gap materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[CrossRef]

Fan, S.

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, “Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap,” Phys. Rev. B 64, 0753131(1–8) (2001).
[CrossRef]

S. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B 18, 960–963 (1998).

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960–963 (1998).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Harris, S. E.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature (London) 397, 594–598 (1999).
[CrossRef]

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50, 36–42 (1997).
[CrossRef]

Hau, L. V.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature (London) 397, 594–598 (1999).
[CrossRef]

Haus, H. A.

S. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B 18, 960–963 (1998).

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960–963 (1998).
[CrossRef]

Imamoglu, A.

M. D. Lukin and A. Imamoglu, “Controlling photons using electromagnetically induced transparency,” Nature (London) 413, 273–276 (2001).
[CrossRef]

Ito, T.

K. Kawano, S. Sekine, H. Takeuchi, M. Wada, M. Kohtoku, N. Yoshimoto, T. Ito, M. Yanagibashi, S. Kondo, and Y. Noguchi, “4×4 InGaAlAs/InAlAs MQW directional coupler waveguide switch modules integrated with spot-size converters and their 10-Gbit/s operation,” Electron. Lett. 31, 96–97 (1995).
[CrossRef]

Joannopoulos, J. D.

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a plane-wave basis,” Opt. Express 8, 173–190 (2001).
[CrossRef] [PubMed]

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, “Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap,” Phys. Rev. B 64, 0753131(1–8) (2001).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, “Three-dimensionally periodic dielectric layered structure with omnidirectional photonic band gap,” Appl. Phys. Lett. 77, 3490–3492 (2000).
[CrossRef]

S. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B 18, 960–963 (1998).

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960–963 (1998).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Johnson, S. G.

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a plane-wave basis,” Opt. Express 8, 173–190 (2001).
[CrossRef] [PubMed]

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, “Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap,” Phys. Rev. B 64, 0753131(1–8) (2001).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, “Three-dimensionally periodic dielectric layered structure with omnidirectional photonic band gap,” Appl. Phys. Lett. 77, 3490–3492 (2000).
[CrossRef]

S. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B 18, 960–963 (1998).

Kawano, K.

K. Kawano, S. Sekine, H. Takeuchi, M. Wada, M. Kohtoku, N. Yoshimoto, T. Ito, M. Yanagibashi, S. Kondo, and Y. Noguchi, “4×4 InGaAlAs/InAlAs MQW directional coupler waveguide switch modules integrated with spot-size converters and their 10-Gbit/s operation,” Electron. Lett. 31, 96–97 (1995).
[CrossRef]

Kohtoku, M.

K. Kawano, S. Sekine, H. Takeuchi, M. Wada, M. Kohtoku, N. Yoshimoto, T. Ito, M. Yanagibashi, S. Kondo, and Y. Noguchi, “4×4 InGaAlAs/InAlAs MQW directional coupler waveguide switch modules integrated with spot-size converters and their 10-Gbit/s operation,” Electron. Lett. 31, 96–97 (1995).
[CrossRef]

Kondo, S.

K. Kawano, S. Sekine, H. Takeuchi, M. Wada, M. Kohtoku, N. Yoshimoto, T. Ito, M. Yanagibashi, S. Kondo, and Y. Noguchi, “4×4 InGaAlAs/InAlAs MQW directional coupler waveguide switch modules integrated with spot-size converters and their 10-Gbit/s operation,” Electron. Lett. 31, 96–97 (1995).
[CrossRef]

Kurland, I.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Lee, R. K.

Lidorikis, E.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Tight-binding parameterization for photonic band gap materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[CrossRef]

Lukin, M. D.

M. D. Lukin and A. Imamoglu, “Controlling photons using electromagnetically induced transparency,” Nature (London) 413, 273–276 (2001).
[CrossRef]

Manolatou, C.

Martin, W. E.

W. E. Martin, “A new waveguide switch/modulator for integrated optics,” Appl. Phys. Lett. 26, 562–564 (1975).
[CrossRef]

Mekis, A.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Miller, B. I.

A. Sneh, J. E. Zucker, and B. I. Miller, “Compact, low-cross-talk, and low-propagation-loss quantum-well Y-branch switches,” IEEE Photonics Technol. Lett. 8, 1644–1646 (1996).
[CrossRef]

Mookherjea, S.

S. Mookherjea and A. Yariv, “Second-harmonic generation with pulses in a coupled-resonator optical waveguide,” Phys. Rev. E 65, 026607(1–8) (2002).
[CrossRef]

S. Mookherjea and A. Yariv, “Coupled resonator optical waveguides,” IEEE J. Sel. Top. Quantum Electron. 8, 448–456 (2002).
[CrossRef]

Noguchi, Y.

K. Kawano, S. Sekine, H. Takeuchi, M. Wada, M. Kohtoku, N. Yoshimoto, T. Ito, M. Yanagibashi, S. Kondo, and Y. Noguchi, “4×4 InGaAlAs/InAlAs MQW directional coupler waveguide switch modules integrated with spot-size converters and their 10-Gbit/s operation,” Electron. Lett. 31, 96–97 (1995).
[CrossRef]

Notomi, M.

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, 235902(1–4) (2001).
[CrossRef]

Ozbay, E.

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]

Povinelli, M. L.

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, “Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap,” Phys. Rev. B 64, 0753131(1–8) (2001).
[CrossRef]

Sajeev, J.

J. Sajeev, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef]

Scherer, A.

Sekine, S.

K. Kawano, S. Sekine, H. Takeuchi, M. Wada, M. Kohtoku, N. Yoshimoto, T. Ito, M. Yanagibashi, S. Kondo, and Y. Noguchi, “4×4 InGaAlAs/InAlAs MQW directional coupler waveguide switch modules integrated with spot-size converters and their 10-Gbit/s operation,” Electron. Lett. 31, 96–97 (1995).
[CrossRef]

Shinya, A.

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, 235902(1–4) (2001).
[CrossRef]

Sigalas, M. M.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Tight-binding parameterization for photonic band gap materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[CrossRef]

Sneh, A.

A. Sneh, J. E. Zucker, and B. I. Miller, “Compact, low-cross-talk, and low-propagation-loss quantum-well Y-branch switches,” IEEE Photonics Technol. Lett. 8, 1644–1646 (1996).
[CrossRef]

Soukoulis, C. M.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, “Tight-binding parameterization for photonic band gap materials,” Phys. Rev. Lett. 81, 1405–1408 (1998).
[CrossRef]

Takahashi, C.

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, 235902(1–4) (2001).
[CrossRef]

Takahashi, J.

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, 235902(1–4) (2001).
[CrossRef]

Takeuchi, H.

K. Kawano, S. Sekine, H. Takeuchi, M. Wada, M. Kohtoku, N. Yoshimoto, T. Ito, M. Yanagibashi, S. Kondo, and Y. Noguchi, “4×4 InGaAlAs/InAlAs MQW directional coupler waveguide switch modules integrated with spot-size converters and their 10-Gbit/s operation,” Electron. Lett. 31, 96–97 (1995).
[CrossRef]

Temelkuran, B.

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]

Villeneuve, P. R.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960–963 (1998).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Wada, M.

K. Kawano, S. Sekine, H. Takeuchi, M. Wada, M. Kohtoku, N. Yoshimoto, T. Ito, M. Yanagibashi, S. Kondo, and Y. Noguchi, “4×4 InGaAlAs/InAlAs MQW directional coupler waveguide switch modules integrated with spot-size converters and their 10-Gbit/s operation,” Electron. Lett. 31, 96–97 (1995).
[CrossRef]

Xu, Y.

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

Yamada, K.

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, 235902(1–4) (2001).
[CrossRef]

Yanagibashi, M.

K. Kawano, S. Sekine, H. Takeuchi, M. Wada, M. Kohtoku, N. Yoshimoto, T. Ito, M. Yanagibashi, S. Kondo, and Y. Noguchi, “4×4 InGaAlAs/InAlAs MQW directional coupler waveguide switch modules integrated with spot-size converters and their 10-Gbit/s operation,” Electron. Lett. 31, 96–97 (1995).
[CrossRef]

Yariv, A.

S. Mookherjea and A. Yariv, “Coupled resonator optical waveguides,” IEEE J. Sel. Top. Quantum Electron. 8, 448–456 (2002).
[CrossRef]

S. Mookherjea and A. Yariv, “Second-harmonic generation with pulses in a coupled-resonator optical waveguide,” Phys. Rev. E 65, 026607(1–8) (2002).
[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]

Yokohama, I.

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, 235902(1–4) (2001).
[CrossRef]

Yoshimoto, N.

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In accord with the frequency-domain prediction, the active region therefore needs to be approximately 16 coupled cavities long if δn/nH=0.002; we find that we actually need δn/nH=0.00166 in the time-domain calculation. We attribute most of the discrepancy to the inadequacy of the tight-binding approximation, the finite bandwidth of the beam, and the numerical inaccuracies of the simulations.

One might wonder about the practicality of applying a large positive field in one arm and a large negative field in the other arm of such a tiny device. All that is required, however, is to establish a strong gradient of the field between the two arms.

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Figures (6)

Fig. 1
Fig. 1

Induced change in the photonic band frequency in a material depends mostly on the induced index of refraction change. However, depending on the local group velocity, this can lead to drastically different changes in the wave vector. Here we show this effect for two dispersion curves: the slow-light band with vG=0.022c used in a device proposed in this paper (green), and the dispersion curve of a uniform material with n=3.5 (blue). We apply the same frequency shift (δω=0.001) to both dispersion curves to get the respective dashed curves. As we can see, the same δω (black) leads to two very different δk (red).

Fig. 2
Fig. 2

Sketch of the Mach–Zehnder interferometer that we used to demonstrate enhancement of nonlinear phase sensitivity that is due to slow light in PCs. The slow-light system that we use is a coupled-cavity waveguide (CCW), as shown in the upper left-hand enlarged area of this figure. (Throughout the paper, cavities are colored green to make them more visible). The signal enters the device on the right, is split equally at the first T branch into the upper and the lower waveguides, and recombines at the T branch on the left. If no index change is induced, the parts of the signal coming from the top and the bottom interfere constructively at the second T branch, and the pulse exists entirely at the output. If we induce the index change in the active region in an appropriate manner, the two parts of the signal interfere destructively, and the pulse is reflected back toward the input, with no signal being observed at the output. The points marked (A), (B), and (C) correspond to field-monitor points during the simulations. The results of observations from these points are displayed in Fig. 3.

Fig. 3
Fig. 3

Demonstration of nonlinear switching in a slow-light PC system. The electric field squared is plotted as a function of time, observed at three different points: (A), (B), and (C) in the system of Fig. 2. The left-hand column corresponds to the case when no index change is induced; most of the incoming signal at (A) exits at the output (C). The column on the right-hand side corresponds to the case when the nonlinear index change is induced; the signal at the output (C) in the right-hand column is drastically reduced compared with the output (C) in the left-hand column. The black and the blue signals represent the pulses traveling from right to left and left to right, respectively, in Fig. 2. The gray pulses are spurious reflections (mostly from the interface between the PC and air at the exits of the device).

Fig. 4
Fig. 4

Snapshots of the electric field pulse in the system of Fig. 2 for the case when no index change is induced. The top panel represents 120,000 time steps, and bottom panel 160,000 time steps. The signal entering at the input exits at the output of the device; the device is in its on state.

Fig. 5
Fig. 5

Snapshots of the electric field pulse in the system of Fig. 2 for the case when an index change is induced. Top panel represents 120,000 time steps, the middle panel 160,000 time steps, and the bottom panel 200,000 time steps. The signal entering at the input is reflected back toward the input; device is in its off state.

Fig. 6
Fig. 6

Mach–Zehnder interferometer operating as a router between two different outputs. This operation is achieved by the termination of the interferometer with a directional coupler rather than with a T branch, as shown in the upper panel. The lower panel gives the calculated intensity at each of the two outputs as a function of the phase difference between the upper and the lower input to the directional coupler.

Equations (5)

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LλAIR12σnδnvGc,
AOUT1=AIN11-iαω-ω0+iα-AIN2iαω-ω0+iα,
AOUT2=AIN21-iαω-ω0+iα-AIN1iαω-ω0+iα,
IOUT1IIN1+IIN2=12(ω-ω0-α)2(ω-ω0)2+α2,
IOUT2IIN1+IIN2=12(ω-ω0+α)2(ω-ω0)2+α2,

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