Abstract

We report on a theoretical study of a refractive-index-change- (Δn-) induced phase shift enhanced by the low group velocity in an air-bridge-type AlGaAs two-dimensional (2-D) photonic crystal (PC) slab waveguide. The calculation was based on a three-dimensional finite-difference time-domain method for the design of a phase-shift arm of the 2-D PC-based symmetric Mach–Zehnder- (SMZ-) type all-optical switch. Δn was assumed to be induced by an optical nonlinearity of InAs quantum dots embedded selectively in the phase-shift arm in the PC SMZ. By changing Δn from 0 to -0.01 and -0.1 for an even guided mode in the triangular-lattice single-line-defect waveguide in the PC SMZ, we calculated a group-velocity-dependent phase shift as well as a band diagram and a transmission spectrum. The result showed that the phase shift is almost inversely proportional to the group velocity. Taking into account Δn of approximately -0.001 predicted for actual InAs quantum dots, we evaluated the length of the phase-shift arm, necessary for the π phase shift in the PC SMZ, to be ∼100 µm for a group velocity of 0.031c and a lattice constant of 0.36 µm at a wavelength of ∼1.3 µm, where c is the light velocity in the vacuum. The length of the phase-shift arm was significantly reduced because of the low group velocity in spite of the small Δn. As a result, it was found that the phase-shift arm can be designed short enough to achieve a compact ultrafast all-optical switch.

© 2004 Optical Society of America

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    [CrossRef]
  4. T. Baba, N. Fukaya, and J. Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electron. Lett. 35, 654–655 (1999).
    [CrossRef]
  5. S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature (London) 407, 608–610 (2000).
    [CrossRef]
  6. S. G. Johnson, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
    [CrossRef]
  7. M. Tokushima, H. Kosaka, K. Tomita, and H. Yamada, “Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide,” Appl. Phys. Lett. 76, 952–954 (2000).
    [CrossRef]
  8. S. Y. Lin, E. Chow, S. G. Johnson, and J. D. Joannopoulos, “Demonstration of highly efficient waveguiding in a photonic crystal slab at the 1.5-μm wavelength,” Opt. Lett. 25, 1297–1299 (2000).
    [CrossRef]
  9. M. Loncar, T. Doll, J. Vuckovic, and A. Scherer, “Design and fabrication of silicon photonic crystal optical waveguides,” J. Lightwave Technol. 18, 1402–1411 (2000).
    [CrossRef]
  10. M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, “Structural tuning of guiding modes of line-defect waveguides of silicon-on-insulator photonic crystal slabs,” IEEE J. Quantum Electron. 38, 736–742 (2002).
    [CrossRef]
  11. Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, “AlGaAs-based two-dimensional photonic crystal slab with defect waveguides for planar lightwave circuit applications,” IEEE J. Quantum Electron. 38, 760–769 (2002).
    [CrossRef]
  12. Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, “Fabrication and characterization of different types of two-dimensional AlGaAs photonic crystal slabs,” J. Appl. Phys. 91, 922–929 (2002).
    [CrossRef]
  13. K. Tajima, “All-optical switch with switch-off time unrestricted by carrier lifetime,” Jpn. J. Appl. Phys. 32, L1746–L1749 (1993).
    [CrossRef]
  14. Y. Sugimoto, Y. Tanaka, N. Ikeda, T. Yang, H. Nakamura, K. Asakawa, K. Inoue, T. Maruyama, K. Miyashita, K. Ishida, and Y. Watanabe, “Design, fabrication, and characterization of coupling-strength-controlled directional coupler based on two-dimensional photonic-crystal slab waveguides,” Appl. Phys. Lett. 83, 3236–3238 (2003).
    [CrossRef]
  15. H. Nakamura, S. Kohmoto, N. Carlsson, Y. Sugimoto, and K. Asakawa, “Large enhancement of optical nonlinearity using quantum dots embedded in a photonic crystal structure for all-optical switch applications,” in Lasers and Electro-Optics Society Proceedings of the 13th Annual Conference (Institute of Electrical and Electronics Engineers, New York, 2000), Vol. 2, pp. 488–489.
  16. 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).
    [CrossRef]
  17. 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]
  18. 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]
  19. See, for example, K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, Boca Raton, Fla., 1993).
  20. J. P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363–379 (1996).
    [CrossRef]
  21. G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).
    [CrossRef]
  22. S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E 66, 066608 (2002).
    [CrossRef]
  23. H. Nakamura, Femtosecond Technology Research Association, Tsukuba 300–2635, Japan, Y. Tanaka, N. Ikeda, Y. Sugimoto, K. Kanamoto, and K. Asakawa are preparing a manuscript to be called “High-efficiency coupling to photonic crystal waveguide with low group velocity by hetero photonic crystal technique.”

2003 (1)

Y. Sugimoto, Y. Tanaka, N. Ikeda, T. Yang, H. Nakamura, K. Asakawa, K. Inoue, T. Maruyama, K. Miyashita, K. Ishida, and Y. Watanabe, “Design, fabrication, and characterization of coupling-strength-controlled directional coupler based on two-dimensional photonic-crystal slab waveguides,” Appl. Phys. Lett. 83, 3236–3238 (2003).
[CrossRef]

2002 (5)

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E 66, 066608 (2002).
[CrossRef]

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, “Structural tuning of guiding modes of line-defect waveguides of silicon-on-insulator photonic crystal slabs,” IEEE J. Quantum Electron. 38, 736–742 (2002).
[CrossRef]

Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, “AlGaAs-based two-dimensional photonic crystal slab with defect waveguides for planar lightwave circuit applications,” IEEE J. Quantum Electron. 38, 760–769 (2002).
[CrossRef]

Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, “Fabrication and characterization of different types of two-dimensional AlGaAs photonic crystal slabs,” J. Appl. Phys. 91, 922–929 (2002).
[CrossRef]

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).
[CrossRef]

2000 (5)

S. Y. Lin, E. Chow, S. G. Johnson, and J. D. Joannopoulos, “Demonstration of highly efficient waveguiding in a photonic crystal slab at the 1.5-μm wavelength,” Opt. Lett. 25, 1297–1299 (2000).
[CrossRef]

M. Loncar, T. Doll, J. Vuckovic, and A. Scherer, “Design and fabrication of silicon photonic crystal optical waveguides,” J. Lightwave Technol. 18, 1402–1411 (2000).
[CrossRef]

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature (London) 407, 608–610 (2000).
[CrossRef]

M. Tokushima, H. Kosaka, K. Tomita, and H. Yamada, “Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide,” Appl. Phys. Lett. 76, 952–954 (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 (3)

T. Baba, N. Fukaya, and J. Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electron. Lett. 35, 654–655 (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]

S. G. Johnson, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

1997 (1)

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

1996 (2)

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature (London) 383, 699–702 (1996).
[CrossRef]

J. P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363–379 (1996).
[CrossRef]

1993 (1)

K. Tajima, “All-optical switch with switch-off time unrestricted by carrier lifetime,” Jpn. J. Appl. Phys. 32, L1746–L1749 (1993).
[CrossRef]

1981 (1)

G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).
[CrossRef]

Asakawa, K.

Y. Sugimoto, Y. Tanaka, N. Ikeda, T. Yang, H. Nakamura, K. Asakawa, K. Inoue, T. Maruyama, K. Miyashita, K. Ishida, and Y. Watanabe, “Design, fabrication, and characterization of coupling-strength-controlled directional coupler based on two-dimensional photonic-crystal slab waveguides,” Appl. Phys. Lett. 83, 3236–3238 (2003).
[CrossRef]

Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, “Fabrication and characterization of different types of two-dimensional AlGaAs photonic crystal slabs,” J. Appl. Phys. 91, 922–929 (2002).
[CrossRef]

Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, “AlGaAs-based two-dimensional photonic crystal slab with defect waveguides for planar lightwave circuit applications,” IEEE J. Quantum Electron. 38, 760–769 (2002).
[CrossRef]

Baba, T.

T. Baba, N. Fukaya, and J. Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electron. Lett. 35, 654–655 (1999).
[CrossRef]

Bardinal, V.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[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]

Benisty, H.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Berenger, J. P.

J. P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363–379 (1996).
[CrossRef]

Bienstman, P.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Brand, S.

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature (London) 383, 699–702 (1996).
[CrossRef]

Carlsson, N.

Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, “AlGaAs-based two-dimensional photonic crystal slab with defect waveguides for planar lightwave circuit applications,” IEEE J. Quantum Electron. 38, 760–769 (2002).
[CrossRef]

Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, “Fabrication and characterization of different types of two-dimensional AlGaAs photonic crystal slabs,” J. Appl. Phys. 91, 922–929 (2002).
[CrossRef]

Cassagne, D.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Chow, E.

Chutinan, A.

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature (London) 407, 608–610 (2000).
[CrossRef]

De La Rue, R. M.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature (London) 383, 699–702 (1996).
[CrossRef]

Doll, T.

Fan, S.

Fukaya, N.

T. Baba, N. Fukaya, and J. Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electron. Lett. 35, 654–655 (1999).
[CrossRef]

Houdré, R.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Ibanescu, M.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E 66, 066608 (2002).
[CrossRef]

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).
[CrossRef]

Ikeda, N.

Y. Sugimoto, Y. Tanaka, N. Ikeda, T. Yang, H. Nakamura, K. Asakawa, K. Inoue, T. Maruyama, K. Miyashita, K. Ishida, and Y. Watanabe, “Design, fabrication, and characterization of coupling-strength-controlled directional coupler based on two-dimensional photonic-crystal slab waveguides,” Appl. Phys. Lett. 83, 3236–3238 (2003).
[CrossRef]

Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, “Fabrication and characterization of different types of two-dimensional AlGaAs photonic crystal slabs,” J. Appl. Phys. 91, 922–929 (2002).
[CrossRef]

Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, “AlGaAs-based two-dimensional photonic crystal slab with defect waveguides for planar lightwave circuit applications,” IEEE J. Quantum Electron. 38, 760–769 (2002).
[CrossRef]

Imada, M.

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature (London) 407, 608–610 (2000).
[CrossRef]

Inoue, K.

Y. Sugimoto, Y. Tanaka, N. Ikeda, T. Yang, H. Nakamura, K. Asakawa, K. Inoue, T. Maruyama, K. Miyashita, K. Ishida, and Y. Watanabe, “Design, fabrication, and characterization of coupling-strength-controlled directional coupler based on two-dimensional photonic-crystal slab waveguides,” Appl. Phys. Lett. 83, 3236–3238 (2003).
[CrossRef]

Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, “Fabrication and characterization of different types of two-dimensional AlGaAs photonic crystal slabs,” J. Appl. Phys. 91, 922–929 (2002).
[CrossRef]

Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, “AlGaAs-based two-dimensional photonic crystal slab with defect waveguides for planar lightwave circuit applications,” IEEE J. Quantum Electron. 38, 760–769 (2002).
[CrossRef]

Ippen, E.

Ishida, K.

Y. Sugimoto, Y. Tanaka, N. Ikeda, T. Yang, H. Nakamura, K. Asakawa, K. Inoue, T. Maruyama, K. Miyashita, K. Ishida, and Y. Watanabe, “Design, fabrication, and characterization of coupling-strength-controlled directional coupler based on two-dimensional photonic-crystal slab waveguides,” Appl. Phys. Lett. 83, 3236–3238 (2003).
[CrossRef]

Joannopoulos, J. D.

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).
[CrossRef]

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E 66, 066608 (2002).
[CrossRef]

S. Y. Lin, E. Chow, S. G. Johnson, and J. D. Joannopoulos, “Demonstration of highly efficient waveguiding in a photonic crystal slab at the 1.5-μm wavelength,” Opt. Lett. 25, 1297–1299 (2000).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

Johnson, S. G.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E 66, 066608 (2002).
[CrossRef]

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).
[CrossRef]

S. Y. Lin, E. Chow, S. G. Johnson, and J. D. Joannopoulos, “Demonstration of highly efficient waveguiding in a photonic crystal slab at the 1.5-μm wavelength,” Opt. Lett. 25, 1297–1299 (2000).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

Jouanin, C.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Kawai, N.

Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, “AlGaAs-based two-dimensional photonic crystal slab with defect waveguides for planar lightwave circuit applications,” IEEE J. Quantum Electron. 38, 760–769 (2002).
[CrossRef]

Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, “Fabrication and characterization of different types of two-dimensional AlGaAs photonic crystal slabs,” J. Appl. Phys. 91, 922–929 (2002).
[CrossRef]

Kosaka, H.

M. Tokushima, H. Kosaka, K. Tomita, and H. Yamada, “Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide,” Appl. Phys. Lett. 76, 952–954 (2000).
[CrossRef]

Krauss, T. F.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature (London) 383, 699–702 (1996).
[CrossRef]

Labilloy, D.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Lee, R. K.

Lidorikis, E.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Lin, S. Y.

Loncar, M.

Maruyama, T.

Y. Sugimoto, Y. Tanaka, N. Ikeda, T. Yang, H. Nakamura, K. Asakawa, K. Inoue, T. Maruyama, K. Miyashita, K. Ishida, and Y. Watanabe, “Design, fabrication, and characterization of coupling-strength-controlled directional coupler based on two-dimensional photonic-crystal slab waveguides,” Appl. Phys. Lett. 83, 3236–3238 (2003).
[CrossRef]

Miyashita, K.

Y. Sugimoto, Y. Tanaka, N. Ikeda, T. Yang, H. Nakamura, K. Asakawa, K. Inoue, T. Maruyama, K. Miyashita, K. Ishida, and Y. Watanabe, “Design, fabrication, and characterization of coupling-strength-controlled directional coupler based on two-dimensional photonic-crystal slab waveguides,” Appl. Phys. Lett. 83, 3236–3238 (2003).
[CrossRef]

Mur, G.

G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).
[CrossRef]

Nakamura, H.

Y. Sugimoto, Y. Tanaka, N. Ikeda, T. Yang, H. Nakamura, K. Asakawa, K. Inoue, T. Maruyama, K. Miyashita, K. Ishida, and Y. Watanabe, “Design, fabrication, and characterization of coupling-strength-controlled directional coupler based on two-dimensional photonic-crystal slab waveguides,” Appl. Phys. Lett. 83, 3236–3238 (2003).
[CrossRef]

Noda, S.

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature (London) 407, 608–610 (2000).
[CrossRef]

Notomi, M.

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, “Structural tuning of guiding modes of line-defect waveguides of silicon-on-insulator photonic crystal slabs,” IEEE J. Quantum Electron. 38, 736–742 (2002).
[CrossRef]

Oesterle, U.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

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[CrossRef]

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S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Soljacic, M.

Sugimoto, Y.

Y. Sugimoto, Y. Tanaka, N. Ikeda, T. Yang, H. Nakamura, K. Asakawa, K. Inoue, T. Maruyama, K. Miyashita, K. Ishida, and Y. Watanabe, “Design, fabrication, and characterization of coupling-strength-controlled directional coupler based on two-dimensional photonic-crystal slab waveguides,” Appl. Phys. Lett. 83, 3236–3238 (2003).
[CrossRef]

Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, “Fabrication and characterization of different types of two-dimensional AlGaAs photonic crystal slabs,” J. Appl. Phys. 91, 922–929 (2002).
[CrossRef]

Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, “AlGaAs-based two-dimensional photonic crystal slab with defect waveguides for planar lightwave circuit applications,” IEEE J. Quantum Electron. 38, 760–769 (2002).
[CrossRef]

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K. Tajima, “All-optical switch with switch-off time unrestricted by carrier lifetime,” Jpn. J. Appl. Phys. 32, L1746–L1749 (1993).
[CrossRef]

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M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, “Structural tuning of guiding modes of line-defect waveguides of silicon-on-insulator photonic crystal slabs,” IEEE J. Quantum Electron. 38, 736–742 (2002).
[CrossRef]

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M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, “Structural tuning of guiding modes of line-defect waveguides of silicon-on-insulator photonic crystal slabs,” IEEE J. Quantum Electron. 38, 736–742 (2002).
[CrossRef]

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Y. Sugimoto, Y. Tanaka, N. Ikeda, T. Yang, H. Nakamura, K. Asakawa, K. Inoue, T. Maruyama, K. Miyashita, K. Ishida, and Y. Watanabe, “Design, fabrication, and characterization of coupling-strength-controlled directional coupler based on two-dimensional photonic-crystal slab waveguides,” Appl. Phys. Lett. 83, 3236–3238 (2003).
[CrossRef]

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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]

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M. Tokushima, H. Kosaka, K. Tomita, and H. Yamada, “Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide,” Appl. Phys. Lett. 76, 952–954 (2000).
[CrossRef]

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M. Tokushima, H. Kosaka, K. Tomita, and H. Yamada, “Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide,” Appl. Phys. Lett. 76, 952–954 (2000).
[CrossRef]

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S. G. Johnson, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

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Y. Sugimoto, Y. Tanaka, N. Ikeda, T. Yang, H. Nakamura, K. Asakawa, K. Inoue, T. Maruyama, K. Miyashita, K. Ishida, and Y. Watanabe, “Design, fabrication, and characterization of coupling-strength-controlled directional coupler based on two-dimensional photonic-crystal slab waveguides,” Appl. Phys. Lett. 83, 3236–3238 (2003).
[CrossRef]

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D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

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M. Tokushima, H. Kosaka, K. Tomita, and H. Yamada, “Lightwave propagation through a 120° sharply bent single-line-defect photonic crystal waveguide,” Appl. Phys. Lett. 76, 952–954 (2000).
[CrossRef]

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M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, “Structural tuning of guiding modes of line-defect waveguides of silicon-on-insulator photonic crystal slabs,” IEEE J. Quantum Electron. 38, 736–742 (2002).
[CrossRef]

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Y. Sugimoto, Y. Tanaka, N. Ikeda, T. Yang, H. Nakamura, K. Asakawa, K. Inoue, T. Maruyama, K. Miyashita, K. Ishida, and Y. Watanabe, “Design, fabrication, and characterization of coupling-strength-controlled directional coupler based on two-dimensional photonic-crystal slab waveguides,” Appl. Phys. Lett. 83, 3236–3238 (2003).
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[CrossRef]

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[CrossRef]

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[CrossRef]

Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, “AlGaAs-based two-dimensional photonic crystal slab with defect waveguides for planar lightwave circuit applications,” IEEE J. Quantum Electron. 38, 760–769 (2002).
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Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, “Fabrication and characterization of different types of two-dimensional AlGaAs photonic crystal slabs,” J. Appl. Phys. 91, 922–929 (2002).
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Phys. Rev. B (1)

S. G. Johnson, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

Phys. Rev. E (1)

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Phys. Rev. Lett. (2)

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]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Other (4)

See, for example, K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, Boca Raton, Fla., 1993).

H. Nakamura, S. Kohmoto, N. Carlsson, Y. Sugimoto, and K. Asakawa, “Large enhancement of optical nonlinearity using quantum dots embedded in a photonic crystal structure for all-optical switch applications,” in Lasers and Electro-Optics Society Proceedings of the 13th Annual Conference (Institute of Electrical and Electronics Engineers, New York, 2000), Vol. 2, pp. 488–489.

H. Nakamura, Femtosecond Technology Research Association, Tsukuba 300–2635, Japan, Y. Tanaka, N. Ikeda, Y. Sugimoto, K. Kanamoto, and K. Asakawa are preparing a manuscript to be called “High-efficiency coupling to photonic crystal waveguide with low group velocity by hetero photonic crystal technique.”

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, Princeton, N.J., 1995).

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Figures (7)

Fig. 1
Fig. 1

Schematic of the 2-D PC-based symmetrical SMZ-type all-optical switch.

Fig. 2
Fig. 2

Principle of the ultrafast optical switching operation in the SMZ all-optical switch.

Fig. 3
Fig. 3

Schematic of 2-D PC slab defect waveguides with triangular-lattice single missing air-hole arrays as phase-shift arms in the PC SMZ device. In-1 and In-2 mark the positions of the light source. Out-1 and Out-2 mark the positions of the detectors.

Fig. 4
Fig. 4

(a) Computational domain of the unit cell for the band calculation. (b) Band diagram for the single-line-defect waveguide.

Fig. 5
Fig. 5

(a) Transmission spectra for the single-line-defect waveguide. (b) Wave forms of the phase-shifted light with f=0.2703c/a detected at the output position of the waveguide. Both results are calculated for Δn=0, -0.01, and -0.1.

Fig. 6
Fig. 6

Calculated relationship among the parameters as a function of f. (a) Dispersion curve for the even mode versus f. (b) Group velocity and group index versus f. (c) Transmittance and phase shift versus f.

Fig. 7
Fig. 7

Schematic of the total PC SMZ waveguide patterns including the phase-shift arms, the length of which is roughly evaluated as 100–200 µm.

Tables (1)

Tables Icon

Table 1 Summarized Results for the Six Frequencies in Terms of Group Velocity Vg, Group Index, Phase Shift in Degrees and Phase Shift in Degrees per Lattice Constant a

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