Abstract

Photonic crystals (PCs) have many potential applications because of their ability to control light-wave propagation and because PC-based waveguides may be integrated into optical interferometers. We propose a novel tunable PC waveguide Mach–Zehnder interferometer based on nematic liquid crystals and investigate its interference properties numerically by using the finite-difference time-domain method. We can change the refractive indices of liquid crystals by rotating the directors of the liquid crystals. Then we can control the phase of light propagation in a PC waveguide Mach-Zehnder interferometer. The interference mechanism is a change in the refractive indices of liquid-crystal waveguides. The novel interferometer can be used either as an optically controlled on–off switch or as an amplitude modulator in optical circuits.

© 2004 Optical Society of America

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  1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [Crossref] [PubMed]
  2. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N. J., 1995).
  3. E. Centeno and D. Felbacq, “Guiding waves with photonic crystals,” Opt. Commun. 160, 57–60 (1999).
    [Crossref]
  4. R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel application of photonic band gap materials: low-loss bends and high-Q cavities,” J. Appl. Phys. 75, 4753–4755 (1994).
    [Crossref]
  5. T. Baba, N. Fukaya, and J. Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electron. Lett. 35, 654–656 (1999).
    [Crossref]
  6. M. H. Shih, W. J. Kim, W. Kuang, J. R. Cao, H. Yukawa, S. J. Choi, J. D. O’Brien, P. D. Dapkus, and W. K. Marshall, “Two-dimensional photonic crystal Mach–Zehnder interferometers,” Appl. Phys. Lett. 84, 460–462 (2004).
    [Crossref]
  7. 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]
  8. 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]
  9. K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, “Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal,” Appl. Phys. Lett. 75, 932–934 (1999).
    [Crossref]
  10. H. Takeda and K. Yoshino, “Electric field tuning of a stop band in a reflection spectrum of synthetic opal infiltrated with nematic liquid crystal,” J. Appl. Phys. 92, 5958–5662 (2002).
  11. H. Takeda and K. Yoshino, “Tunable light propagation in Y-shaped waveguides in two-dimensional photonic crystals utilizing liquid crystals as linear defects,” Phys. Rev. B 67, 073106 (2003).
    [Crossref]
  12. H. Takeda and K. Yoshino, “Tunable light propagation in Y-shaped waveguides in two-dimensional photonic crystals composed of semiconductors depending on temperature,” Opt. Commun. 219, 177–182 (2003).
    [Crossref]
  13. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite Difference Time Domain Method (Artech House, Boston, Mass., 1998).
  14. M. Koshiba, Y. Tsuji, and Saski, “High-performance absorbing boundary conditions for photonic crystal waveguide simulations,” IEEE Microwave Wireless Compon. Lett. 11, 152–154 (2001).
    [Crossref]
  15. H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, and T. F. Krauss, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
    [Crossref]
  16. I.-C. Khoo and S.-T. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, Singapore, 1993).
    [Crossref]
  17. Y. Shimoda, M. Ozaki, and K. Yoshino, “Electric field tuning of a stop band in a reflection spectrum of synthetic opal infiltrated with nematic liquid crystal,” Appl. Phys. Lett. 79, 3627–3629 (2001).
    [Crossref]
  18. A. V. Zakharov and L. V. Mirantsev, “Dynamic and dielectric properties of liquid crystals,” Phys. Solid State 45, 183–188 (2003).
    [Crossref]
  19. S. Khalfallah, P. Dubreuil, R. Legros, C. Fontaine, A. Munoz-Yagűe, B. Beche, H. Porte, R. Warno, and M. Karpierz, “Highly unbalanced GaAlAs-GaAs integrated Mach—Zehnder interferometer for coherence modulation at 1.3 µm,” Opt. Commun. 167, 67–79 (1999).
    [Crossref]

2004 (1)

M. H. Shih, W. J. Kim, W. Kuang, J. R. Cao, H. Yukawa, S. J. Choi, J. D. O’Brien, P. D. Dapkus, and W. K. Marshall, “Two-dimensional photonic crystal Mach–Zehnder interferometers,” Appl. Phys. Lett. 84, 460–462 (2004).
[Crossref]

2003 (4)

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]

H. Takeda and K. Yoshino, “Tunable light propagation in Y-shaped waveguides in two-dimensional photonic crystals utilizing liquid crystals as linear defects,” Phys. Rev. B 67, 073106 (2003).
[Crossref]

H. Takeda and K. Yoshino, “Tunable light propagation in Y-shaped waveguides in two-dimensional photonic crystals composed of semiconductors depending on temperature,” Opt. Commun. 219, 177–182 (2003).
[Crossref]

A. V. Zakharov and L. V. Mirantsev, “Dynamic and dielectric properties of liquid crystals,” Phys. Solid State 45, 183–188 (2003).
[Crossref]

2002 (2)

H. Takeda and K. Yoshino, “Electric field tuning of a stop band in a reflection spectrum of synthetic opal infiltrated with nematic liquid crystal,” J. Appl. Phys. 92, 5958–5662 (2002).

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]

2001 (2)

Y. Shimoda, M. Ozaki, and K. Yoshino, “Electric field tuning of a stop band in a reflection spectrum of synthetic opal infiltrated with nematic liquid crystal,” Appl. Phys. Lett. 79, 3627–3629 (2001).
[Crossref]

M. Koshiba, Y. Tsuji, and Saski, “High-performance absorbing boundary conditions for photonic crystal waveguide simulations,” IEEE Microwave Wireless Compon. Lett. 11, 152–154 (2001).
[Crossref]

1999 (5)

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, and T. F. Krauss, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[Crossref]

S. Khalfallah, P. Dubreuil, R. Legros, C. Fontaine, A. Munoz-Yagűe, B. Beche, H. Porte, R. Warno, and M. Karpierz, “Highly unbalanced GaAlAs-GaAs integrated Mach—Zehnder interferometer for coherence modulation at 1.3 µm,” Opt. Commun. 167, 67–79 (1999).
[Crossref]

K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, “Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal,” Appl. Phys. Lett. 75, 932–934 (1999).
[Crossref]

E. Centeno and D. Felbacq, “Guiding waves with photonic crystals,” Opt. Commun. 160, 57–60 (1999).
[Crossref]

T. Baba, N. Fukaya, and J. Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electron. Lett. 35, 654–656 (1999).
[Crossref]

1994 (1)

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel application of photonic band gap materials: low-loss bends and high-Q cavities,” J. Appl. Phys. 75, 4753–4755 (1994).
[Crossref]

1987 (1)

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

Alerhand, O. L.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel application of photonic band gap materials: low-loss bends and high-Q cavities,” J. Appl. Phys. 75, 4753–4755 (1994).
[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]

Baba, T.

T. Baba, N. Fukaya, and J. Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electron. Lett. 35, 654–656 (1999).
[Crossref]

Beche, B.

S. Khalfallah, P. Dubreuil, R. Legros, C. Fontaine, A. Munoz-Yagűe, B. Beche, H. Porte, R. Warno, and M. Karpierz, “Highly unbalanced GaAlAs-GaAs integrated Mach—Zehnder interferometer for coherence modulation at 1.3 µm,” Opt. Commun. 167, 67–79 (1999).
[Crossref]

Benisty, H.

Cao, J. R.

M. H. Shih, W. J. Kim, W. Kuang, J. R. Cao, H. Yukawa, S. J. Choi, J. D. O’Brien, P. D. Dapkus, and W. K. Marshall, “Two-dimensional photonic crystal Mach–Zehnder interferometers,” Appl. Phys. Lett. 84, 460–462 (2004).
[Crossref]

Carlsson, N.

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]

Centeno, E.

E. Centeno and D. Felbacq, “Guiding waves with photonic crystals,” Opt. Commun. 160, 57–60 (1999).
[Crossref]

Choi, S. J.

M. H. Shih, W. J. Kim, W. Kuang, J. R. Cao, H. Yukawa, S. J. Choi, J. D. O’Brien, P. D. Dapkus, and W. K. Marshall, “Two-dimensional photonic crystal Mach–Zehnder interferometers,” Appl. Phys. Lett. 84, 460–462 (2004).
[Crossref]

Dapkus, P. D.

M. H. Shih, W. J. Kim, W. Kuang, J. R. Cao, H. Yukawa, S. J. Choi, J. D. O’Brien, P. D. Dapkus, and W. K. Marshall, “Two-dimensional photonic crystal Mach–Zehnder interferometers,” Appl. Phys. Lett. 84, 460–462 (2004).
[Crossref]

Devenyi, A.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel application of photonic band gap materials: low-loss bends and high-Q cavities,” J. Appl. Phys. 75, 4753–4755 (1994).
[Crossref]

Dubreuil, P.

S. Khalfallah, P. Dubreuil, R. Legros, C. Fontaine, A. Munoz-Yagűe, B. Beche, H. Porte, R. Warno, and M. Karpierz, “Highly unbalanced GaAlAs-GaAs integrated Mach—Zehnder interferometer for coherence modulation at 1.3 µm,” Opt. Commun. 167, 67–79 (1999).
[Crossref]

Felbacq, D.

E. Centeno and D. Felbacq, “Guiding waves with photonic crystals,” Opt. Commun. 160, 57–60 (1999).
[Crossref]

Fontaine, C.

S. Khalfallah, P. Dubreuil, R. Legros, C. Fontaine, A. Munoz-Yagűe, B. Beche, H. Porte, R. Warno, and M. Karpierz, “Highly unbalanced GaAlAs-GaAs integrated Mach—Zehnder interferometer for coherence modulation at 1.3 µm,” Opt. Commun. 167, 67–79 (1999).
[Crossref]

Fukaya, N.

T. Baba, N. Fukaya, and J. Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electron. Lett. 35, 654–656 (1999).
[Crossref]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite Difference Time Domain Method (Artech House, Boston, Mass., 1998).

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]

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]

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.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel application of photonic band gap materials: low-loss bends and high-Q cavities,” J. Appl. Phys. 75, 4753–4755 (1994).
[Crossref]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N. J., 1995).

Karpierz, M.

S. Khalfallah, P. Dubreuil, R. Legros, C. Fontaine, A. Munoz-Yagűe, B. Beche, H. Porte, R. Warno, and M. Karpierz, “Highly unbalanced GaAlAs-GaAs integrated Mach—Zehnder interferometer for coherence modulation at 1.3 µm,” Opt. Commun. 167, 67–79 (1999).
[Crossref]

Kash, K.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel application of photonic band gap materials: low-loss bends and high-Q cavities,” J. Appl. Phys. 75, 4753–4755 (1994).
[Crossref]

Kawagishi, Y.

K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, “Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal,” Appl. Phys. Lett. 75, 932–934 (1999).
[Crossref]

Kawai, N.

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]

Khalfallah, S.

S. Khalfallah, P. Dubreuil, R. Legros, C. Fontaine, A. Munoz-Yagűe, B. Beche, H. Porte, R. Warno, and M. Karpierz, “Highly unbalanced GaAlAs-GaAs integrated Mach—Zehnder interferometer for coherence modulation at 1.3 µm,” Opt. Commun. 167, 67–79 (1999).
[Crossref]

Khoo, I.-C.

I.-C. Khoo and S.-T. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, Singapore, 1993).
[Crossref]

Kim, W. J.

M. H. Shih, W. J. Kim, W. Kuang, J. R. Cao, H. Yukawa, S. J. Choi, J. D. O’Brien, P. D. Dapkus, and W. K. Marshall, “Two-dimensional photonic crystal Mach–Zehnder interferometers,” Appl. Phys. Lett. 84, 460–462 (2004).
[Crossref]

Koshiba, M.

M. Koshiba, Y. Tsuji, and Saski, “High-performance absorbing boundary conditions for photonic crystal waveguide simulations,” IEEE Microwave Wireless Compon. Lett. 11, 152–154 (2001).
[Crossref]

Krauss, T. F.

Kuang, W.

M. H. Shih, W. J. Kim, W. Kuang, J. R. Cao, H. Yukawa, S. J. Choi, J. D. O’Brien, P. D. Dapkus, and W. K. Marshall, “Two-dimensional photonic crystal Mach–Zehnder interferometers,” Appl. Phys. Lett. 84, 460–462 (2004).
[Crossref]

Labilloy, D.

Legros, R.

S. Khalfallah, P. Dubreuil, R. Legros, C. Fontaine, A. Munoz-Yagűe, B. Beche, H. Porte, R. Warno, and M. Karpierz, “Highly unbalanced GaAlAs-GaAs integrated Mach—Zehnder interferometer for coherence modulation at 1.3 µm,” Opt. Commun. 167, 67–79 (1999).
[Crossref]

Marshall, W. K.

M. H. Shih, W. J. Kim, W. Kuang, J. R. Cao, H. Yukawa, S. J. Choi, J. D. O’Brien, P. D. Dapkus, and W. K. Marshall, “Two-dimensional photonic crystal Mach–Zehnder interferometers,” Appl. Phys. Lett. 84, 460–462 (2004).
[Crossref]

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]

Meade, R. D.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel application of photonic band gap materials: low-loss bends and high-Q cavities,” J. Appl. Phys. 75, 4753–4755 (1994).
[Crossref]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N. J., 1995).

Mirantsev, L. V.

A. V. Zakharov and L. V. Mirantsev, “Dynamic and dielectric properties of liquid crystals,” Phys. Solid State 45, 183–188 (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]

Munoz-Yague, A.

S. Khalfallah, P. Dubreuil, R. Legros, C. Fontaine, A. Munoz-Yagűe, B. Beche, H. Porte, R. Warno, and M. Karpierz, “Highly unbalanced GaAlAs-GaAs integrated Mach—Zehnder interferometer for coherence modulation at 1.3 µm,” Opt. Commun. 167, 67–79 (1999).
[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]

Nakayama, K.

K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, “Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal,” Appl. Phys. Lett. 75, 932–934 (1999).
[Crossref]

O’Brien, J. D.

M. H. Shih, W. J. Kim, W. Kuang, J. R. Cao, H. Yukawa, S. J. Choi, J. D. O’Brien, P. D. Dapkus, and W. K. Marshall, “Two-dimensional photonic crystal Mach–Zehnder interferometers,” Appl. Phys. Lett. 84, 460–462 (2004).
[Crossref]

Ozaki, M.

Y. Shimoda, M. Ozaki, and K. Yoshino, “Electric field tuning of a stop band in a reflection spectrum of synthetic opal infiltrated with nematic liquid crystal,” Appl. Phys. Lett. 79, 3627–3629 (2001).
[Crossref]

K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, “Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal,” Appl. Phys. Lett. 75, 932–934 (1999).
[Crossref]

Porte, H.

S. Khalfallah, P. Dubreuil, R. Legros, C. Fontaine, A. Munoz-Yagűe, B. Beche, H. Porte, R. Warno, and M. Karpierz, “Highly unbalanced GaAlAs-GaAs integrated Mach—Zehnder interferometer for coherence modulation at 1.3 µm,” Opt. Commun. 167, 67–79 (1999).
[Crossref]

Rattier, M.

Saski,

M. Koshiba, Y. Tsuji, and Saski, “High-performance absorbing boundary conditions for photonic crystal waveguide simulations,” IEEE Microwave Wireless Compon. Lett. 11, 152–154 (2001).
[Crossref]

Shih, M. H.

M. H. Shih, W. J. Kim, W. Kuang, J. R. Cao, H. Yukawa, S. J. Choi, J. D. O’Brien, P. D. Dapkus, and W. K. Marshall, “Two-dimensional photonic crystal Mach–Zehnder interferometers,” Appl. Phys. Lett. 84, 460–462 (2004).
[Crossref]

Shimoda, Y.

Y. Shimoda, M. Ozaki, and K. Yoshino, “Electric field tuning of a stop band in a reflection spectrum of synthetic opal infiltrated with nematic liquid crystal,” Appl. Phys. Lett. 79, 3627–3629 (2001).
[Crossref]

K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, “Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal,” Appl. Phys. Lett. 75, 932–934 (1999).
[Crossref]

Smith, C. J. M.

Smith, D. A.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel application of photonic band gap materials: low-loss bends and high-Q cavities,” J. Appl. Phys. 75, 4753–4755 (1994).
[Crossref]

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]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite Difference Time Domain Method (Artech House, Boston, Mass., 1998).

Takeda, H.

H. Takeda and K. Yoshino, “Tunable light propagation in Y-shaped waveguides in two-dimensional photonic crystals utilizing liquid crystals as linear defects,” Phys. Rev. B 67, 073106 (2003).
[Crossref]

H. Takeda and K. Yoshino, “Tunable light propagation in Y-shaped waveguides in two-dimensional photonic crystals composed of semiconductors depending on temperature,” Opt. Commun. 219, 177–182 (2003).
[Crossref]

H. Takeda and K. Yoshino, “Electric field tuning of a stop band in a reflection spectrum of synthetic opal infiltrated with nematic liquid crystal,” J. Appl. Phys. 92, 5958–5662 (2002).

Tanaka, 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]

Tsuji, Y.

M. Koshiba, Y. Tsuji, and Saski, “High-performance absorbing boundary conditions for photonic crystal waveguide simulations,” IEEE Microwave Wireless Compon. Lett. 11, 152–154 (2001).
[Crossref]

Warno, R.

S. Khalfallah, P. Dubreuil, R. Legros, C. Fontaine, A. Munoz-Yagűe, B. Beche, H. Porte, R. Warno, and M. Karpierz, “Highly unbalanced GaAlAs-GaAs integrated Mach—Zehnder interferometer for coherence modulation at 1.3 µm,” Opt. Commun. 167, 67–79 (1999).
[Crossref]

Watanabe, 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]

Weisbuch, C.

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N. J., 1995).

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[Crossref]

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

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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]

Yonekura, J.

T. Baba, N. Fukaya, and J. Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electron. Lett. 35, 654–656 (1999).
[Crossref]

Yoshino, K.

H. Takeda and K. Yoshino, “Tunable light propagation in Y-shaped waveguides in two-dimensional photonic crystals composed of semiconductors depending on temperature,” Opt. Commun. 219, 177–182 (2003).
[Crossref]

H. Takeda and K. Yoshino, “Tunable light propagation in Y-shaped waveguides in two-dimensional photonic crystals utilizing liquid crystals as linear defects,” Phys. Rev. B 67, 073106 (2003).
[Crossref]

H. Takeda and K. Yoshino, “Electric field tuning of a stop band in a reflection spectrum of synthetic opal infiltrated with nematic liquid crystal,” J. Appl. Phys. 92, 5958–5662 (2002).

Y. Shimoda, M. Ozaki, and K. Yoshino, “Electric field tuning of a stop band in a reflection spectrum of synthetic opal infiltrated with nematic liquid crystal,” Appl. Phys. Lett. 79, 3627–3629 (2001).
[Crossref]

K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, “Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal,” Appl. Phys. Lett. 75, 932–934 (1999).
[Crossref]

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M. H. Shih, W. J. Kim, W. Kuang, J. R. Cao, H. Yukawa, S. J. Choi, J. D. O’Brien, P. D. Dapkus, and W. K. Marshall, “Two-dimensional photonic crystal Mach–Zehnder interferometers,” Appl. Phys. Lett. 84, 460–462 (2004).
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Zakharov, A. V.

A. V. Zakharov and L. V. Mirantsev, “Dynamic and dielectric properties of liquid crystals,” Phys. Solid State 45, 183–188 (2003).
[Crossref]

Appl. Phys. Lett. (4)

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]

K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, “Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal,” Appl. Phys. Lett. 75, 932–934 (1999).
[Crossref]

M. H. Shih, W. J. Kim, W. Kuang, J. R. Cao, H. Yukawa, S. J. Choi, J. D. O’Brien, P. D. Dapkus, and W. K. Marshall, “Two-dimensional photonic crystal Mach–Zehnder interferometers,” Appl. Phys. Lett. 84, 460–462 (2004).
[Crossref]

Y. Shimoda, M. Ozaki, and K. Yoshino, “Electric field tuning of a stop band in a reflection spectrum of synthetic opal infiltrated with nematic liquid crystal,” Appl. Phys. Lett. 79, 3627–3629 (2001).
[Crossref]

Electron. Lett. (1)

T. Baba, N. Fukaya, and J. Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electron. Lett. 35, 654–656 (1999).
[Crossref]

IEEE Microwave Wireless Compon. Lett. (1)

M. Koshiba, Y. Tsuji, and Saski, “High-performance absorbing boundary conditions for photonic crystal waveguide simulations,” IEEE Microwave Wireless Compon. Lett. 11, 152–154 (2001).
[Crossref]

J. Appl. Phys. (3)

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]

H. Takeda and K. Yoshino, “Electric field tuning of a stop band in a reflection spectrum of synthetic opal infiltrated with nematic liquid crystal,” J. Appl. Phys. 92, 5958–5662 (2002).

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel application of photonic band gap materials: low-loss bends and high-Q cavities,” J. Appl. Phys. 75, 4753–4755 (1994).
[Crossref]

J. Lightwave Technol. (1)

Opt. Commun. (3)

H. Takeda and K. Yoshino, “Tunable light propagation in Y-shaped waveguides in two-dimensional photonic crystals composed of semiconductors depending on temperature,” Opt. Commun. 219, 177–182 (2003).
[Crossref]

E. Centeno and D. Felbacq, “Guiding waves with photonic crystals,” Opt. Commun. 160, 57–60 (1999).
[Crossref]

S. Khalfallah, P. Dubreuil, R. Legros, C. Fontaine, A. Munoz-Yagűe, B. Beche, H. Porte, R. Warno, and M. Karpierz, “Highly unbalanced GaAlAs-GaAs integrated Mach—Zehnder interferometer for coherence modulation at 1.3 µm,” Opt. Commun. 167, 67–79 (1999).
[Crossref]

Phys. Rev. B (1)

H. Takeda and K. Yoshino, “Tunable light propagation in Y-shaped waveguides in two-dimensional photonic crystals utilizing liquid crystals as linear defects,” Phys. Rev. B 67, 073106 (2003).
[Crossref]

Phys. Rev. Lett. (1)

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

Phys. Solid State (1)

A. V. Zakharov and L. V. Mirantsev, “Dynamic and dielectric properties of liquid crystals,” Phys. Solid State 45, 183–188 (2003).
[Crossref]

Other (3)

I.-C. Khoo and S.-T. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, Singapore, 1993).
[Crossref]

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite Difference Time Domain Method (Artech House, Boston, Mass., 1998).

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N. J., 1995).

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Figures (9)

Fig. 1.
Fig. 1.

Photonic band structure for the triangular array of dielectric columns. Inset, the Brillouin zone.

Fig. 2.
Fig. 2.

PC waveguide Mach–Zehnder interferometer with path-length differences of (a) 0 and (b) 4a. Inset, lattice constant a and radius of rods r.

Fig. 3.
Fig. 3.

Electric field patterns observed in the frequency domain of the PC waveguide Mach–Zehnder interferometer with path-length differences of (a) 0 and (b) 4a.

Fig. 4.
Fig. 4.

PC waveguide Mach–Zehnder interferometer with LCs. Shaded regions, parts infiltrated with LC waveguides. Diagram at lower left, director of a LC.

Fig. 5.
Fig. 5.

Dispersion relations of guided modes in the PC waveguide with a nematic LC at ϕ=0°, 45°, 90°. Shaded regions, projected band structures of the perfect crystals.

Fig. 6.
Fig. 6.

The refractive index profile of cross-section AA of Fig. 4 with phases (a) ϕ 1=0 °, ϕ 2=0 ° and (b) ϕ 1=0 °, ϕ 2=90 °.

Fig. 7.
Fig. 7.

Transmission spectrum for the structure in Fig. 4 with input wavelength λ=1.42 µm and variable rotation angle ϕ 2.

Fig. 8.
Fig. 8.

Calculated rotation angle ϕ as a function of normalized voltage. V th is the threshold voltage.

Fig. 9.
Fig. 9.

Electric field patterns observed in the frequency domain of the tunable PC waveguide Mach–Zehnder interferometer with LCs at ϕ 2=0 °, ±45 °, ±90 °.

Equations (5)

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

× [ 1 ε ( r ) × H ( r ) ] = ( ω c ) 2 H ( r ) ,
ε xx ( r ) = ε o ( r ) sin 2 ϕ + ε e ( r ) cos 2 ϕ ,
ε zz ( r ) = ε o ( r ) cos 2 ϕ + ε e ( r ) sin 2 ϕ ,
ε xz ( r ) = ε zx ( r ) = [ ε e ( r ) ε o ( r ) ] cos ϕ sin ϕ ,
ϕ d = 2 π λ [ n e ( ϕ 2 ) n e ( ϕ 1 ) ] L LC ,

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