Abstract

We demonstrate highly tunable one-dimensional photonic band structures under normal incidence. The system consists of a multilayer film that alternates two anisotropic layers. The band-structure characteristics of this multilayer stack, such as location and width of stop bands, can be tailored by altering the relative orientation of the optical axes of the adjacent layers. This structure can be realized by employing liquid crystals and transparent electrodes. In some cases, we observe the ability of this structure to distinguish between different linear polarizations. We propose a depolarizing and filtering device based on this multilayer medium.

© 2006 Optical Society of America

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  1. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals, Molding the Flow of Light (Princeton U. Press, 1995).
  2. K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, 2001).
  3. M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696-10705 (2000).
    [CrossRef]
  4. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
    [CrossRef]
  5. C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104(R) (2002).
    [CrossRef]
  6. K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of photonic gaps in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
    [CrossRef] [PubMed]
  7. E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
    [CrossRef] [PubMed]
  8. 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]
  9. S. Noda, A. Chutinan, and I. Imada, "Trapping and emission of photons by a simple defect in a photonic bandgap structure," Nature 407, 608-610 (2000).
    [CrossRef] [PubMed]
  10. V. Lousse and J. P. Vigneron, "Use of Fano resonances for bistable optical transfer through photonic crystal films," Phys. Rev. B 69, 155106 (2004).
    [CrossRef]
  11. P. Yeh, Optical Waves in Layered Media, 2nd ed. (Wiley, 2005).
  12. A. Dereux, J. P. Vigneron, P. Lambin, and A. A. Lucas, "Polaritons in semiconductor multilayered materials," Phys. Rev. B 38, 5438-5452 (1988).
    [CrossRef]
  13. Z.-Y. Li, J. Wang, and B.-Y. Gu, "Creation of partial band gaps in anisotropic photonic-band-gap structures," Phys. Rev. B 58, 3721-3729 (1998).
    [CrossRef]
  14. Z.-Y. Li, B.-Y. Gu, and G.-Z. Yang, "Large absolute band gap in 2D anisotropic photonic crystals," Phys. Rev. Lett. 81, 2574-2577 (1998).
    [CrossRef]
  15. K. Busch and S. John, "Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum," Phys. Rev. Lett. 83, 967-970 (1999).
    [CrossRef]
  16. Y. K. Ha, Y. C. Yang, J. E. Kim, H. Y. Park, C. S. Kee, H. Lin, and J. C. Lee, "Tunable omnidirectional reflection bands and defect modes of a one-dimensional photonic band structure with liquid crystals," Appl. Phys. Lett. 79, 15-17 (2001).
    [CrossRef]
  17. A. Mandatori, C. Sibilia, M. Centini, G. D'Aguanno, M. Bertolotti, M. Scalora, M. Bloemer, and C. M. Bowden, "Birefringence in one-dimensional finite photonic bandgap structure," J. Opt. Soc. Am. B 20, 504-512 (2003).
    [CrossRef]
  18. A. Figotin and I. Vitebskiy, "Oblique frozen modes in periodic layered media," Phys. Rev. E 68, 036609 (2003).
    [CrossRef]
  19. J. Ballato, A. Ballato, A. Figotin, and I. Vitebskiy, "Frozen light in periodic stacks of anisotropic layers," Phys. Rev. E 71, 036612 (2005).
    [CrossRef]
  20. G. Alagappan, X. W. Sun, P. Shum, M. B. Yu, and M. T. Doan, "One-dimensional anisotropic photonic crystal with a tunable bandgap," J. Opt. Soc. Am. B 23, 159-167 (2006).
    [CrossRef]
  21. P. Yeh, "Electromagnetic propagation in birefringent layered media," J. Opt. Soc. Am. 69, 742-756 (1979).
    [CrossRef]
  22. I. Solc, "A new kind of double refracting filter," Czech. J. Phys. Sect. A 4, 53-66 (1954).
  23. I. Solc, "Birefringent chain filters," J. Opt. Soc. Am. 55, 621-625 (1965).
    [CrossRef]
  24. E. Cojocaru, "Birefringence dispersion in Solc-type anisotropic periodic bandgap structures," Appl. Opt. 40, 1089-1097 (2001).
    [CrossRef]
  25. I. Abdulhalim, "Omnidirectional reflection from anisotropic periodic dielectric stack," Opt. Commun. 174, 43-50 (2000).
    [CrossRef]
  26. H. J. Deuling, "Elasticity of nematic liquid crystals," in Liquid Crystals (Solid State Physics, Supplement 14), L.Liebert, ed. (Academic, 1978), pp. 77-107.
  27. L. M. Blinov and V. G. Chigrinov, Electro-Optics Effects in Liquid Crystal Materials (Springer, 1994).
    [CrossRef]

2006 (1)

2005 (1)

J. Ballato, A. Ballato, A. Figotin, and I. Vitebskiy, "Frozen light in periodic stacks of anisotropic layers," Phys. Rev. E 71, 036612 (2005).
[CrossRef]

2004 (1)

V. Lousse and J. P. Vigneron, "Use of Fano resonances for bistable optical transfer through photonic crystal films," Phys. Rev. B 69, 155106 (2004).
[CrossRef]

2003 (2)

2002 (1)

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104(R) (2002).
[CrossRef]

2001 (2)

Y. K. Ha, Y. C. Yang, J. E. Kim, H. Y. Park, C. S. Kee, H. Lin, and J. C. Lee, "Tunable omnidirectional reflection bands and defect modes of a one-dimensional photonic band structure with liquid crystals," Appl. Phys. Lett. 79, 15-17 (2001).
[CrossRef]

E. Cojocaru, "Birefringence dispersion in Solc-type anisotropic periodic bandgap structures," Appl. Opt. 40, 1089-1097 (2001).
[CrossRef]

2000 (3)

I. Abdulhalim, "Omnidirectional reflection from anisotropic periodic dielectric stack," Opt. Commun. 174, 43-50 (2000).
[CrossRef]

M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696-10705 (2000).
[CrossRef]

S. Noda, A. Chutinan, and I. Imada, "Trapping and emission of photons by a simple defect in a photonic bandgap structure," Nature 407, 608-610 (2000).
[CrossRef] [PubMed]

1999 (1)

K. Busch and S. John, "Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum," Phys. Rev. Lett. 83, 967-970 (1999).
[CrossRef]

1998 (4)

Z.-Y. Li, J. Wang, and B.-Y. Gu, "Creation of partial band gaps in anisotropic photonic-band-gap structures," Phys. Rev. B 58, 3721-3729 (1998).
[CrossRef]

Z.-Y. Li, B.-Y. Gu, and G.-Z. Yang, "Large absolute band gap in 2D anisotropic photonic crystals," Phys. Rev. Lett. 81, 2574-2577 (1998).
[CrossRef]

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]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

1990 (1)

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of photonic gaps in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

1988 (1)

A. Dereux, J. P. Vigneron, P. Lambin, and A. A. Lucas, "Polaritons in semiconductor multilayered materials," Phys. Rev. B 38, 5438-5452 (1988).
[CrossRef]

1987 (1)

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

1979 (1)

1965 (1)

1954 (1)

I. Solc, "A new kind of double refracting filter," Czech. J. Phys. Sect. A 4, 53-66 (1954).

Abdulhalim, I.

I. Abdulhalim, "Omnidirectional reflection from anisotropic periodic dielectric stack," Opt. Commun. 174, 43-50 (2000).
[CrossRef]

Alagappan, G.

Ballato, A.

J. Ballato, A. Ballato, A. Figotin, and I. Vitebskiy, "Frozen light in periodic stacks of anisotropic layers," Phys. Rev. E 71, 036612 (2005).
[CrossRef]

Ballato, J.

J. Ballato, A. Ballato, A. Figotin, and I. Vitebskiy, "Frozen light in periodic stacks of anisotropic layers," Phys. Rev. E 71, 036612 (2005).
[CrossRef]

Bertolotti, M.

Blinov, L. M.

L. M. Blinov and V. G. Chigrinov, Electro-Optics Effects in Liquid Crystal Materials (Springer, 1994).
[CrossRef]

Bloemer, M.

Bowden, C. M.

Busch, K.

K. Busch and S. John, "Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum," Phys. Rev. Lett. 83, 967-970 (1999).
[CrossRef]

Centini, M.

Chan, C. T.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of photonic gaps in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Chigrinov, V. G.

L. M. Blinov and V. G. Chigrinov, Electro-Optics Effects in Liquid Crystal Materials (Springer, 1994).
[CrossRef]

Chutinan, A.

S. Noda, A. Chutinan, and I. Imada, "Trapping and emission of photons by a simple defect in a photonic bandgap structure," Nature 407, 608-610 (2000).
[CrossRef] [PubMed]

Cojocaru, E.

D'Aguanno, G.

Dereux, A.

A. Dereux, J. P. Vigneron, P. Lambin, and A. A. Lucas, "Polaritons in semiconductor multilayered materials," Phys. Rev. B 38, 5438-5452 (1988).
[CrossRef]

Deuling, H. J.

H. J. Deuling, "Elasticity of nematic liquid crystals," in Liquid Crystals (Solid State Physics, Supplement 14), L.Liebert, ed. (Academic, 1978), pp. 77-107.

Doan, M. T.

Fan, S.

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]

Figotin, A.

J. Ballato, A. Ballato, A. Figotin, and I. Vitebskiy, "Frozen light in periodic stacks of anisotropic layers," Phys. Rev. E 71, 036612 (2005).
[CrossRef]

A. Figotin and I. Vitebskiy, "Oblique frozen modes in periodic layered media," Phys. Rev. E 68, 036609 (2003).
[CrossRef]

Gu, B.-Y.

Z.-Y. Li, B.-Y. Gu, and G.-Z. Yang, "Large absolute band gap in 2D anisotropic photonic crystals," Phys. Rev. Lett. 81, 2574-2577 (1998).
[CrossRef]

Z.-Y. Li, J. Wang, and B.-Y. Gu, "Creation of partial band gaps in anisotropic photonic-band-gap structures," Phys. Rev. B 58, 3721-3729 (1998).
[CrossRef]

Ha, Y. K.

Y. K. Ha, Y. C. Yang, J. E. Kim, H. Y. Park, C. S. Kee, H. Lin, and J. C. Lee, "Tunable omnidirectional reflection bands and defect modes of a one-dimensional photonic band structure with liquid crystals," Appl. Phys. Lett. 79, 15-17 (2001).
[CrossRef]

Haus, H. A.

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]

Ho, K. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of photonic gaps in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Imada, I.

S. Noda, A. Chutinan, and I. Imada, "Trapping and emission of photons by a simple defect in a photonic bandgap structure," Nature 407, 608-610 (2000).
[CrossRef] [PubMed]

Joannopoulos, J. D.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104(R) (2002).
[CrossRef]

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]

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

John, S.

K. Busch and S. John, "Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum," Phys. Rev. Lett. 83, 967-970 (1999).
[CrossRef]

Johnson, S. G.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104(R) (2002).
[CrossRef]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Kee, C. S.

Y. K. Ha, Y. C. Yang, J. E. Kim, H. Y. Park, C. S. Kee, H. Lin, and J. C. Lee, "Tunable omnidirectional reflection bands and defect modes of a one-dimensional photonic band structure with liquid crystals," Appl. Phys. Lett. 79, 15-17 (2001).
[CrossRef]

Kim, J. E.

Y. K. Ha, Y. C. Yang, J. E. Kim, H. Y. Park, C. S. Kee, H. Lin, and J. C. Lee, "Tunable omnidirectional reflection bands and defect modes of a one-dimensional photonic band structure with liquid crystals," Appl. Phys. Lett. 79, 15-17 (2001).
[CrossRef]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Lambin, P.

A. Dereux, J. P. Vigneron, P. Lambin, and A. A. Lucas, "Polaritons in semiconductor multilayered materials," Phys. Rev. B 38, 5438-5452 (1988).
[CrossRef]

Lee, J. C.

Y. K. Ha, Y. C. Yang, J. E. Kim, H. Y. Park, C. S. Kee, H. Lin, and J. C. Lee, "Tunable omnidirectional reflection bands and defect modes of a one-dimensional photonic band structure with liquid crystals," Appl. Phys. Lett. 79, 15-17 (2001).
[CrossRef]

Li, Z.-Y.

Z.-Y. Li, J. Wang, and B.-Y. Gu, "Creation of partial band gaps in anisotropic photonic-band-gap structures," Phys. Rev. B 58, 3721-3729 (1998).
[CrossRef]

Z.-Y. Li, B.-Y. Gu, and G.-Z. Yang, "Large absolute band gap in 2D anisotropic photonic crystals," Phys. Rev. Lett. 81, 2574-2577 (1998).
[CrossRef]

Lin, H.

Y. K. Ha, Y. C. Yang, J. E. Kim, H. Y. Park, C. S. Kee, H. Lin, and J. C. Lee, "Tunable omnidirectional reflection bands and defect modes of a one-dimensional photonic band structure with liquid crystals," Appl. Phys. Lett. 79, 15-17 (2001).
[CrossRef]

Lousse, V.

V. Lousse and J. P. Vigneron, "Use of Fano resonances for bistable optical transfer through photonic crystal films," Phys. Rev. B 69, 155106 (2004).
[CrossRef]

Lucas, A. A.

A. Dereux, J. P. Vigneron, P. Lambin, and A. A. Lucas, "Polaritons in semiconductor multilayered materials," Phys. Rev. B 38, 5438-5452 (1988).
[CrossRef]

Luo, C.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104(R) (2002).
[CrossRef]

Mandatori, A.

Meade, R. D.

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

Noda, S.

S. Noda, A. Chutinan, and I. Imada, "Trapping and emission of photons by a simple defect in a photonic bandgap structure," Nature 407, 608-610 (2000).
[CrossRef] [PubMed]

Notomi, M.

M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696-10705 (2000).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Park, H. Y.

Y. K. Ha, Y. C. Yang, J. E. Kim, H. Y. Park, C. S. Kee, H. Lin, and J. C. Lee, "Tunable omnidirectional reflection bands and defect modes of a one-dimensional photonic band structure with liquid crystals," Appl. Phys. Lett. 79, 15-17 (2001).
[CrossRef]

Pendry, J. B.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104(R) (2002).
[CrossRef]

Sakoda, K.

K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, 2001).

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Scalora, M.

Shum, P.

Sibilia, C.

Solc, I.

I. Solc, "Birefringent chain filters," J. Opt. Soc. Am. 55, 621-625 (1965).
[CrossRef]

I. Solc, "A new kind of double refracting filter," Czech. J. Phys. Sect. A 4, 53-66 (1954).

Soukoulis, C. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of photonic gaps in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Sun, X. W.

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Vigneron, J. P.

V. Lousse and J. P. Vigneron, "Use of Fano resonances for bistable optical transfer through photonic crystal films," Phys. Rev. B 69, 155106 (2004).
[CrossRef]

A. Dereux, J. P. Vigneron, P. Lambin, and A. A. Lucas, "Polaritons in semiconductor multilayered materials," Phys. Rev. B 38, 5438-5452 (1988).
[CrossRef]

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]

Vitebskiy, I.

J. Ballato, A. Ballato, A. Figotin, and I. Vitebskiy, "Frozen light in periodic stacks of anisotropic layers," Phys. Rev. E 71, 036612 (2005).
[CrossRef]

A. Figotin and I. Vitebskiy, "Oblique frozen modes in periodic layered media," Phys. Rev. E 68, 036609 (2003).
[CrossRef]

Wang, J.

Z.-Y. Li, J. Wang, and B.-Y. Gu, "Creation of partial band gaps in anisotropic photonic-band-gap structures," Phys. Rev. B 58, 3721-3729 (1998).
[CrossRef]

Winn, J. N.

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

Yablonovitch, E.

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

Yang, G.-Z.

Z.-Y. Li, B.-Y. Gu, and G.-Z. Yang, "Large absolute band gap in 2D anisotropic photonic crystals," Phys. Rev. Lett. 81, 2574-2577 (1998).
[CrossRef]

Yang, Y. C.

Y. K. Ha, Y. C. Yang, J. E. Kim, H. Y. Park, C. S. Kee, H. Lin, and J. C. Lee, "Tunable omnidirectional reflection bands and defect modes of a one-dimensional photonic band structure with liquid crystals," Appl. Phys. Lett. 79, 15-17 (2001).
[CrossRef]

Yeh, P.

Yu, M. B.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

Y. K. Ha, Y. C. Yang, J. E. Kim, H. Y. Park, C. S. Kee, H. Lin, and J. C. Lee, "Tunable omnidirectional reflection bands and defect modes of a one-dimensional photonic band structure with liquid crystals," Appl. Phys. Lett. 79, 15-17 (2001).
[CrossRef]

Czech. J. Phys. Sect. A (1)

I. Solc, "A new kind of double refracting filter," Czech. J. Phys. Sect. A 4, 53-66 (1954).

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. B (2)

Nature (1)

S. Noda, A. Chutinan, and I. Imada, "Trapping and emission of photons by a simple defect in a photonic bandgap structure," Nature 407, 608-610 (2000).
[CrossRef] [PubMed]

Opt. Commun. (1)

I. Abdulhalim, "Omnidirectional reflection from anisotropic periodic dielectric stack," Opt. Commun. 174, 43-50 (2000).
[CrossRef]

Phys. Rev. B (6)

A. Dereux, J. P. Vigneron, P. Lambin, and A. A. Lucas, "Polaritons in semiconductor multilayered materials," Phys. Rev. B 38, 5438-5452 (1988).
[CrossRef]

Z.-Y. Li, J. Wang, and B.-Y. Gu, "Creation of partial band gaps in anisotropic photonic-band-gap structures," Phys. Rev. B 58, 3721-3729 (1998).
[CrossRef]

V. Lousse and J. P. Vigneron, "Use of Fano resonances for bistable optical transfer through photonic crystal films," Phys. Rev. B 69, 155106 (2004).
[CrossRef]

M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696-10705 (2000).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104(R) (2002).
[CrossRef]

Phys. Rev. E (2)

A. Figotin and I. Vitebskiy, "Oblique frozen modes in periodic layered media," Phys. Rev. E 68, 036609 (2003).
[CrossRef]

J. Ballato, A. Ballato, A. Figotin, and I. Vitebskiy, "Frozen light in periodic stacks of anisotropic layers," Phys. Rev. E 71, 036612 (2005).
[CrossRef]

Phys. Rev. Lett. (5)

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of photonic gaps in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

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

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]

Z.-Y. Li, B.-Y. Gu, and G.-Z. Yang, "Large absolute band gap in 2D anisotropic photonic crystals," Phys. Rev. Lett. 81, 2574-2577 (1998).
[CrossRef]

K. Busch and S. John, "Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum," Phys. Rev. Lett. 83, 967-970 (1999).
[CrossRef]

Other (5)

H. J. Deuling, "Elasticity of nematic liquid crystals," in Liquid Crystals (Solid State Physics, Supplement 14), L.Liebert, ed. (Academic, 1978), pp. 77-107.

L. M. Blinov and V. G. Chigrinov, Electro-Optics Effects in Liquid Crystal Materials (Springer, 1994).
[CrossRef]

P. Yeh, Optical Waves in Layered Media, 2nd ed. (Wiley, 2005).

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

K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, 2001).

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Figures (13)

Fig. 1
Fig. 1

Photonic crystal under study. The period a is composed of two slabs made of different anisotropic materials. The first layer is a uniaxial material with a fixed optical axis, while the other layer has a dielectric response corresponding to a uniaxial material with a mobile axis. The periodicity axis is the Z axis. The thickness of each layer is d = a 2 .

Fig. 2
Fig. 2

Two optical axes (O.A.), in the X Y plane, are shown by dashed lines. The indices 1 and 2 refer to the two layers. O . A . 2 can be rotated around the Z axis. Its angle with the Z axis is denoted as α. The O . A . 1 axis is fixed and parallel to the X direction.

Fig. 3
Fig. 3

Band structure (left) and reflection coefficients R (middle and right) of a uniaxial 1D photonic crystal. R x . ( R x x or R x y ) and R y . ( R y x or R y y ) indicate reflection coefficients for an incident electric field parallel to the X and Y axes, respectively. Calculation is developed for a superposition of layers with dielectric tensors [ ϵ 1 ] and [ ϵ 2 ] [Eqs. (14, 15)]. For the sake of clarity, the retained values for ϵ and ϵ are 13.00 and 2.25, respectively. The angle α is the angle between the optical axis of the second layer and the X axis. It is here equal to zero ( α = 0 ) . The thickness of the two layers is d = a 2 , where a is the period. Reflectance spectra are determined for multilayer stacks made with five periods. For the reflectance spectra, the first layer of the period is layer 2.

Fig. 4
Fig. 4

Same as Fig. 3 but α = 30 ° . The curve with the solid circles represents the proportion of reflected energy that undergoes a change of polarization.

Fig. 5
Fig. 5

Same as Fig. 3 but α = 60 ° . The curve with the solid circles represents the proportion of reflected energy that undergoes a change of polarization.

Fig. 6
Fig. 6

Same as Fig. 3 but α = 90 ° .

Fig. 7
Fig. 7

Gap to midgap frequency ratio ( Δ ω ω 0 ) of the first gap modification with the external voltage normalized to the critical voltage ( V V c ) in the case of a multilayer stack made of LC 5CB.

Fig. 8
Fig. 8

Dependence of the reflection coefficients R x x (top), R x y (middle), and R y y (bottom) with the applied voltage. The multilayer stack is made of LC 5 CB . The solid curve, the curve with triangles, and the curve with circles are calculated for a ratio V V c equal to 1.000, 1.277, and 4.040, respectively. Reflectance spectra are determined for multilayer stacks made with five periods.

Fig. 9
Fig. 9

Optical axes (O.A.) of the two layers are in the Y Z plane. They are shown by dashed lines. The indices 1 and 2 refer to the two layers. O . A . 1 is fixed along the Z direction. O . A . 2 can be rotated around the X axis, and its angle with O . A . 1 is denoted as α.

Fig. 10
Fig. 10

Band structure (left) and reflection coefficients R (middle and right) of a uniaxial 1D photonic crystal. R x . , and R y . , indicate the reflection coefficient for an incident electric field parallel to the X and Y axes, respectively Calculation is developed for a superposition of layers with dielectric tensors [ ϵ 1 ] and [ ϵ 2 ] [Eqs. (17, 18)]. For the sake of clarity, the retained values for ϵ and ϵ are 13.00 and 2.25, respectively. The angle α is the angle between the optical axis of the second layer and the Z axis is equal to zero ( α = 0 ) . The thickness of the two layers is d = a 2 , where a is the period. Reflectance spectra are determined for multilayer stacks made with five periods. For the reflectance spectra, the first layer of the period is layer 2.

Fig. 11
Fig. 11

Same as Fig.10 but α = 30 ° .

Fig. 12
Fig. 12

Same as Fig.10 but α = 60 ° .

Fig. 13
Fig. 13

Same as Fig.10 but α = 90 ° .

Equations (19)

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( ω c ) 2 ϵ x x γ 2 ( ω c ) 2 ϵ x y ( ω c ) 2 ϵ x z ( ω c ) 2 ϵ y x ( ω c ) 2 ϵ y y γ 2 ( ω c ) 2 ϵ y z ( ω c ) 2 ϵ z x ( ω c ) 2 ϵ z y ( ω c ) 2 ϵ z z = 0 .
k × ( k × E ) + ( ω c ) 2 [ ϵ ] E = 0 .
E ( j ) = σ = 1 4 A σ ( j ) p σ ( j ) e i [ γ σ ( j ) ( z z j ) ω t ] ,
p σ = N σ ( ( ω c ) 2 ϵ z z [ ( ω c ) 2 ϵ y y γ σ 2 ] ( ω c ) 4 ϵ y z 2 ( ω c ) 4 ϵ y z ϵ x z ( ω c ) 4 ϵ x y ϵ z z ( ω c ) 4 ϵ x y ϵ y z ( ω c ) 2 ϵ x z [ ( ω c ) 2 ϵ y y γ σ 2 ] ) .
H ( j ) = σ = 1 4 A σ ( j ) q σ ( j ) e i [ γ σ ( j ) ( z z j ) ω t ] ,
q σ ( j ) = γ σ μ 0 ω e z × p σ ( j ) .
D ( n ) = ( e x p 1 ( n ) e x p 2 ( n ) e x p 3 ( n ) e x p 4 ( n ) e y q 1 ( n ) e y q 2 ( n ) e y q 3 ( n ) e y q 4 ( n ) e y p 1 ( n ) e y p 2 ( n ) e y p 3 ( n ) e y p 4 ( n ) e x q 1 ( n ) e x q 2 ( n ) e x q 3 ( n ) e x q 4 ( n ) ) ,
P ( n ) = [ exp [ i γ 1 ( n ) d n ] 0 0 0 0 exp [ i γ 2 ( n ) d n ] 0 0 0 0 exp [ i γ 3 ( n ) d n ] 0 0 0 0 exp [ i γ 4 ( n ) d n ] ] .
T p A ( n ) = e i k z a A ( n ) ,
R x x = T ( 2 , 1 ) T ( 3 , 3 ) T ( 2 , 3 ) T ( 3 , 1 ) T ( 1 , 1 ) T ( 3 , 3 ) T ( 1 , 3 ) T ( 3 , 1 ) 2 ,
R x y = T ( 4 , 1 ) T ( 3 , 3 ) T ( 4 , 3 ) T ( 3 , 1 ) T ( 1 , 1 ) T ( 3 , 3 ) T ( 1 , 3 ) T ( 3 , 1 ) 2 ,
R y x = T ( 1 , 1 ) T ( 2 , 3 ) T ( 2 , 1 ) T ( 1 , 3 ) T ( 1 , 1 ) T ( 3 , 3 ) T ( 1 , 3 ) T ( 3 , 1 ) 2 ,
R y y = T ( 1 , 1 ) T ( 4 , 3 ) T ( 4 , 1 ) T ( 1 , 3 ) T ( 1 , 1 ) T ( 3 , 3 ) T ( 1 , 3 ) T ( 3 , 1 ) 2 .
[ ϵ 1 ] = ( ϵ 0 0 0 ϵ 0 0 0 ϵ ) .
[ ϵ 2 ] = ( ϵ cos 2 α + ϵ sin 2 α ( ϵ ϵ ) cos α sin α 0 ( ϵ ϵ ) cos α sin α ϵ cos 2 α + ϵ sin 2 α 0 0 0 ϵ ) .
V V c = 2 π 0 π 2 1 + γ sin 2 α 1 + γ sin 2 α sin 2 ψ 1 + κ sin 2 α sin 2 ψ 1 sin 2 α sin 2 ψ d ψ ,
[ ϵ 1 ] = ( ϵ 0 0 0 ϵ 0 0 0 ϵ ) ,
[ ϵ 2 ] = ( ϵ 0 0 0 ϵ cos 2 α + ϵ sin 2 α ( ϵ ϵ ) cos α sin α 0 ( ϵ ϵ ) cos α sin α ϵ cos 2 α + ϵ sin 2 α ) .
ϵ eo = 1 ( cos 2 α ϵ ) + ( sin 2 α ϵ ) .

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