Abstract

Abstract: The photonic band structure and transmission properties of a cholesteric blue phase II liquid crystal, which is elongated in the [100] direction by electrostriction, are analyzed by finite-difference time-domain method. The simple cubic lattice deforms into a tetragonal lattice under the influence of an electric field, resulting in a change of the photonic band structure. Moreover, we show that the circular polarization dependence of the transmittance spectrum changes in an electric field, a behavior that has yet to be observed in experiment.

© 2014 Optical Society of America

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  1. D. L. Johnson, J. H. Flack, P. P. Crooker, “Structure and properties of the cholesteric blue phases,” Phys. Rev. Lett. 45(8), 641–644 (1980).
    [CrossRef]
  2. D. C. Wright, N. D. Mermin, “Crystalline liquids the blue phases,” Rev. Mod. Phys. 61(2), 385–432 (1989).
    [CrossRef]
  3. Y. Hisakado, H. Kikuchi, T. Nagamura, T. Kajiyama, “Large electro-optic Kerr effect in polymer-stabilized liquid-crystalline blue phases,” Adv. Mater. 17(1), 96–98 (2005).
    [CrossRef]
  4. H. Kikuchi, M. Yokota, Y. Hisakado, H. Yang, T. Kajiyama, “Polymer-stabilized liquid crystal blue phases,” Nat. Mater. 1(1), 64–68 (2002).
    [CrossRef] [PubMed]
  5. J. Yan, L. Rao, M. Jiao, Y. Li, H. C. Cheng, S. T. Wu, “Polymer-stabilized optically isotropic liquid crystals for next-generation display and photonics applications,” J. Mater. Chem. 21(22), 7870–7877 (2011).
    [CrossRef]
  6. J. Yan, Z. Luo, S. T. Wu, J. W. Shiu, Y. C. Lai, K. L. Cheng, S. H. Liu, P. J. Hsieh, Y. C. Tsai, “Low voltage and high contrast blue phase liquid crystal with red-shifted Bragg reflection,” Appl. Phys. Lett. 102(1), 011113 (2013).
    [CrossRef]
  7. G. Heppke, B. Jérôme, H. S. Kitzerow, P. Pieranski, “Electrostriction of BPI and BPII for blue phase systems with negative dielectric anisotropy,” J. Phys. France 50(5), 549–562 (1989).
    [CrossRef]
  8. G. Heppke, B. Jérôme, H. S. Kitzerow, P. Pieranski, “Electrostriction of the cholesteric blue phases BPI and BPII in mixtures with positive dielectric anisotropy,” J. Phys. France 50(19), 2991–2998 (1989).
    [CrossRef]
  9. H. S. Kitzerow, “The effect of electric fields on blue phases,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 202(1), 51–83 (1991).
    [CrossRef]
  10. M. Ravnik, G. P. Alexander, J. M. Yeomans, S. Zumer, “Mesoscopic modelling of colloids in chiral nematics,” Faraday Discuss. 144, 159–169, discussion 203–222, 467–481 (2009).
    [CrossRef] [PubMed]
  11. M. Ravnik, G. P. Alexander, J. M. Yeomans, S. Žumer, “Three-dimensional colloidal crystals in liquid crystalline blue phases,” Proc. Natl. Acad. Sci. U.S.A. 108(13), 5188–5192 (2011).
    [CrossRef] [PubMed]
  12. R. M. Hornreich, S. Shtrikman, C. Sommers, “Photonic bands in simple and body-centered-cubic cholesteric blue phases,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 47(3), 2067–2072 (1993).
    [CrossRef] [PubMed]
  13. D. W. Berreman, “Optics in stratified and anisotropic media: 4 × 4-matrix formulation,” J. Opt. Soc. Am. 62(4), 502–510 (1972).
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    [CrossRef]
  15. Y. Ogawa, J. Fukuda, H. Yoshida, M. Ozaki, “Finite-difference time-domain analysis of cholesteric blue phase II using the Landau-de Gennes tensor order parameter model,” Opt. Lett. 38(17), 3380–3383 (2013).
    [CrossRef] [PubMed]
  16. J. Fukuda, M. Yoneya, H. Yokoyama, “Simulation of cholesteric blue phases using a Landau-de Gennes theory: effect of an applied electric field,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(3), 031706 (2009).
    [CrossRef] [PubMed]
  17. S. Urban, B. Gestblom, W. Kuczynski, S. Pawlus, A. Würflinger, “Nematic order parameter as determined from dielectric relaxation data and other methods,” Phys. Chem. Chem. Phys. 5(5), 924–928 (2003).
    [CrossRef]
  18. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
    [CrossRef]
  19. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
    [CrossRef]
  20. N. R. Chen, J. T. Ho, “Electric-field-induced phase diagrams of blue-phase systems,” Phys. Rev. A 35(11), 4886–4888 (1987).
    [CrossRef] [PubMed]
  21. P. Pieranski, P. E. Cladis, T. Garel, R. Barbetmassin, “Orientation of crystals of blue phases by electric fields,” J. Phys. 47(1), 139–143 (1986).
    [CrossRef]

2013 (2)

J. Yan, Z. Luo, S. T. Wu, J. W. Shiu, Y. C. Lai, K. L. Cheng, S. H. Liu, P. J. Hsieh, Y. C. Tsai, “Low voltage and high contrast blue phase liquid crystal with red-shifted Bragg reflection,” Appl. Phys. Lett. 102(1), 011113 (2013).
[CrossRef]

Y. Ogawa, J. Fukuda, H. Yoshida, M. Ozaki, “Finite-difference time-domain analysis of cholesteric blue phase II using the Landau-de Gennes tensor order parameter model,” Opt. Lett. 38(17), 3380–3383 (2013).
[CrossRef] [PubMed]

2011 (2)

M. Ravnik, G. P. Alexander, J. M. Yeomans, S. Žumer, “Three-dimensional colloidal crystals in liquid crystalline blue phases,” Proc. Natl. Acad. Sci. U.S.A. 108(13), 5188–5192 (2011).
[CrossRef] [PubMed]

J. Yan, L. Rao, M. Jiao, Y. Li, H. C. Cheng, S. T. Wu, “Polymer-stabilized optically isotropic liquid crystals for next-generation display and photonics applications,” J. Mater. Chem. 21(22), 7870–7877 (2011).
[CrossRef]

2010 (1)

M. Ojima, Y. Ogawa, R. Ozaki, H. Moritake, H. Yoshida, A. Fujii, M. Ozaki, “Finite-difference time-domain analysis of polarization dependent transmission in cholesteric blue phase II,” Appl. Phys. Express 3(3), 032001 (2010).
[CrossRef]

2009 (2)

M. Ravnik, G. P. Alexander, J. M. Yeomans, S. Zumer, “Mesoscopic modelling of colloids in chiral nematics,” Faraday Discuss. 144, 159–169, discussion 203–222, 467–481 (2009).
[CrossRef] [PubMed]

J. Fukuda, M. Yoneya, H. Yokoyama, “Simulation of cholesteric blue phases using a Landau-de Gennes theory: effect of an applied electric field,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(3), 031706 (2009).
[CrossRef] [PubMed]

2005 (1)

Y. Hisakado, H. Kikuchi, T. Nagamura, T. Kajiyama, “Large electro-optic Kerr effect in polymer-stabilized liquid-crystalline blue phases,” Adv. Mater. 17(1), 96–98 (2005).
[CrossRef]

2003 (1)

S. Urban, B. Gestblom, W. Kuczynski, S. Pawlus, A. Würflinger, “Nematic order parameter as determined from dielectric relaxation data and other methods,” Phys. Chem. Chem. Phys. 5(5), 924–928 (2003).
[CrossRef]

2002 (1)

H. Kikuchi, M. Yokota, Y. Hisakado, H. Yang, T. Kajiyama, “Polymer-stabilized liquid crystal blue phases,” Nat. Mater. 1(1), 64–68 (2002).
[CrossRef] [PubMed]

1994 (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[CrossRef]

1993 (1)

R. M. Hornreich, S. Shtrikman, C. Sommers, “Photonic bands in simple and body-centered-cubic cholesteric blue phases,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 47(3), 2067–2072 (1993).
[CrossRef] [PubMed]

1991 (1)

H. S. Kitzerow, “The effect of electric fields on blue phases,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 202(1), 51–83 (1991).
[CrossRef]

1989 (3)

G. Heppke, B. Jérôme, H. S. Kitzerow, P. Pieranski, “Electrostriction of BPI and BPII for blue phase systems with negative dielectric anisotropy,” J. Phys. France 50(5), 549–562 (1989).
[CrossRef]

G. Heppke, B. Jérôme, H. S. Kitzerow, P. Pieranski, “Electrostriction of the cholesteric blue phases BPI and BPII in mixtures with positive dielectric anisotropy,” J. Phys. France 50(19), 2991–2998 (1989).
[CrossRef]

D. C. Wright, N. D. Mermin, “Crystalline liquids the blue phases,” Rev. Mod. Phys. 61(2), 385–432 (1989).
[CrossRef]

1987 (1)

N. R. Chen, J. T. Ho, “Electric-field-induced phase diagrams of blue-phase systems,” Phys. Rev. A 35(11), 4886–4888 (1987).
[CrossRef] [PubMed]

1986 (1)

P. Pieranski, P. E. Cladis, T. Garel, R. Barbetmassin, “Orientation of crystals of blue phases by electric fields,” J. Phys. 47(1), 139–143 (1986).
[CrossRef]

1980 (1)

D. L. Johnson, J. H. Flack, P. P. Crooker, “Structure and properties of the cholesteric blue phases,” Phys. Rev. Lett. 45(8), 641–644 (1980).
[CrossRef]

1972 (1)

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[CrossRef]

Alexander, G. P.

M. Ravnik, G. P. Alexander, J. M. Yeomans, S. Žumer, “Three-dimensional colloidal crystals in liquid crystalline blue phases,” Proc. Natl. Acad. Sci. U.S.A. 108(13), 5188–5192 (2011).
[CrossRef] [PubMed]

M. Ravnik, G. P. Alexander, J. M. Yeomans, S. Zumer, “Mesoscopic modelling of colloids in chiral nematics,” Faraday Discuss. 144, 159–169, discussion 203–222, 467–481 (2009).
[CrossRef] [PubMed]

Barbetmassin, R.

P. Pieranski, P. E. Cladis, T. Garel, R. Barbetmassin, “Orientation of crystals of blue phases by electric fields,” J. Phys. 47(1), 139–143 (1986).
[CrossRef]

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[CrossRef]

Berreman, D. W.

Chen, N. R.

N. R. Chen, J. T. Ho, “Electric-field-induced phase diagrams of blue-phase systems,” Phys. Rev. A 35(11), 4886–4888 (1987).
[CrossRef] [PubMed]

Cheng, H. C.

J. Yan, L. Rao, M. Jiao, Y. Li, H. C. Cheng, S. T. Wu, “Polymer-stabilized optically isotropic liquid crystals for next-generation display and photonics applications,” J. Mater. Chem. 21(22), 7870–7877 (2011).
[CrossRef]

Cheng, K. L.

J. Yan, Z. Luo, S. T. Wu, J. W. Shiu, Y. C. Lai, K. L. Cheng, S. H. Liu, P. J. Hsieh, Y. C. Tsai, “Low voltage and high contrast blue phase liquid crystal with red-shifted Bragg reflection,” Appl. Phys. Lett. 102(1), 011113 (2013).
[CrossRef]

Cladis, P. E.

P. Pieranski, P. E. Cladis, T. Garel, R. Barbetmassin, “Orientation of crystals of blue phases by electric fields,” J. Phys. 47(1), 139–143 (1986).
[CrossRef]

Crooker, P. P.

D. L. Johnson, J. H. Flack, P. P. Crooker, “Structure and properties of the cholesteric blue phases,” Phys. Rev. Lett. 45(8), 641–644 (1980).
[CrossRef]

Flack, J. H.

D. L. Johnson, J. H. Flack, P. P. Crooker, “Structure and properties of the cholesteric blue phases,” Phys. Rev. Lett. 45(8), 641–644 (1980).
[CrossRef]

Fujii, A.

M. Ojima, Y. Ogawa, R. Ozaki, H. Moritake, H. Yoshida, A. Fujii, M. Ozaki, “Finite-difference time-domain analysis of polarization dependent transmission in cholesteric blue phase II,” Appl. Phys. Express 3(3), 032001 (2010).
[CrossRef]

Fukuda, J.

Y. Ogawa, J. Fukuda, H. Yoshida, M. Ozaki, “Finite-difference time-domain analysis of cholesteric blue phase II using the Landau-de Gennes tensor order parameter model,” Opt. Lett. 38(17), 3380–3383 (2013).
[CrossRef] [PubMed]

J. Fukuda, M. Yoneya, H. Yokoyama, “Simulation of cholesteric blue phases using a Landau-de Gennes theory: effect of an applied electric field,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(3), 031706 (2009).
[CrossRef] [PubMed]

Garel, T.

P. Pieranski, P. E. Cladis, T. Garel, R. Barbetmassin, “Orientation of crystals of blue phases by electric fields,” J. Phys. 47(1), 139–143 (1986).
[CrossRef]

Gestblom, B.

S. Urban, B. Gestblom, W. Kuczynski, S. Pawlus, A. Würflinger, “Nematic order parameter as determined from dielectric relaxation data and other methods,” Phys. Chem. Chem. Phys. 5(5), 924–928 (2003).
[CrossRef]

Heppke, G.

G. Heppke, B. Jérôme, H. S. Kitzerow, P. Pieranski, “Electrostriction of the cholesteric blue phases BPI and BPII in mixtures with positive dielectric anisotropy,” J. Phys. France 50(19), 2991–2998 (1989).
[CrossRef]

G. Heppke, B. Jérôme, H. S. Kitzerow, P. Pieranski, “Electrostriction of BPI and BPII for blue phase systems with negative dielectric anisotropy,” J. Phys. France 50(5), 549–562 (1989).
[CrossRef]

Hisakado, Y.

Y. Hisakado, H. Kikuchi, T. Nagamura, T. Kajiyama, “Large electro-optic Kerr effect in polymer-stabilized liquid-crystalline blue phases,” Adv. Mater. 17(1), 96–98 (2005).
[CrossRef]

H. Kikuchi, M. Yokota, Y. Hisakado, H. Yang, T. Kajiyama, “Polymer-stabilized liquid crystal blue phases,” Nat. Mater. 1(1), 64–68 (2002).
[CrossRef] [PubMed]

Ho, J. T.

N. R. Chen, J. T. Ho, “Electric-field-induced phase diagrams of blue-phase systems,” Phys. Rev. A 35(11), 4886–4888 (1987).
[CrossRef] [PubMed]

Hornreich, R. M.

R. M. Hornreich, S. Shtrikman, C. Sommers, “Photonic bands in simple and body-centered-cubic cholesteric blue phases,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 47(3), 2067–2072 (1993).
[CrossRef] [PubMed]

Hsieh, P. J.

J. Yan, Z. Luo, S. T. Wu, J. W. Shiu, Y. C. Lai, K. L. Cheng, S. H. Liu, P. J. Hsieh, Y. C. Tsai, “Low voltage and high contrast blue phase liquid crystal with red-shifted Bragg reflection,” Appl. Phys. Lett. 102(1), 011113 (2013).
[CrossRef]

Jérôme, B.

G. Heppke, B. Jérôme, H. S. Kitzerow, P. Pieranski, “Electrostriction of the cholesteric blue phases BPI and BPII in mixtures with positive dielectric anisotropy,” J. Phys. France 50(19), 2991–2998 (1989).
[CrossRef]

G. Heppke, B. Jérôme, H. S. Kitzerow, P. Pieranski, “Electrostriction of BPI and BPII for blue phase systems with negative dielectric anisotropy,” J. Phys. France 50(5), 549–562 (1989).
[CrossRef]

Jiao, M.

J. Yan, L. Rao, M. Jiao, Y. Li, H. C. Cheng, S. T. Wu, “Polymer-stabilized optically isotropic liquid crystals for next-generation display and photonics applications,” J. Mater. Chem. 21(22), 7870–7877 (2011).
[CrossRef]

Johnson, D. L.

D. L. Johnson, J. H. Flack, P. P. Crooker, “Structure and properties of the cholesteric blue phases,” Phys. Rev. Lett. 45(8), 641–644 (1980).
[CrossRef]

Kajiyama, T.

Y. Hisakado, H. Kikuchi, T. Nagamura, T. Kajiyama, “Large electro-optic Kerr effect in polymer-stabilized liquid-crystalline blue phases,” Adv. Mater. 17(1), 96–98 (2005).
[CrossRef]

H. Kikuchi, M. Yokota, Y. Hisakado, H. Yang, T. Kajiyama, “Polymer-stabilized liquid crystal blue phases,” Nat. Mater. 1(1), 64–68 (2002).
[CrossRef] [PubMed]

Kikuchi, H.

Y. Hisakado, H. Kikuchi, T. Nagamura, T. Kajiyama, “Large electro-optic Kerr effect in polymer-stabilized liquid-crystalline blue phases,” Adv. Mater. 17(1), 96–98 (2005).
[CrossRef]

H. Kikuchi, M. Yokota, Y. Hisakado, H. Yang, T. Kajiyama, “Polymer-stabilized liquid crystal blue phases,” Nat. Mater. 1(1), 64–68 (2002).
[CrossRef] [PubMed]

Kitzerow, H. S.

H. S. Kitzerow, “The effect of electric fields on blue phases,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 202(1), 51–83 (1991).
[CrossRef]

G. Heppke, B. Jérôme, H. S. Kitzerow, P. Pieranski, “Electrostriction of BPI and BPII for blue phase systems with negative dielectric anisotropy,” J. Phys. France 50(5), 549–562 (1989).
[CrossRef]

G. Heppke, B. Jérôme, H. S. Kitzerow, P. Pieranski, “Electrostriction of the cholesteric blue phases BPI and BPII in mixtures with positive dielectric anisotropy,” J. Phys. France 50(19), 2991–2998 (1989).
[CrossRef]

Kuczynski, W.

S. Urban, B. Gestblom, W. Kuczynski, S. Pawlus, A. Würflinger, “Nematic order parameter as determined from dielectric relaxation data and other methods,” Phys. Chem. Chem. Phys. 5(5), 924–928 (2003).
[CrossRef]

Lai, Y. C.

J. Yan, Z. Luo, S. T. Wu, J. W. Shiu, Y. C. Lai, K. L. Cheng, S. H. Liu, P. J. Hsieh, Y. C. Tsai, “Low voltage and high contrast blue phase liquid crystal with red-shifted Bragg reflection,” Appl. Phys. Lett. 102(1), 011113 (2013).
[CrossRef]

Li, Y.

J. Yan, L. Rao, M. Jiao, Y. Li, H. C. Cheng, S. T. Wu, “Polymer-stabilized optically isotropic liquid crystals for next-generation display and photonics applications,” J. Mater. Chem. 21(22), 7870–7877 (2011).
[CrossRef]

Liu, S. H.

J. Yan, Z. Luo, S. T. Wu, J. W. Shiu, Y. C. Lai, K. L. Cheng, S. H. Liu, P. J. Hsieh, Y. C. Tsai, “Low voltage and high contrast blue phase liquid crystal with red-shifted Bragg reflection,” Appl. Phys. Lett. 102(1), 011113 (2013).
[CrossRef]

Luo, Z.

J. Yan, Z. Luo, S. T. Wu, J. W. Shiu, Y. C. Lai, K. L. Cheng, S. H. Liu, P. J. Hsieh, Y. C. Tsai, “Low voltage and high contrast blue phase liquid crystal with red-shifted Bragg reflection,” Appl. Phys. Lett. 102(1), 011113 (2013).
[CrossRef]

Mermin, N. D.

D. C. Wright, N. D. Mermin, “Crystalline liquids the blue phases,” Rev. Mod. Phys. 61(2), 385–432 (1989).
[CrossRef]

Moritake, H.

M. Ojima, Y. Ogawa, R. Ozaki, H. Moritake, H. Yoshida, A. Fujii, M. Ozaki, “Finite-difference time-domain analysis of polarization dependent transmission in cholesteric blue phase II,” Appl. Phys. Express 3(3), 032001 (2010).
[CrossRef]

Nagamura, T.

Y. Hisakado, H. Kikuchi, T. Nagamura, T. Kajiyama, “Large electro-optic Kerr effect in polymer-stabilized liquid-crystalline blue phases,” Adv. Mater. 17(1), 96–98 (2005).
[CrossRef]

Ogawa, Y.

Y. Ogawa, J. Fukuda, H. Yoshida, M. Ozaki, “Finite-difference time-domain analysis of cholesteric blue phase II using the Landau-de Gennes tensor order parameter model,” Opt. Lett. 38(17), 3380–3383 (2013).
[CrossRef] [PubMed]

M. Ojima, Y. Ogawa, R. Ozaki, H. Moritake, H. Yoshida, A. Fujii, M. Ozaki, “Finite-difference time-domain analysis of polarization dependent transmission in cholesteric blue phase II,” Appl. Phys. Express 3(3), 032001 (2010).
[CrossRef]

Ojima, M.

M. Ojima, Y. Ogawa, R. Ozaki, H. Moritake, H. Yoshida, A. Fujii, M. Ozaki, “Finite-difference time-domain analysis of polarization dependent transmission in cholesteric blue phase II,” Appl. Phys. Express 3(3), 032001 (2010).
[CrossRef]

Ozaki, M.

Y. Ogawa, J. Fukuda, H. Yoshida, M. Ozaki, “Finite-difference time-domain analysis of cholesteric blue phase II using the Landau-de Gennes tensor order parameter model,” Opt. Lett. 38(17), 3380–3383 (2013).
[CrossRef] [PubMed]

M. Ojima, Y. Ogawa, R. Ozaki, H. Moritake, H. Yoshida, A. Fujii, M. Ozaki, “Finite-difference time-domain analysis of polarization dependent transmission in cholesteric blue phase II,” Appl. Phys. Express 3(3), 032001 (2010).
[CrossRef]

Ozaki, R.

M. Ojima, Y. Ogawa, R. Ozaki, H. Moritake, H. Yoshida, A. Fujii, M. Ozaki, “Finite-difference time-domain analysis of polarization dependent transmission in cholesteric blue phase II,” Appl. Phys. Express 3(3), 032001 (2010).
[CrossRef]

Pawlus, S.

S. Urban, B. Gestblom, W. Kuczynski, S. Pawlus, A. Würflinger, “Nematic order parameter as determined from dielectric relaxation data and other methods,” Phys. Chem. Chem. Phys. 5(5), 924–928 (2003).
[CrossRef]

Pieranski, P.

G. Heppke, B. Jérôme, H. S. Kitzerow, P. Pieranski, “Electrostriction of the cholesteric blue phases BPI and BPII in mixtures with positive dielectric anisotropy,” J. Phys. France 50(19), 2991–2998 (1989).
[CrossRef]

G. Heppke, B. Jérôme, H. S. Kitzerow, P. Pieranski, “Electrostriction of BPI and BPII for blue phase systems with negative dielectric anisotropy,” J. Phys. France 50(5), 549–562 (1989).
[CrossRef]

P. Pieranski, P. E. Cladis, T. Garel, R. Barbetmassin, “Orientation of crystals of blue phases by electric fields,” J. Phys. 47(1), 139–143 (1986).
[CrossRef]

Rao, L.

J. Yan, L. Rao, M. Jiao, Y. Li, H. C. Cheng, S. T. Wu, “Polymer-stabilized optically isotropic liquid crystals for next-generation display and photonics applications,” J. Mater. Chem. 21(22), 7870–7877 (2011).
[CrossRef]

Ravnik, M.

M. Ravnik, G. P. Alexander, J. M. Yeomans, S. Žumer, “Three-dimensional colloidal crystals in liquid crystalline blue phases,” Proc. Natl. Acad. Sci. U.S.A. 108(13), 5188–5192 (2011).
[CrossRef] [PubMed]

M. Ravnik, G. P. Alexander, J. M. Yeomans, S. Zumer, “Mesoscopic modelling of colloids in chiral nematics,” Faraday Discuss. 144, 159–169, discussion 203–222, 467–481 (2009).
[CrossRef] [PubMed]

Shiu, J. W.

J. Yan, Z. Luo, S. T. Wu, J. W. Shiu, Y. C. Lai, K. L. Cheng, S. H. Liu, P. J. Hsieh, Y. C. Tsai, “Low voltage and high contrast blue phase liquid crystal with red-shifted Bragg reflection,” Appl. Phys. Lett. 102(1), 011113 (2013).
[CrossRef]

Shtrikman, S.

R. M. Hornreich, S. Shtrikman, C. Sommers, “Photonic bands in simple and body-centered-cubic cholesteric blue phases,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 47(3), 2067–2072 (1993).
[CrossRef] [PubMed]

Sommers, C.

R. M. Hornreich, S. Shtrikman, C. Sommers, “Photonic bands in simple and body-centered-cubic cholesteric blue phases,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 47(3), 2067–2072 (1993).
[CrossRef] [PubMed]

Tsai, Y. C.

J. Yan, Z. Luo, S. T. Wu, J. W. Shiu, Y. C. Lai, K. L. Cheng, S. H. Liu, P. J. Hsieh, Y. C. Tsai, “Low voltage and high contrast blue phase liquid crystal with red-shifted Bragg reflection,” Appl. Phys. Lett. 102(1), 011113 (2013).
[CrossRef]

Urban, S.

S. Urban, B. Gestblom, W. Kuczynski, S. Pawlus, A. Würflinger, “Nematic order parameter as determined from dielectric relaxation data and other methods,” Phys. Chem. Chem. Phys. 5(5), 924–928 (2003).
[CrossRef]

Wright, D. C.

D. C. Wright, N. D. Mermin, “Crystalline liquids the blue phases,” Rev. Mod. Phys. 61(2), 385–432 (1989).
[CrossRef]

Wu, S. T.

J. Yan, Z. Luo, S. T. Wu, J. W. Shiu, Y. C. Lai, K. L. Cheng, S. H. Liu, P. J. Hsieh, Y. C. Tsai, “Low voltage and high contrast blue phase liquid crystal with red-shifted Bragg reflection,” Appl. Phys. Lett. 102(1), 011113 (2013).
[CrossRef]

J. Yan, L. Rao, M. Jiao, Y. Li, H. C. Cheng, S. T. Wu, “Polymer-stabilized optically isotropic liquid crystals for next-generation display and photonics applications,” J. Mater. Chem. 21(22), 7870–7877 (2011).
[CrossRef]

Würflinger, A.

S. Urban, B. Gestblom, W. Kuczynski, S. Pawlus, A. Würflinger, “Nematic order parameter as determined from dielectric relaxation data and other methods,” Phys. Chem. Chem. Phys. 5(5), 924–928 (2003).
[CrossRef]

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J. Yan, Z. Luo, S. T. Wu, J. W. Shiu, Y. C. Lai, K. L. Cheng, S. H. Liu, P. J. Hsieh, Y. C. Tsai, “Low voltage and high contrast blue phase liquid crystal with red-shifted Bragg reflection,” Appl. Phys. Lett. 102(1), 011113 (2013).
[CrossRef]

J. Yan, L. Rao, M. Jiao, Y. Li, H. C. Cheng, S. T. Wu, “Polymer-stabilized optically isotropic liquid crystals for next-generation display and photonics applications,” J. Mater. Chem. 21(22), 7870–7877 (2011).
[CrossRef]

Yang, H.

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[CrossRef] [PubMed]

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K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[CrossRef]

Yeomans, J. M.

M. Ravnik, G. P. Alexander, J. M. Yeomans, S. Žumer, “Three-dimensional colloidal crystals in liquid crystalline blue phases,” Proc. Natl. Acad. Sci. U.S.A. 108(13), 5188–5192 (2011).
[CrossRef] [PubMed]

M. Ravnik, G. P. Alexander, J. M. Yeomans, S. Zumer, “Mesoscopic modelling of colloids in chiral nematics,” Faraday Discuss. 144, 159–169, discussion 203–222, 467–481 (2009).
[CrossRef] [PubMed]

Yokota, M.

H. Kikuchi, M. Yokota, Y. Hisakado, H. Yang, T. Kajiyama, “Polymer-stabilized liquid crystal blue phases,” Nat. Mater. 1(1), 64–68 (2002).
[CrossRef] [PubMed]

Yokoyama, H.

J. Fukuda, M. Yoneya, H. Yokoyama, “Simulation of cholesteric blue phases using a Landau-de Gennes theory: effect of an applied electric field,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(3), 031706 (2009).
[CrossRef] [PubMed]

Yoneya, M.

J. Fukuda, M. Yoneya, H. Yokoyama, “Simulation of cholesteric blue phases using a Landau-de Gennes theory: effect of an applied electric field,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(3), 031706 (2009).
[CrossRef] [PubMed]

Yoshida, H.

Y. Ogawa, J. Fukuda, H. Yoshida, M. Ozaki, “Finite-difference time-domain analysis of cholesteric blue phase II using the Landau-de Gennes tensor order parameter model,” Opt. Lett. 38(17), 3380–3383 (2013).
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M. Ojima, Y. Ogawa, R. Ozaki, H. Moritake, H. Yoshida, A. Fujii, M. Ozaki, “Finite-difference time-domain analysis of polarization dependent transmission in cholesteric blue phase II,” Appl. Phys. Express 3(3), 032001 (2010).
[CrossRef]

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M. Ravnik, G. P. Alexander, J. M. Yeomans, S. Zumer, “Mesoscopic modelling of colloids in chiral nematics,” Faraday Discuss. 144, 159–169, discussion 203–222, 467–481 (2009).
[CrossRef] [PubMed]

Žumer, S.

M. Ravnik, G. P. Alexander, J. M. Yeomans, S. Žumer, “Three-dimensional colloidal crystals in liquid crystalline blue phases,” Proc. Natl. Acad. Sci. U.S.A. 108(13), 5188–5192 (2011).
[CrossRef] [PubMed]

Adv. Mater. (1)

Y. Hisakado, H. Kikuchi, T. Nagamura, T. Kajiyama, “Large electro-optic Kerr effect in polymer-stabilized liquid-crystalline blue phases,” Adv. Mater. 17(1), 96–98 (2005).
[CrossRef]

Appl. Phys. Express (1)

M. Ojima, Y. Ogawa, R. Ozaki, H. Moritake, H. Yoshida, A. Fujii, M. Ozaki, “Finite-difference time-domain analysis of polarization dependent transmission in cholesteric blue phase II,” Appl. Phys. Express 3(3), 032001 (2010).
[CrossRef]

Appl. Phys. Lett. (1)

J. Yan, Z. Luo, S. T. Wu, J. W. Shiu, Y. C. Lai, K. L. Cheng, S. H. Liu, P. J. Hsieh, Y. C. Tsai, “Low voltage and high contrast blue phase liquid crystal with red-shifted Bragg reflection,” Appl. Phys. Lett. 102(1), 011113 (2013).
[CrossRef]

Faraday Discuss. (1)

M. Ravnik, G. P. Alexander, J. M. Yeomans, S. Zumer, “Mesoscopic modelling of colloids in chiral nematics,” Faraday Discuss. 144, 159–169, discussion 203–222, 467–481 (2009).
[CrossRef] [PubMed]

IEEE Trans. Antenn. Propag. (1)

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[CrossRef]

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[CrossRef]

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[CrossRef]

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J. Phys. (1)

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[CrossRef]

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[CrossRef]

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[CrossRef]

Mol. Cryst. Liq. Cryst. (Phila. Pa.) (1)

H. S. Kitzerow, “The effect of electric fields on blue phases,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 202(1), 51–83 (1991).
[CrossRef]

Nat. Mater. (1)

H. Kikuchi, M. Yokota, Y. Hisakado, H. Yang, T. Kajiyama, “Polymer-stabilized liquid crystal blue phases,” Nat. Mater. 1(1), 64–68 (2002).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Chem. Chem. Phys. (1)

S. Urban, B. Gestblom, W. Kuczynski, S. Pawlus, A. Würflinger, “Nematic order parameter as determined from dielectric relaxation data and other methods,” Phys. Chem. Chem. Phys. 5(5), 924–928 (2003).
[CrossRef]

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[CrossRef] [PubMed]

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J. Fukuda, M. Yoneya, H. Yokoyama, “Simulation of cholesteric blue phases using a Landau-de Gennes theory: effect of an applied electric field,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(3), 031706 (2009).
[CrossRef] [PubMed]

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M. Ravnik, G. P. Alexander, J. M. Yeomans, S. Žumer, “Three-dimensional colloidal crystals in liquid crystalline blue phases,” Proc. Natl. Acad. Sci. U.S.A. 108(13), 5188–5192 (2011).
[CrossRef] [PubMed]

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[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

(a) Scheme of the lattice deformation of BPII having Δεele > 0 by an applied electric field parallel to the [100] direction, and (b) first Brillouin zone of the simple tetragonal structure.

Fig. 2
Fig. 2

Photonic band structure of the BPII under electric field (a) 2 = 0, (b) 2 = 0.05, (c) 2 = 0.10, and (d) 2 = 0.20.

Fig. 3
Fig. 3

Transmission spectrum of deformed BPII for RC polarized light (a) in the [100] direction and (c) in the [001] direction. (b) and (d) shows the applied electric field dependence of the reflection peak wavelength and lattice constant of the BPII along the light propagation direction.

Fig. 4
Fig. 4

Circular polarization dependence of the photonic band structure in the Γ-X direction ((a)-(d)), and transmission spectra of BPII in the [100] direction ((e)-(h)). The normalized strengths of the electric field are 2 = 0 ((a), (e)), 2 = 0.05 ((b), (f)), 2 = 0.10 ((c), (g)), and 2 = 0.20 ((d), (h)).

Fig. 5
Fig. 5

Circular polarization dependence of the photonic band structure in the Γ-Z direction ((a)-(d)), and transmission spectra of BPII in the [001] direction ((e)-(h)). The normalized strengths of the electric field are 2 = 0 ((a), (e)), 2 = 0.05 ((b), (f)), 2 = 0.10 ((c), (g)), and 2 = 0.20 ((d), (h)).

Equations (7)

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f= f local + f grad + f ele ,
f local =cTr Q 2 6 bTr Q 3 +a ( Tr Q 2 ) 2 ,
f grad = 1 4 K 1 [ ( ×Q ) αβ +2 q 0 Q αβ ] 2 + 1 4 K 0 [ ( Q ) α ] 2 ,
f ele =Δ ε ele E α E β Q αβ .
φ ele = E ˜ 2 e ^ α e ^ β χ αβ .
ε αβ = 2 3 Δε× χ αβ + ε ave δ αβ .
S 2 = 3 2 Tr( χ 2 ).

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