Abstract

A polymer-wall-confined transmissive switchable liquid crystal grating is proposed and investigated by two-dimensional finite-difference time-domain optical calculation and liquid-crystal-director calculation, to our knowledge for the first time. The results show how to obtain optimized conditions for high diffraction efficiency by adjusting the liquid crystal parameters, grating geometric structure, and applied voltages. The light propagation direction and efficiency can be accurately calculated and visualized concurrently.

© 2004 Optical Society of America

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  1. R. L. Sutherland, L. V. Natarajan, T. J. Bunning, V. P. Tondiglia, “Switchable holographic polymer-dispersed liquid crystals,” in Vol. 7 of Liquid Crystals, Display and Laser Materials,Handbook of Advanced Electronic and Photonic Materials and Devices (Academic, San Diego, Calif., 2001), Chap. 2, pp. 67–102.
  2. R. L. Sutherland, L. V. Natarajan, V. P. Tondiglia, T. J. Bunning, “Bragg gratings in an acrylate polymer consisting of periodic polymer-dispersed liquid-crystal planes,” Chem. Mater. 5, 1533–1538 (1993).
    [Crossref]
  3. T. J. Bunning, L. V. Natarajan, V. P. Tondiglia, G. Dougherty, R. L. Sutherland, “Morphology of aniosotropic polymer-dispersed liquid crystal and the monomer functionality,” J. Polym. Sci. Part B Polym. Phys. 35, 2825–2833 (1997).
    [Crossref]
  4. C. C. Bowley, G. P. Crawford, “Diffusion kinetics of formation of holographic polymer-dispersed liquid crystal display materials,” Appl. Phys. Lett. 76, 2235–2237 (2000).
    [Crossref]
  5. K. Tanaka, K. Kato, M. Date, “Fabrication of holographic polymer dispersed liquid crystal (hpdlc) with high reflection efficiency,” 38, 277–278 (1999).
  6. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
    [Crossref]
  7. M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).
    [Crossref]
  8. C. D. Hoke, P. J. Bos, “Multidimensional alignment structure for the liquid crystal director field,” J. Appl. Phys. 88, 2302–2304 (2000).
    [Crossref]
  9. B. Wang, J. E. Anderson, C. D. Hoke, D. B. Chung, P. J. Bos, “Long term bistable twisted nematic liquid crystal display and its computer simulations,” Jpn. J. Appl. Phys. 41, 2939–2943 (2002).
    [Crossref]
  10. J. Anderson, P. E. Watson, P. J. Bos, LC3D: Liquid Crystal Display 3-D Director Simulation Software and Technology Guide (Artech House, Boston, Mass., 2001).
  11. P. G. de Gennes, J. Prost, The Physics of Liquid Crystal (Oxford Science, Oxford, UK, 1993).
  12. D. W. Berreman, “Numerical modeling of twisted nematic devices,” Philos. Trans. R. Soc. London Ser. A 309, 203–216 (1983).
    [Crossref]
  13. H. Mori, E. C. Gartland, J. R. Kelly, P. J. Bos, “Multidimensional director modeling using the q tensor representation in a liquid crystal cell and its application to the π cell with patterned electrodes,” Jpn. J. Appl. Phys. 38, 135–146 (1999).
    [Crossref]
  14. M. G. Moharam, T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 73, 1105–1112 (1983).
    [Crossref]
  15. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
    [Crossref]
  16. A. Taflove, S. C. Hagness, Computational Electrodynamics:The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 2000).
  17. E. E. Kriezis, S. J. Elston, “Light wave propagation in liquid crystal display by the 2-D finite-difference time-domain method,” Opt. Commun. 177, 69–77 (2000).
    [Crossref]
  18. C. M. Titus, P. J. Bos, J. R. Kelly, E. C. Gartland, “Comparison of analytical calculations to finite-difference time-domain simulations of one-dimensional spatially varying anisotropic liquid crystal structures,” Jpn. J. Appl. Phys. 38, 1488–1494 (1999).
    [Crossref]
  19. A. Yefet, P. G. Petropoulos, “A staggered fourth-order accuracy explicit finite difference scheme for the time-domain Maxwell’s equations,” J. Comput. Phys. 168, 286–315 (2001).
    [Crossref]
  20. J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
    [Crossref]
  21. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).
  22. C. M. Titus, “Refractive and diffractive liquid crystal beam steering devices,” Ph.D. dissertation (Kent State University, Kent, Ohio, 2000).
  23. E. E. Kriezis, S. K. Filippov, S. J. Elston, “Light propagation in domain walls in ferroelectric liquid crystal devices by the finite-difference time-domain method,” J. Opt. A Pure Appl. Opt. 2, 27–33 (2000).
    [Crossref]

2002 (1)

B. Wang, J. E. Anderson, C. D. Hoke, D. B. Chung, P. J. Bos, “Long term bistable twisted nematic liquid crystal display and its computer simulations,” Jpn. J. Appl. Phys. 41, 2939–2943 (2002).
[Crossref]

2001 (1)

A. Yefet, P. G. Petropoulos, “A staggered fourth-order accuracy explicit finite difference scheme for the time-domain Maxwell’s equations,” J. Comput. Phys. 168, 286–315 (2001).
[Crossref]

2000 (4)

E. E. Kriezis, S. K. Filippov, S. J. Elston, “Light propagation in domain walls in ferroelectric liquid crystal devices by the finite-difference time-domain method,” J. Opt. A Pure Appl. Opt. 2, 27–33 (2000).
[Crossref]

E. E. Kriezis, S. J. Elston, “Light wave propagation in liquid crystal display by the 2-D finite-difference time-domain method,” Opt. Commun. 177, 69–77 (2000).
[Crossref]

C. D. Hoke, P. J. Bos, “Multidimensional alignment structure for the liquid crystal director field,” J. Appl. Phys. 88, 2302–2304 (2000).
[Crossref]

C. C. Bowley, G. P. Crawford, “Diffusion kinetics of formation of holographic polymer-dispersed liquid crystal display materials,” Appl. Phys. Lett. 76, 2235–2237 (2000).
[Crossref]

1999 (3)

K. Tanaka, K. Kato, M. Date, “Fabrication of holographic polymer dispersed liquid crystal (hpdlc) with high reflection efficiency,” 38, 277–278 (1999).

C. M. Titus, P. J. Bos, J. R. Kelly, E. C. Gartland, “Comparison of analytical calculations to finite-difference time-domain simulations of one-dimensional spatially varying anisotropic liquid crystal structures,” Jpn. J. Appl. Phys. 38, 1488–1494 (1999).
[Crossref]

H. Mori, E. C. Gartland, J. R. Kelly, P. J. Bos, “Multidimensional director modeling using the q tensor representation in a liquid crystal cell and its application to the π cell with patterned electrodes,” Jpn. J. Appl. Phys. 38, 135–146 (1999).
[Crossref]

1997 (1)

T. J. Bunning, L. V. Natarajan, V. P. Tondiglia, G. Dougherty, R. L. Sutherland, “Morphology of aniosotropic polymer-dispersed liquid crystal and the monomer functionality,” J. Polym. Sci. Part B Polym. Phys. 35, 2825–2833 (1997).
[Crossref]

1994 (1)

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

1993 (1)

R. L. Sutherland, L. V. Natarajan, V. P. Tondiglia, T. J. Bunning, “Bragg gratings in an acrylate polymer consisting of periodic polymer-dispersed liquid-crystal planes,” Chem. Mater. 5, 1533–1538 (1993).
[Crossref]

1983 (2)

D. W. Berreman, “Numerical modeling of twisted nematic devices,” Philos. Trans. R. Soc. London Ser. A 309, 203–216 (1983).
[Crossref]

M. G. Moharam, T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 73, 1105–1112 (1983).
[Crossref]

1981 (1)

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[Crossref]

1966 (1)

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

Anderson, J.

J. Anderson, P. E. Watson, P. J. Bos, LC3D: Liquid Crystal Display 3-D Director Simulation Software and Technology Guide (Artech House, Boston, Mass., 2001).

Anderson, J. E.

B. Wang, J. E. Anderson, C. D. Hoke, D. B. Chung, P. J. Bos, “Long term bistable twisted nematic liquid crystal display and its computer simulations,” Jpn. J. Appl. Phys. 41, 2939–2943 (2002).
[Crossref]

Berenger, J.-P.

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

Berreman, D. W.

D. W. Berreman, “Numerical modeling of twisted nematic devices,” Philos. Trans. R. Soc. London Ser. A 309, 203–216 (1983).
[Crossref]

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).

Bos, P. J.

B. Wang, J. E. Anderson, C. D. Hoke, D. B. Chung, P. J. Bos, “Long term bistable twisted nematic liquid crystal display and its computer simulations,” Jpn. J. Appl. Phys. 41, 2939–2943 (2002).
[Crossref]

C. D. Hoke, P. J. Bos, “Multidimensional alignment structure for the liquid crystal director field,” J. Appl. Phys. 88, 2302–2304 (2000).
[Crossref]

H. Mori, E. C. Gartland, J. R. Kelly, P. J. Bos, “Multidimensional director modeling using the q tensor representation in a liquid crystal cell and its application to the π cell with patterned electrodes,” Jpn. J. Appl. Phys. 38, 135–146 (1999).
[Crossref]

C. M. Titus, P. J. Bos, J. R. Kelly, E. C. Gartland, “Comparison of analytical calculations to finite-difference time-domain simulations of one-dimensional spatially varying anisotropic liquid crystal structures,” Jpn. J. Appl. Phys. 38, 1488–1494 (1999).
[Crossref]

J. Anderson, P. E. Watson, P. J. Bos, LC3D: Liquid Crystal Display 3-D Director Simulation Software and Technology Guide (Artech House, Boston, Mass., 2001).

Bowley, C. C.

C. C. Bowley, G. P. Crawford, “Diffusion kinetics of formation of holographic polymer-dispersed liquid crystal display materials,” Appl. Phys. Lett. 76, 2235–2237 (2000).
[Crossref]

Bunning, T. J.

T. J. Bunning, L. V. Natarajan, V. P. Tondiglia, G. Dougherty, R. L. Sutherland, “Morphology of aniosotropic polymer-dispersed liquid crystal and the monomer functionality,” J. Polym. Sci. Part B Polym. Phys. 35, 2825–2833 (1997).
[Crossref]

R. L. Sutherland, L. V. Natarajan, V. P. Tondiglia, T. J. Bunning, “Bragg gratings in an acrylate polymer consisting of periodic polymer-dispersed liquid-crystal planes,” Chem. Mater. 5, 1533–1538 (1993).
[Crossref]

R. L. Sutherland, L. V. Natarajan, T. J. Bunning, V. P. Tondiglia, “Switchable holographic polymer-dispersed liquid crystals,” in Vol. 7 of Liquid Crystals, Display and Laser Materials,Handbook of Advanced Electronic and Photonic Materials and Devices (Academic, San Diego, Calif., 2001), Chap. 2, pp. 67–102.

Chung, D. B.

B. Wang, J. E. Anderson, C. D. Hoke, D. B. Chung, P. J. Bos, “Long term bistable twisted nematic liquid crystal display and its computer simulations,” Jpn. J. Appl. Phys. 41, 2939–2943 (2002).
[Crossref]

Crawford, G. P.

C. C. Bowley, G. P. Crawford, “Diffusion kinetics of formation of holographic polymer-dispersed liquid crystal display materials,” Appl. Phys. Lett. 76, 2235–2237 (2000).
[Crossref]

Date, M.

K. Tanaka, K. Kato, M. Date, “Fabrication of holographic polymer dispersed liquid crystal (hpdlc) with high reflection efficiency,” 38, 277–278 (1999).

de Gennes, P. G.

P. G. de Gennes, J. Prost, The Physics of Liquid Crystal (Oxford Science, Oxford, UK, 1993).

Dougherty, G.

T. J. Bunning, L. V. Natarajan, V. P. Tondiglia, G. Dougherty, R. L. Sutherland, “Morphology of aniosotropic polymer-dispersed liquid crystal and the monomer functionality,” J. Polym. Sci. Part B Polym. Phys. 35, 2825–2833 (1997).
[Crossref]

Elston, S. J.

E. E. Kriezis, S. J. Elston, “Light wave propagation in liquid crystal display by the 2-D finite-difference time-domain method,” Opt. Commun. 177, 69–77 (2000).
[Crossref]

E. E. Kriezis, S. K. Filippov, S. J. Elston, “Light propagation in domain walls in ferroelectric liquid crystal devices by the finite-difference time-domain method,” J. Opt. A Pure Appl. Opt. 2, 27–33 (2000).
[Crossref]

Filippov, S. K.

E. E. Kriezis, S. K. Filippov, S. J. Elston, “Light propagation in domain walls in ferroelectric liquid crystal devices by the finite-difference time-domain method,” J. Opt. A Pure Appl. Opt. 2, 27–33 (2000).
[Crossref]

Gartland, E. C.

C. M. Titus, P. J. Bos, J. R. Kelly, E. C. Gartland, “Comparison of analytical calculations to finite-difference time-domain simulations of one-dimensional spatially varying anisotropic liquid crystal structures,” Jpn. J. Appl. Phys. 38, 1488–1494 (1999).
[Crossref]

H. Mori, E. C. Gartland, J. R. Kelly, P. J. Bos, “Multidimensional director modeling using the q tensor representation in a liquid crystal cell and its application to the π cell with patterned electrodes,” Jpn. J. Appl. Phys. 38, 135–146 (1999).
[Crossref]

Gaylord, T. K.

Hagness, S. C.

A. Taflove, S. C. Hagness, Computational Electrodynamics:The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 2000).

Hoke, C. D.

B. Wang, J. E. Anderson, C. D. Hoke, D. B. Chung, P. J. Bos, “Long term bistable twisted nematic liquid crystal display and its computer simulations,” Jpn. J. Appl. Phys. 41, 2939–2943 (2002).
[Crossref]

C. D. Hoke, P. J. Bos, “Multidimensional alignment structure for the liquid crystal director field,” J. Appl. Phys. 88, 2302–2304 (2000).
[Crossref]

Kato, K.

K. Tanaka, K. Kato, M. Date, “Fabrication of holographic polymer dispersed liquid crystal (hpdlc) with high reflection efficiency,” 38, 277–278 (1999).

Kelly, J. R.

H. Mori, E. C. Gartland, J. R. Kelly, P. J. Bos, “Multidimensional director modeling using the q tensor representation in a liquid crystal cell and its application to the π cell with patterned electrodes,” Jpn. J. Appl. Phys. 38, 135–146 (1999).
[Crossref]

C. M. Titus, P. J. Bos, J. R. Kelly, E. C. Gartland, “Comparison of analytical calculations to finite-difference time-domain simulations of one-dimensional spatially varying anisotropic liquid crystal structures,” Jpn. J. Appl. Phys. 38, 1488–1494 (1999).
[Crossref]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[Crossref]

Kriezis, E. E.

E. E. Kriezis, S. J. Elston, “Light wave propagation in liquid crystal display by the 2-D finite-difference time-domain method,” Opt. Commun. 177, 69–77 (2000).
[Crossref]

E. E. Kriezis, S. K. Filippov, S. J. Elston, “Light propagation in domain walls in ferroelectric liquid crystal devices by the finite-difference time-domain method,” J. Opt. A Pure Appl. Opt. 2, 27–33 (2000).
[Crossref]

Moharam, M. G.

Mori, H.

H. Mori, E. C. Gartland, J. R. Kelly, P. J. Bos, “Multidimensional director modeling using the q tensor representation in a liquid crystal cell and its application to the π cell with patterned electrodes,” Jpn. J. Appl. Phys. 38, 135–146 (1999).
[Crossref]

Natarajan, L. V.

T. J. Bunning, L. V. Natarajan, V. P. Tondiglia, G. Dougherty, R. L. Sutherland, “Morphology of aniosotropic polymer-dispersed liquid crystal and the monomer functionality,” J. Polym. Sci. Part B Polym. Phys. 35, 2825–2833 (1997).
[Crossref]

R. L. Sutherland, L. V. Natarajan, V. P. Tondiglia, T. J. Bunning, “Bragg gratings in an acrylate polymer consisting of periodic polymer-dispersed liquid-crystal planes,” Chem. Mater. 5, 1533–1538 (1993).
[Crossref]

R. L. Sutherland, L. V. Natarajan, T. J. Bunning, V. P. Tondiglia, “Switchable holographic polymer-dispersed liquid crystals,” in Vol. 7 of Liquid Crystals, Display and Laser Materials,Handbook of Advanced Electronic and Photonic Materials and Devices (Academic, San Diego, Calif., 2001), Chap. 2, pp. 67–102.

Petropoulos, P. G.

A. Yefet, P. G. Petropoulos, “A staggered fourth-order accuracy explicit finite difference scheme for the time-domain Maxwell’s equations,” J. Comput. Phys. 168, 286–315 (2001).
[Crossref]

Prost, J.

P. G. de Gennes, J. Prost, The Physics of Liquid Crystal (Oxford Science, Oxford, UK, 1993).

Sutherland, R. L.

T. J. Bunning, L. V. Natarajan, V. P. Tondiglia, G. Dougherty, R. L. Sutherland, “Morphology of aniosotropic polymer-dispersed liquid crystal and the monomer functionality,” J. Polym. Sci. Part B Polym. Phys. 35, 2825–2833 (1997).
[Crossref]

R. L. Sutherland, L. V. Natarajan, V. P. Tondiglia, T. J. Bunning, “Bragg gratings in an acrylate polymer consisting of periodic polymer-dispersed liquid-crystal planes,” Chem. Mater. 5, 1533–1538 (1993).
[Crossref]

R. L. Sutherland, L. V. Natarajan, T. J. Bunning, V. P. Tondiglia, “Switchable holographic polymer-dispersed liquid crystals,” in Vol. 7 of Liquid Crystals, Display and Laser Materials,Handbook of Advanced Electronic and Photonic Materials and Devices (Academic, San Diego, Calif., 2001), Chap. 2, pp. 67–102.

Taflove, A.

A. Taflove, S. C. Hagness, Computational Electrodynamics:The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 2000).

Tanaka, K.

K. Tanaka, K. Kato, M. Date, “Fabrication of holographic polymer dispersed liquid crystal (hpdlc) with high reflection efficiency,” 38, 277–278 (1999).

Titus, C. M.

C. M. Titus, P. J. Bos, J. R. Kelly, E. C. Gartland, “Comparison of analytical calculations to finite-difference time-domain simulations of one-dimensional spatially varying anisotropic liquid crystal structures,” Jpn. J. Appl. Phys. 38, 1488–1494 (1999).
[Crossref]

C. M. Titus, “Refractive and diffractive liquid crystal beam steering devices,” Ph.D. dissertation (Kent State University, Kent, Ohio, 2000).

Tondiglia, V. P.

T. J. Bunning, L. V. Natarajan, V. P. Tondiglia, G. Dougherty, R. L. Sutherland, “Morphology of aniosotropic polymer-dispersed liquid crystal and the monomer functionality,” J. Polym. Sci. Part B Polym. Phys. 35, 2825–2833 (1997).
[Crossref]

R. L. Sutherland, L. V. Natarajan, V. P. Tondiglia, T. J. Bunning, “Bragg gratings in an acrylate polymer consisting of periodic polymer-dispersed liquid-crystal planes,” Chem. Mater. 5, 1533–1538 (1993).
[Crossref]

R. L. Sutherland, L. V. Natarajan, T. J. Bunning, V. P. Tondiglia, “Switchable holographic polymer-dispersed liquid crystals,” in Vol. 7 of Liquid Crystals, Display and Laser Materials,Handbook of Advanced Electronic and Photonic Materials and Devices (Academic, San Diego, Calif., 2001), Chap. 2, pp. 67–102.

Wang, B.

B. Wang, J. E. Anderson, C. D. Hoke, D. B. Chung, P. J. Bos, “Long term bistable twisted nematic liquid crystal display and its computer simulations,” Jpn. J. Appl. Phys. 41, 2939–2943 (2002).
[Crossref]

Watson, P. E.

J. Anderson, P. E. Watson, P. J. Bos, LC3D: Liquid Crystal Display 3-D Director Simulation Software and Technology Guide (Artech House, Boston, Mass., 2001).

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).

Yee, K.

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

Yefet, A.

A. Yefet, P. G. Petropoulos, “A staggered fourth-order accuracy explicit finite difference scheme for the time-domain Maxwell’s equations,” J. Comput. Phys. 168, 286–315 (2001).
[Crossref]

Appl. Phys. Lett. (1)

C. C. Bowley, G. P. Crawford, “Diffusion kinetics of formation of holographic polymer-dispersed liquid crystal display materials,” Appl. Phys. Lett. 76, 2235–2237 (2000).
[Crossref]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[Crossref]

Chem. Mater. (1)

R. L. Sutherland, L. V. Natarajan, V. P. Tondiglia, T. J. Bunning, “Bragg gratings in an acrylate polymer consisting of periodic polymer-dispersed liquid-crystal planes,” Chem. Mater. 5, 1533–1538 (1993).
[Crossref]

Fabrication of holographic polymer dispersed liquid crystal (hpdlc) with high reflection efficiency (1)

K. Tanaka, K. Kato, M. Date, “Fabrication of holographic polymer dispersed liquid crystal (hpdlc) with high reflection efficiency,” 38, 277–278 (1999).

IEEE Trans. Antennas Propag. (1)

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

J. Appl. Phys. (1)

C. D. Hoke, P. J. Bos, “Multidimensional alignment structure for the liquid crystal director field,” J. Appl. Phys. 88, 2302–2304 (2000).
[Crossref]

J. Comput. Phys. (2)

A. Yefet, P. G. Petropoulos, “A staggered fourth-order accuracy explicit finite difference scheme for the time-domain Maxwell’s equations,” J. Comput. Phys. 168, 286–315 (2001).
[Crossref]

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

J. Opt. A Pure Appl. Opt. (1)

E. E. Kriezis, S. K. Filippov, S. J. Elston, “Light propagation in domain walls in ferroelectric liquid crystal devices by the finite-difference time-domain method,” J. Opt. A Pure Appl. Opt. 2, 27–33 (2000).
[Crossref]

J. Opt. Soc. Am. (2)

J. Polym. Sci. Part B Polym. Phys. (1)

T. J. Bunning, L. V. Natarajan, V. P. Tondiglia, G. Dougherty, R. L. Sutherland, “Morphology of aniosotropic polymer-dispersed liquid crystal and the monomer functionality,” J. Polym. Sci. Part B Polym. Phys. 35, 2825–2833 (1997).
[Crossref]

Jpn. J. Appl. Phys. (3)

B. Wang, J. E. Anderson, C. D. Hoke, D. B. Chung, P. J. Bos, “Long term bistable twisted nematic liquid crystal display and its computer simulations,” Jpn. J. Appl. Phys. 41, 2939–2943 (2002).
[Crossref]

H. Mori, E. C. Gartland, J. R. Kelly, P. J. Bos, “Multidimensional director modeling using the q tensor representation in a liquid crystal cell and its application to the π cell with patterned electrodes,” Jpn. J. Appl. Phys. 38, 135–146 (1999).
[Crossref]

C. M. Titus, P. J. Bos, J. R. Kelly, E. C. Gartland, “Comparison of analytical calculations to finite-difference time-domain simulations of one-dimensional spatially varying anisotropic liquid crystal structures,” Jpn. J. Appl. Phys. 38, 1488–1494 (1999).
[Crossref]

Opt. Commun. (1)

E. E. Kriezis, S. J. Elston, “Light wave propagation in liquid crystal display by the 2-D finite-difference time-domain method,” Opt. Commun. 177, 69–77 (2000).
[Crossref]

Philos. Trans. R. Soc. London Ser. A (1)

D. W. Berreman, “Numerical modeling of twisted nematic devices,” Philos. Trans. R. Soc. London Ser. A 309, 203–216 (1983).
[Crossref]

Other (6)

R. L. Sutherland, L. V. Natarajan, T. J. Bunning, V. P. Tondiglia, “Switchable holographic polymer-dispersed liquid crystals,” in Vol. 7 of Liquid Crystals, Display and Laser Materials,Handbook of Advanced Electronic and Photonic Materials and Devices (Academic, San Diego, Calif., 2001), Chap. 2, pp. 67–102.

A. Taflove, S. C. Hagness, Computational Electrodynamics:The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 2000).

J. Anderson, P. E. Watson, P. J. Bos, LC3D: Liquid Crystal Display 3-D Director Simulation Software and Technology Guide (Artech House, Boston, Mass., 2001).

P. G. de Gennes, J. Prost, The Physics of Liquid Crystal (Oxford Science, Oxford, UK, 1993).

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).

C. M. Titus, “Refractive and diffractive liquid crystal beam steering devices,” Ph.D. dissertation (Kent State University, Kent, Ohio, 2000).

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Figures (6)

Fig. 1
Fig. 1

Formation of polymer walls from aligned monomer units. The rubbing direction of the cell’s bottom substrate is along the z direction; the top substrate has a homeotropic alignment layer.

Fig. 2
Fig. 2

Two-dimensional hybrid director field at voltages of (a) 0.0 V, (c) 5.0 V, (e) 6.0 V, and (g) 10.0 V; the corresponding refractive-index profile of the device at those voltages are shown in (b), (d), (f), and (h).

Fig. 3
Fig. 3

Geometrical setup of a two-dimensional in-plane transmissive diffraction grating.

Fig. 4
Fig. 4

Layout of the two-dimensional FDTD computational domain in the XY plane. A plane wave is incident at 30° from the bottom of the grating, and the beam width equals the width of the calculation domain. L1, Width of the liquid crystal; L2, width of the polymer wall. The periodicity Λs of the grating is L1+L2, and the grating thickness is d.

Fig. 5
Fig. 5

Geometry of the two-dimensional diffraction problem. The diffraction object lies in the y=y0 plane between x=-d and x=d. The normal to the diffracting object is n=y. Diffracted light is observed at (xfar, yfar).

Fig. 6
Fig. 6

FDTD near-field calculation for αi=30°, λ=1.55 μm, Λs=1.5 μm at voltage of (a) 0.0 V, (c) 5.0 V, (e) 6.0 V, and (g) 10.0 V. The corresponding far-field calculations are shown in (b), (d), (f), and (h).

Equations (16)

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fg=12K11(  n)2+12K22(n  ×n+q0)2+12K33(n××n)2-12D  E.
ninew=niold-Δtγ1 [fg]ni,i=x, y, z.
[fg]ni=fgni-ddxfg(dni/dx)-ddyfg(dni/dy).
n1sin αi+n3sin βm=mλΛs,m=0, ±1, ±2,,
βm=sin-1mλn3Λs-n1n3sin αi,
(r) E(r)t=×H(r),
μ0(r) H(r)t=-×E(r),
(r)=+ΔnxnxΔnxnyΔnxnzΔnynx+ΔnynyΔnynzΔnznxΔnzny+Δnznz,
Ezn+1=Ezn+Δtzz-1Hyn+1/2x-Hxn+1/2y,
Hxn+1/2=Hxn-1/2+Δtμ0-Ezny,
Hyn+1/2=Hyn-1/2+Δtμ0Eznx,
Ψfar(r)=14πSn  [Ψnear(r)  G-G  Ψnear(r)]ds,
Ψfar(xfar, yfar)
=exp[(-iπ)/4]8πk-ddexp(ikR)Ry Ψnear(x, y0)
+ik(yfar-y0)Ψnear(x, y0)Rdx,
R=[(x-xfar)2+(y0-yfar)2]1/2,k=2π/λ.

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