Abstract

Spatial modulation of liquid crystals can be controlled and adjusted by light polarization, the degree of pretilt on the substrates, anchoring strength, and the experimental geometry. In particular, strong anchoring can affect the liquid crystal orientation in opposite ways, depending on the polarization of the incident light. Here we present a theoretical model that describes the liquid crystal modulation and how it can be controlled and optimized. The model is valid for electric fields with a uniform component that is large with respect to the spatial modulation, a situation typical of spatial light modulators and photorefractive cells.

© 2012 Optical Society of America

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  9. G. Mínguez-Vega, V. R. Supradeepa, O. Mendoza-Yero, and A. M. Weiner, “Reconfigurable all-diffractive optical filters using phase-only spatial light modulators,” Opt. Lett. 35, 2406–2408 (2010).
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    [CrossRef]
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    [CrossRef]
  15. G. Cook, A. V. Glushchenko, V. Y. Reshetnyak, E. R. Beckel, M. A. Saleh, and D. R. Evans, “Liquid crystal inorganic hybrid photorefractives,” Winter Topical Meeting Series, 2008 (IEEE/LEOS, 2008), pp. 129–130.
  16. G. Cook, A. V. Glushchenko, V. Reshetnyak, A. T. Griffith, M. A. Saleh, and D. R. Evans, “Nanoparticle doped organic-inorganic hybrid photorefractives,” Opt. Express 16, 4015–4022 (2008).
    [CrossRef]
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    [CrossRef]
  19. R. R. Shah and N. L. Abbott, “Principles for measurement of chemical exposure based on recognition-driven anchoring transitions in liquid crystals,” Science 293, 1296–1299 (2001).
    [CrossRef]
  20. G. Pawlik, W. Walasik, A. C. Mitus, and I. C. Khoo, “Large gradients of refractive index in nanosphere dispersed liquid crystal metamaterial with inhomogeneous anchoring: Monte Carlo study,” Opt. Mater. 33, 1459–1463 (2011).
    [CrossRef]
  21. K. R. Daly, G. D’Alessandro, and M. Kaczmarek, “Regime independent coupled-wave equations in anisotropic photorefractive media,” Appl. Phys. B: Lasers Opt. 95, 589–596 (2009).
    [CrossRef]
  22. K. R. Daly, G. D’Alessandro, and M. Kaczmarek, “An efficient Q-tensor-based algorithm for liquid crystal alignment away from defects,” SIAM J. Appl. Math. 70, 2844–2860 (2010).
    [CrossRef]
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    [CrossRef]
  24. A. Rapini and M. Papoular, “Distorsion d’une lamelle nematique sous champ magnetique conditions d’ancrage aux parois,” Le Journal de Physique Colloques 30, 54–56 (1969).
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  26. K. R. Daly, S. B. Abbott, G. D’Alessandro, D. C. Smith, and M. Kaczmarek, “Theory of hybrid photorefractive plasmonic liquid crystal cells,” J. Opt. Soc. Am. B 28, 1874–1881 (2011).
    [CrossRef]
  27. R. H. Self, C. P. Please, and T. J. Sluckin, “Deformation of nematic liquid crystals in an electric field,” Eur. J. Appl. Math. 13, 1–23 (2002).
    [CrossRef]
  28. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Oxford University, 1993).
  29. A. Sonnet, A. Kilian, and S. Hess, “Alignment tensor versus director: description of defects in nematic liquid crystals,” Phys. Rev. E 52, 718–722 (1995).
    [CrossRef]

2011 (4)

J. Beeckman, K. Neyts, and P. J. M. Vanbrabant, “Liquid-crystal photonic applications,” Opt. Eng. 50, 081202 (2011).
[CrossRef]

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy.” Laser Photon. Rev. 5, 81–101 (2011).
[CrossRef]

G. Pawlik, W. Walasik, A. C. Mitus, and I. C. Khoo, “Large gradients of refractive index in nanosphere dispersed liquid crystal metamaterial with inhomogeneous anchoring: Monte Carlo study,” Opt. Mater. 33, 1459–1463 (2011).
[CrossRef]

K. R. Daly, S. B. Abbott, G. D’Alessandro, D. C. Smith, and M. Kaczmarek, “Theory of hybrid photorefractive plasmonic liquid crystal cells,” J. Opt. Soc. Am. B 28, 1874–1881 (2011).
[CrossRef]

2010 (3)

2009 (2)

K. R. Daly, G. D’Alessandro, and M. Kaczmarek, “Regime independent coupled-wave equations in anisotropic photorefractive media,” Appl. Phys. B: Lasers Opt. 95, 589–596 (2009).
[CrossRef]

V. O. Kubytskyi, V. Y. Reshetnyak, T. J. Sluckin, and S. J. Cox, “Theory of surface-potential-mediated photorefractivelike effects in liquid crystals,” Phys. Rev. E 79, 11703 (2009).
[CrossRef]

2008 (3)

V. O. Kubytskyi, V. Y. Reshetnyak, T. J. Sluckin, and S. J. Cox, “Simulation of photorefractive effect in thin liquid crystal film,” Mol. Cryst. Liq. Cryst. 489, 204–213 (2008).
[CrossRef]

S. Residori, U. Bortolozzo, and J. P. Huignard, “Slow and fast light in liquid crystal light valves,” Phys. Rev. Lett. 100, 203603 (2008).
[CrossRef]

G. Cook, A. V. Glushchenko, V. Reshetnyak, A. T. Griffith, M. A. Saleh, and D. R. Evans, “Nanoparticle doped organic-inorganic hybrid photorefractives,” Opt. Express 16, 4015–4022 (2008).
[CrossRef]

2006 (1)

U. Bortolozzo, M. G. Clerc, C. Falcon, S. Residori, and R. Rojas, “Localized states in bistable pattern-forming systems,” Phys. Rev. Lett. 96, 214501 (2006).
[CrossRef]

2004 (2)

M. Kaczmarek, A. Dyadyusha, S. Slussarenko, and I. C. Khoo, “The role of surface charge field in two-beam coupling in liquid crystal cells with photoconducting polymer layers,” J. Appl. Phys. 96, 2616–2623 (2004).
[CrossRef]

D. C. Jones and G. Cook, “Theory of beam coupling in a hybrid photorefractive-liquid crystal cell,” Opt. Commun. 232, 399–409 (2004).
[CrossRef]

2002 (1)

R. H. Self, C. P. Please, and T. J. Sluckin, “Deformation of nematic liquid crystals in an electric field,” Eur. J. Appl. Math. 13, 1–23 (2002).
[CrossRef]

2001 (2)

R. R. Shah and N. L. Abbott, “Principles for measurement of chemical exposure based on recognition-driven anchoring transitions in liquid crystals,” Science 293, 1296–1299 (2001).
[CrossRef]

A. Miniewicz, K. Komorowska, J. Vanhanen, and J. Parka, “Surface-assisted optical storage in a nematic liquid crystal cell via photoinduced charge-density modulation,” Org. Electron. 2, 155–163 (2001).
[CrossRef]

1995 (1)

A. Sonnet, A. Kilian, and S. Hess, “Alignment tensor versus director: description of defects in nematic liquid crystals,” Phys. Rev. E 52, 718–722 (1995).
[CrossRef]

1989 (1)

1987 (1)

1982 (1)

1969 (1)

A. Rapini and M. Papoular, “Distorsion d’une lamelle nematique sous champ magnetique conditions d’ancrage aux parois,” Le Journal de Physique Colloques 30, 54–56 (1969).

Abbott, N. L.

R. R. Shah and N. L. Abbott, “Principles for measurement of chemical exposure based on recognition-driven anchoring transitions in liquid crystals,” Science 293, 1296–1299 (2001).
[CrossRef]

Abbott, S. B.

Alberucci, A.

Armitage, D.

Ashley, P. R.

Assanto, G.

Aubourg, P.

Bahadur, B.

B. Bahadur, Liquid Crystals: Applications and Uses (World Scientific, 1990).

Beckel, E. R.

G. Cook, A. V. Glushchenko, V. Y. Reshetnyak, E. R. Beckel, M. A. Saleh, and D. R. Evans, “Liquid crystal inorganic hybrid photorefractives,” Winter Topical Meeting Series, 2008 (IEEE/LEOS, 2008), pp. 129–130.

Beeckman, J.

J. Beeckman, K. Neyts, and P. J. M. Vanbrabant, “Liquid-crystal photonic applications,” Opt. Eng. 50, 081202 (2011).
[CrossRef]

Bernet, S.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy.” Laser Photon. Rev. 5, 81–101 (2011).
[CrossRef]

Billingham, J.

A. C. King, J. Billingham, and S. R. Otto, Differential Equations: Linear, Nonlinear, Ordinary, Partial (Cambridge University, 2003).

Bortolozzo, U.

A. Alberucci, A. Piccardi, U. Bortolozzo, S. Residori, and G. Assanto, “Nematicon all-optical control in liquid crystal light valves,” Opt. Lett. 35, 390–392 (2010).
[CrossRef]

S. Residori, U. Bortolozzo, and J. P. Huignard, “Slow and fast light in liquid crystal light valves,” Phys. Rev. Lett. 100, 203603 (2008).
[CrossRef]

U. Bortolozzo, M. G. Clerc, C. Falcon, S. Residori, and R. Rojas, “Localized states in bistable pattern-forming systems,” Phys. Rev. Lett. 96, 214501 (2006).
[CrossRef]

Clerc, M. G.

U. Bortolozzo, M. G. Clerc, C. Falcon, S. Residori, and R. Rojas, “Localized states in bistable pattern-forming systems,” Phys. Rev. Lett. 96, 214501 (2006).
[CrossRef]

Cook, G.

G. Cook, A. V. Glushchenko, V. Reshetnyak, A. T. Griffith, M. A. Saleh, and D. R. Evans, “Nanoparticle doped organic-inorganic hybrid photorefractives,” Opt. Express 16, 4015–4022 (2008).
[CrossRef]

D. C. Jones and G. Cook, “Theory of beam coupling in a hybrid photorefractive-liquid crystal cell,” Opt. Commun. 232, 399–409 (2004).
[CrossRef]

G. Cook, A. V. Glushchenko, V. Y. Reshetnyak, E. R. Beckel, M. A. Saleh, and D. R. Evans, “Liquid crystal inorganic hybrid photorefractives,” Winter Topical Meeting Series, 2008 (IEEE/LEOS, 2008), pp. 129–130.

Cox, S. J.

V. O. Kubytskyi, V. Y. Reshetnyak, T. J. Sluckin, and S. J. Cox, “Theory of surface-potential-mediated photorefractivelike effects in liquid crystals,” Phys. Rev. E 79, 11703 (2009).
[CrossRef]

V. O. Kubytskyi, V. Y. Reshetnyak, T. J. Sluckin, and S. J. Cox, “Simulation of photorefractive effect in thin liquid crystal film,” Mol. Cryst. Liq. Cryst. 489, 204–213 (2008).
[CrossRef]

D’Alessandro, G.

K. R. Daly, S. B. Abbott, G. D’Alessandro, D. C. Smith, and M. Kaczmarek, “Theory of hybrid photorefractive plasmonic liquid crystal cells,” J. Opt. Soc. Am. B 28, 1874–1881 (2011).
[CrossRef]

K. R. Daly, G. D’Alessandro, and M. Kaczmarek, “An efficient Q-tensor-based algorithm for liquid crystal alignment away from defects,” SIAM J. Appl. Math. 70, 2844–2860 (2010).
[CrossRef]

K. R. Daly, G. D’Alessandro, and M. Kaczmarek, “Regime independent coupled-wave equations in anisotropic photorefractive media,” Appl. Phys. B: Lasers Opt. 95, 589–596 (2009).
[CrossRef]

Daly, K. R.

K. R. Daly, S. B. Abbott, G. D’Alessandro, D. C. Smith, and M. Kaczmarek, “Theory of hybrid photorefractive plasmonic liquid crystal cells,” J. Opt. Soc. Am. B 28, 1874–1881 (2011).
[CrossRef]

K. R. Daly, G. D’Alessandro, and M. Kaczmarek, “An efficient Q-tensor-based algorithm for liquid crystal alignment away from defects,” SIAM J. Appl. Math. 70, 2844–2860 (2010).
[CrossRef]

K. R. Daly, G. D’Alessandro, and M. Kaczmarek, “Regime independent coupled-wave equations in anisotropic photorefractive media,” Appl. Phys. B: Lasers Opt. 95, 589–596 (2009).
[CrossRef]

Davis, J. H.

de Gennes, P. G.

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Oxford University, 1993).

Dyadyusha, A.

M. Kaczmarek, A. Dyadyusha, S. Slussarenko, and I. C. Khoo, “The role of surface charge field in two-beam coupling in liquid crystal cells with photoconducting polymer layers,” J. Appl. Phys. 96, 2616–2623 (2004).
[CrossRef]

Eades, W. D.

Efron, U.

U. Efron, Spatial Light Modulator Technology: Materials, Devices, and Applications (Dekker, 1995).

Evans, D. R.

G. Cook, A. V. Glushchenko, V. Reshetnyak, A. T. Griffith, M. A. Saleh, and D. R. Evans, “Nanoparticle doped organic-inorganic hybrid photorefractives,” Opt. Express 16, 4015–4022 (2008).
[CrossRef]

G. Cook, A. V. Glushchenko, V. Y. Reshetnyak, E. R. Beckel, M. A. Saleh, and D. R. Evans, “Liquid crystal inorganic hybrid photorefractives,” Winter Topical Meeting Series, 2008 (IEEE/LEOS, 2008), pp. 129–130.

Falcon, C.

U. Bortolozzo, M. G. Clerc, C. Falcon, S. Residori, and R. Rojas, “Localized states in bistable pattern-forming systems,” Phys. Rev. Lett. 96, 214501 (2006).
[CrossRef]

Glushchenko, A. V.

G. Cook, A. V. Glushchenko, V. Reshetnyak, A. T. Griffith, M. A. Saleh, and D. R. Evans, “Nanoparticle doped organic-inorganic hybrid photorefractives,” Opt. Express 16, 4015–4022 (2008).
[CrossRef]

G. Cook, A. V. Glushchenko, V. Y. Reshetnyak, E. R. Beckel, M. A. Saleh, and D. R. Evans, “Liquid crystal inorganic hybrid photorefractives,” Winter Topical Meeting Series, 2008 (IEEE/LEOS, 2008), pp. 129–130.

Griffith, A. T.

Hareng, M.

Hess, S.

A. Sonnet, A. Kilian, and S. Hess, “Alignment tensor versus director: description of defects in nematic liquid crystals,” Phys. Rev. E 52, 718–722 (1995).
[CrossRef]

Huignard, J. P.

Jesacher, A.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy.” Laser Photon. Rev. 5, 81–101 (2011).
[CrossRef]

Jones, D. C.

D. C. Jones and G. Cook, “Theory of beam coupling in a hybrid photorefractive-liquid crystal cell,” Opt. Commun. 232, 399–409 (2004).
[CrossRef]

Kaczmarek, M.

K. R. Daly, S. B. Abbott, G. D’Alessandro, D. C. Smith, and M. Kaczmarek, “Theory of hybrid photorefractive plasmonic liquid crystal cells,” J. Opt. Soc. Am. B 28, 1874–1881 (2011).
[CrossRef]

K. R. Daly, G. D’Alessandro, and M. Kaczmarek, “An efficient Q-tensor-based algorithm for liquid crystal alignment away from defects,” SIAM J. Appl. Math. 70, 2844–2860 (2010).
[CrossRef]

K. R. Daly, G. D’Alessandro, and M. Kaczmarek, “Regime independent coupled-wave equations in anisotropic photorefractive media,” Appl. Phys. B: Lasers Opt. 95, 589–596 (2009).
[CrossRef]

M. Kaczmarek, A. Dyadyusha, S. Slussarenko, and I. C. Khoo, “The role of surface charge field in two-beam coupling in liquid crystal cells with photoconducting polymer layers,” J. Appl. Phys. 96, 2616–2623 (2004).
[CrossRef]

Khoo, I. C.

G. Pawlik, W. Walasik, A. C. Mitus, and I. C. Khoo, “Large gradients of refractive index in nanosphere dispersed liquid crystal metamaterial with inhomogeneous anchoring: Monte Carlo study,” Opt. Mater. 33, 1459–1463 (2011).
[CrossRef]

M. Kaczmarek, A. Dyadyusha, S. Slussarenko, and I. C. Khoo, “The role of surface charge field in two-beam coupling in liquid crystal cells with photoconducting polymer layers,” J. Appl. Phys. 96, 2616–2623 (2004).
[CrossRef]

I. C. Khoo, Liquid Crystals (Wiley, 2007).

Kilian, A.

A. Sonnet, A. Kilian, and S. Hess, “Alignment tensor versus director: description of defects in nematic liquid crystals,” Phys. Rev. E 52, 718–722 (1995).
[CrossRef]

King, A. C.

A. C. King, J. Billingham, and S. R. Otto, Differential Equations: Linear, Nonlinear, Ordinary, Partial (Cambridge University, 2003).

Komorowska, K.

A. Miniewicz, K. Komorowska, J. Vanhanen, and J. Parka, “Surface-assisted optical storage in a nematic liquid crystal cell via photoinduced charge-density modulation,” Org. Electron. 2, 155–163 (2001).
[CrossRef]

Kubytskyi, V. O.

V. O. Kubytskyi, V. Y. Reshetnyak, T. J. Sluckin, and S. J. Cox, “Theory of surface-potential-mediated photorefractivelike effects in liquid crystals,” Phys. Rev. E 79, 11703 (2009).
[CrossRef]

V. O. Kubytskyi, V. Y. Reshetnyak, T. J. Sluckin, and S. J. Cox, “Simulation of photorefractive effect in thin liquid crystal film,” Mol. Cryst. Liq. Cryst. 489, 204–213 (2008).
[CrossRef]

Maurer, C.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy.” Laser Photon. Rev. 5, 81–101 (2011).
[CrossRef]

Mendoza-Yero, O.

Mínguez-Vega, G.

Miniewicz, A.

A. Miniewicz, K. Komorowska, J. Vanhanen, and J. Parka, “Surface-assisted optical storage in a nematic liquid crystal cell via photoinduced charge-density modulation,” Org. Electron. 2, 155–163 (2001).
[CrossRef]

Mitus, A. C.

G. Pawlik, W. Walasik, A. C. Mitus, and I. C. Khoo, “Large gradients of refractive index in nanosphere dispersed liquid crystal metamaterial with inhomogeneous anchoring: Monte Carlo study,” Opt. Mater. 33, 1459–1463 (2011).
[CrossRef]

Mullen, R. A.

Neyts, K.

J. Beeckman, K. Neyts, and P. J. M. Vanbrabant, “Liquid-crystal photonic applications,” Opt. Eng. 50, 081202 (2011).
[CrossRef]

Otto, S. R.

A. C. King, J. Billingham, and S. R. Otto, Differential Equations: Linear, Nonlinear, Ordinary, Partial (Cambridge University, 2003).

Papoular, M.

A. Rapini and M. Papoular, “Distorsion d’une lamelle nematique sous champ magnetique conditions d’ancrage aux parois,” Le Journal de Physique Colloques 30, 54–56 (1969).

Parka, J.

A. Miniewicz, K. Komorowska, J. Vanhanen, and J. Parka, “Surface-assisted optical storage in a nematic liquid crystal cell via photoinduced charge-density modulation,” Org. Electron. 2, 155–163 (2001).
[CrossRef]

Pawlik, G.

G. Pawlik, W. Walasik, A. C. Mitus, and I. C. Khoo, “Large gradients of refractive index in nanosphere dispersed liquid crystal metamaterial with inhomogeneous anchoring: Monte Carlo study,” Opt. Mater. 33, 1459–1463 (2011).
[CrossRef]

Piccardi, A.

Please, C. P.

R. H. Self, C. P. Please, and T. J. Sluckin, “Deformation of nematic liquid crystals in an electric field,” Eur. J. Appl. Math. 13, 1–23 (2002).
[CrossRef]

Prost, J.

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Oxford University, 1993).

Rapini, A.

A. Rapini and M. Papoular, “Distorsion d’une lamelle nematique sous champ magnetique conditions d’ancrage aux parois,” Le Journal de Physique Colloques 30, 54–56 (1969).

Reshetnyak, V.

Reshetnyak, V. Y.

V. O. Kubytskyi, V. Y. Reshetnyak, T. J. Sluckin, and S. J. Cox, “Theory of surface-potential-mediated photorefractivelike effects in liquid crystals,” Phys. Rev. E 79, 11703 (2009).
[CrossRef]

V. O. Kubytskyi, V. Y. Reshetnyak, T. J. Sluckin, and S. J. Cox, “Simulation of photorefractive effect in thin liquid crystal film,” Mol. Cryst. Liq. Cryst. 489, 204–213 (2008).
[CrossRef]

G. Cook, A. V. Glushchenko, V. Y. Reshetnyak, E. R. Beckel, M. A. Saleh, and D. R. Evans, “Liquid crystal inorganic hybrid photorefractives,” Winter Topical Meeting Series, 2008 (IEEE/LEOS, 2008), pp. 129–130.

Residori, S.

A. Alberucci, A. Piccardi, U. Bortolozzo, S. Residori, and G. Assanto, “Nematicon all-optical control in liquid crystal light valves,” Opt. Lett. 35, 390–392 (2010).
[CrossRef]

S. Residori, U. Bortolozzo, and J. P. Huignard, “Slow and fast light in liquid crystal light valves,” Phys. Rev. Lett. 100, 203603 (2008).
[CrossRef]

U. Bortolozzo, M. G. Clerc, C. Falcon, S. Residori, and R. Rojas, “Localized states in bistable pattern-forming systems,” Phys. Rev. Lett. 96, 214501 (2006).
[CrossRef]

Ritsch-Marte, M.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy.” Laser Photon. Rev. 5, 81–101 (2011).
[CrossRef]

Rojas, R.

U. Bortolozzo, M. G. Clerc, C. Falcon, S. Residori, and R. Rojas, “Localized states in bistable pattern-forming systems,” Phys. Rev. Lett. 96, 214501 (2006).
[CrossRef]

Saleh, M. A.

G. Cook, A. V. Glushchenko, V. Reshetnyak, A. T. Griffith, M. A. Saleh, and D. R. Evans, “Nanoparticle doped organic-inorganic hybrid photorefractives,” Opt. Express 16, 4015–4022 (2008).
[CrossRef]

G. Cook, A. V. Glushchenko, V. Y. Reshetnyak, E. R. Beckel, M. A. Saleh, and D. R. Evans, “Liquid crystal inorganic hybrid photorefractives,” Winter Topical Meeting Series, 2008 (IEEE/LEOS, 2008), pp. 129–130.

Self, R. H.

R. H. Self, C. P. Please, and T. J. Sluckin, “Deformation of nematic liquid crystals in an electric field,” Eur. J. Appl. Math. 13, 1–23 (2002).
[CrossRef]

Shah, R. R.

R. R. Shah and N. L. Abbott, “Principles for measurement of chemical exposure based on recognition-driven anchoring transitions in liquid crystals,” Science 293, 1296–1299 (2001).
[CrossRef]

Sluckin, T. J.

V. O. Kubytskyi, V. Y. Reshetnyak, T. J. Sluckin, and S. J. Cox, “Theory of surface-potential-mediated photorefractivelike effects in liquid crystals,” Phys. Rev. E 79, 11703 (2009).
[CrossRef]

V. O. Kubytskyi, V. Y. Reshetnyak, T. J. Sluckin, and S. J. Cox, “Simulation of photorefractive effect in thin liquid crystal film,” Mol. Cryst. Liq. Cryst. 489, 204–213 (2008).
[CrossRef]

R. H. Self, C. P. Please, and T. J. Sluckin, “Deformation of nematic liquid crystals in an electric field,” Eur. J. Appl. Math. 13, 1–23 (2002).
[CrossRef]

Slussarenko, S.

M. Kaczmarek, A. Dyadyusha, S. Slussarenko, and I. C. Khoo, “The role of surface charge field in two-beam coupling in liquid crystal cells with photoconducting polymer layers,” J. Appl. Phys. 96, 2616–2623 (2004).
[CrossRef]

Smith, D. C.

Sonnet, A.

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K. R. Daly, G. D’Alessandro, and M. Kaczmarek, “Regime independent coupled-wave equations in anisotropic photorefractive media,” Appl. Phys. B: Lasers Opt. 95, 589–596 (2009).
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M. Kaczmarek, A. Dyadyusha, S. Slussarenko, and I. C. Khoo, “The role of surface charge field in two-beam coupling in liquid crystal cells with photoconducting polymer layers,” J. Appl. Phys. 96, 2616–2623 (2004).
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C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy.” Laser Photon. Rev. 5, 81–101 (2011).
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V. O. Kubytskyi, V. Y. Reshetnyak, T. J. Sluckin, and S. J. Cox, “Simulation of photorefractive effect in thin liquid crystal film,” Mol. Cryst. Liq. Cryst. 489, 204–213 (2008).
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D. C. Jones and G. Cook, “Theory of beam coupling in a hybrid photorefractive-liquid crystal cell,” Opt. Commun. 232, 399–409 (2004).
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[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Opt. Mater. (1)

G. Pawlik, W. Walasik, A. C. Mitus, and I. C. Khoo, “Large gradients of refractive index in nanosphere dispersed liquid crystal metamaterial with inhomogeneous anchoring: Monte Carlo study,” Opt. Mater. 33, 1459–1463 (2011).
[CrossRef]

Org. Electron. (1)

A. Miniewicz, K. Komorowska, J. Vanhanen, and J. Parka, “Surface-assisted optical storage in a nematic liquid crystal cell via photoinduced charge-density modulation,” Org. Electron. 2, 155–163 (2001).
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V. O. Kubytskyi, V. Y. Reshetnyak, T. J. Sluckin, and S. J. Cox, “Theory of surface-potential-mediated photorefractivelike effects in liquid crystals,” Phys. Rev. E 79, 11703 (2009).
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Figures (8)

Fig. 1.
Fig. 1.

Diagram of a photorefractive cell.

Fig. 2.
Fig. 2.

Plots of ϕ0 as a function of the distance into the cell for different values of the anchoring energy (top) and of the pretilt angle at y=0 (bottom).

Fig. 3.
Fig. 3.

Coefficients of the director field for the TE and TM configurations as a function of the distance into the cell for different values of the anchoring energy (top) and pretilt angle (bottom). Parameter values: ψ0=5V (both), ϕs=0 (top), and Ws=106 (bottom).

Fig. 4.
Fig. 4.

Coefficients of the director field for the in-plane configuration as a function of the distance into the cell for different values of the anchoring energy (top) and pretilt angle (bottom). Parameter values: ψ0=5V (both), ϕs=0 (top), and Ws=106 (bottom).

Fig. 5.
Fig. 5.

Schematic diagram of the photorefractive cell in the TE/TM (a) and in-plane; (b) configurations. The facets of the cell are parallel to the (x,z) plane. The small thick (gold) lines indicate the surface alignment of the liquid crystal in the case of zero pretilt and correspond to θ=π/2 and ϕ=0 in both configurations. The dashed double arrows indicate the direction of polarization of the light electric field at input. The uniform alignment field ψ0e^y is parallel to the y-axis (green arrow), while the modulated potential is a function of z and x in the TE/TM and in-plane configurations, respectively.

Fig. 6.
Fig. 6.

Contour plots of the first order diffraction efficiency in the TE configuration as a function of the applied voltage and (left) the pretilt at anchoring energy Ws=106 or (right) the logarithm of the anchoring energy at zero pretilt angle for 0 (top) and 35° cell tilt (bottom). The color coding is logarithmic base 10, with 1 corresponding to 10% of the input power being transferred from the input beam to the 1 diffracted order.

Fig. 7.
Fig. 7.

Same as Fig. 6, but for the TM configuration.

Fig. 8.
Fig. 8.

Same as Fig. 6 but for the in-plane configuration.

Tables (1)

Tables Icon

Table 1. Default Parameter Values Used in All Figures, Comparable to Typical Values for the Liquid Crystal Compound E7

Equations (48)

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ψ(x,0,z)=ψ0+ψ1cos(Kg·x),
ϵ[2ψx2+2ψz2]+ϵ2ψy2=0.
ζ(x)=sinh[ϱKg(1y)]Kgsinh(ϱKg)cos(Kg·x),
E=ψ0[e^yψ˜1ζ(x)].
ζx(x)=sinh[ϱKg(1y)]sinh(ϱKg)sin(β)sin(Kg·x),
ζy(x)=ϱcosh[ϱKg(1y)]sinh(ϱKg)cos(Kg·x),
ζz(x)=sinh[ϱKg(1y)]sinh(ϱKg)cos(β)sin(Kg·x).
F=VFd(n^)+Fe(n^)dV+SFs(n^)dS,
Fd=12|θ|2+12sin2θ|ϕ|2,
Fe=χa[sin2θcos2ϕEx2+sin2θsin2ϕEy2+cos2θEz2+sin2θcos2ϕExEy+sin2θcosϕExEz+sin2θsinϕEyEz],
Fs=Ws2[(ϕϕs)2+(θθs)2],
η=Kdε0Δε1ψ0andV1=2KgΔψε0ΔεKdψ0,
2θ12sin2θ|ϕ|2+1η2{sin2θsin2ϕ[1+ηV1ζy(x)]+ηV1[cos2θsinϕζz(x)+12sin2θcos2ϕζx(x)]}=0,
·(sin2θϕ)+1η2{sin2ϕsin2θ[1+ηV1ζy(x))+ηV1[sin2cos2ϕζx(x)+12cosϕsin2θζz(x)]}=0,
θyW˜sη(θθs)|y=0=0,ϕyW˜sη(ϕϕs)|y=0=0.
2θ012sin2θ0|ϕ0|2+1η2sin2θ0sin2ϕ0=0
·(sin2θ0ϕ0)+1η2sin2ϕ0sin2θ0=0.
sin2ϕ0(o)sin2θ0(o)=0,sin2ϕ0(o)sin2θ0(o)=0.
2ϕ0(i)y¯2+sin2ϕ0(i)=0.
(ϕ0(i)y¯)2cos2ϕ0(i)=C0.
ϕ0(i)=arctan(C12e22y¯12C1e2y¯).
22W˜scosϕ0(i)(ϕ0(i)ϕs)|y=0=0.
C1=secϕ0(i)tanϕ0(i)|y=0.
2θ1+θ1|ϕ0|2+1η2{2θ1sin2ϕ0V1sinϕ0ζz(x)}=0
2ϕ1+1η2{2ϕ1cos2ϕ0+V1[sin2ϕ0ζy(x)cos2ϕ0ζx(x)]}=0,
θ1yW˜sηθ1|y=0andϕ1yW˜sηϕ1|y=0.
θ1(o)=V12ζz(x)andϕ1(o)=V12ζx(x).
2θ1(i)y2+2θ1(i)cos2ϕ0(i)=Fθ1(ϕ0(i)),
2ϕ1(i)y2+2ϕ1(i)cos2ϕ0(i)=Fϕ1(ϕ0(i)),
Fθ1(ϕ0(i))=sinϕ0(i)V1ζz(x),Fϕ1(ϕ0(i))=V1[cos2ϕ0(i)ζx(x)sin2ϕ0(i)ζy(x)].
θ1(i)=V12e2yCθ+C12e22ye22y+C12ζz(x),
ϕ1(i)=V12[C1(e2y+2e2y2y)+Cϕce2ye22y+C12]ζy(x)+V12[1+e2yCϕse22y+C12]ζx(x).
Cϕc=C1[(1+C12)W˜s2(1+3C12)](1+C12)W˜s+2(1C12),
Cϕs=(C12+1)2W˜s(W˜sW˜sC122+2C12),
Cθ=(C141)W˜s+42C12(C12+1)W˜s2(C121).
θ=(θ0(i,0)+θ0(i,1)θ0(o))+η(θ1(i,0)+θ1(i,1)θ1(o)),ϕ=(ϕ0(i,0)+ϕ0(i,1)ϕ0(o))+η(ϕ1(i,0)+ϕ1(i,1)ϕ1(o)).
ϵu=ϵ+2ϵ3andΔϵ=ϵϵ.
Q=Qu+η(Qϕϕ1+Qθθ1),
Qu=12((1+cos2ϕ0)13sin2ϕ00sin2ϕ0(1cos2ϕ0)1300013),
Qϕ=(sin2ϕ0cos2ϕ00cos2ϕ0sin2ϕ00000),Qθ=(00cosϕ000sinϕ0cosϕ0sinϕ00).
κn,n±1=E^(n)·[Qϕ(ϕ1,c+iϕ1,s)+iQθθ1,s]E^(n±1),
Q=p=15apT(p),
T(1)=[e^xe^xe^ye^y+2e^ze^z],T(2)=[e^xe^xe^ye^y],T(3)=[e^xe^y+e^ye^x],T(4)=[e^xe^z+e^ze^x],T(5)=[e^ye^z+e^ze^y].
er=a1anuma1,
κn,n±1(E,E)=Ex(n)a2Ex(n±1),
κn,n±1(E,M)=a3(Ex(n)Ey(n±1)+Ey(n)Ex(n±1))+a4(Ex(n)Ez(n±1)+Ez(n)Ex(n±1)),
κn,n±1(M,M)=Ey(n)a2Ey(n±1)+a5(Ey(n)Ez(n±1)+Ez(n)Ey(n±1)),
κn,n±1(P,P)=a2(Ex(n)Ex(n+1)Ey(n)Ey(n+1))+a3(Ex(n)Ey(n+1)+Ey(n)Ex(n+1)),

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