Abstract

Formation of a desired liquid crystal (LC) director distribution by the use of inhomogeneous anchoring and pre-tilt angle for electrically controlled diffractive optical elements (DOE) is studied. Such LC DOE can have high periodicity and diffraction efficiency. At the same time they are free of constructive regularities, e.g. a periodic arrangement of the electrodes or thickness deviations, which have undesired impact on diffractive characteristics of LC DOE of other types. We focus on evaluation of potential functional abilities of LC DOE with inhomogeneous alignment. The reasons causing restriction of the LC DOE diffraction efficiency and periodicity are considered. Approaches for improvement of characteristics of the LC DOE are discussed.

© 2012 OSA

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2012 (1)

S. Gauza, P. Kula, R. Dabrowski, G. Sasnouski, and V. Lapanik, “High optical anisotropy nematic single compounds and mixtures,” Trans. Electr. Electron. Mater. 13(1), 2–5 (2012).
[CrossRef]

2011 (3)

J. Beeckman, K. Neyts, and P. J. M. Vanbrabant, “Liquid-crystal photonic applications,” Opt. Eng. 50(8), 081202 (2011).
[CrossRef]

T. M. de Jong, D. K. G. de Boer, and C. W. M. Bastiaansen, “Surface-relief and polarization gratings for solar concentrators,” Opt. Express 19(16), 15127–15142 (2011).
[CrossRef] [PubMed]

M. C. Tseng, F. Fan, C. Y. Lee, A. Murauski, V. Chigrinov, and H. S. Kwok, “Tunable lens by spatially varying liquid crystal pretilt angles,” J. Appl. Phys. 109(8), 083109 (2011).
[CrossRef]

2010 (2)

A. V. Dubtsov, S. V. Pasechnik, A. D. Kiselev, D. V. Shmeliova, and V. G. Chigrinov, “Electrically assisted light-induced azimuthal gliding of the nematic liquid-crystal easy axis on photoaligned substrates,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82(1), 011702 (2010).
[CrossRef] [PubMed]

S. Valyukh, I. Valyukh, V. Chigrinov, H. S. Kwok, and H. Arwin, “Liquid crystal light deflecting devices based on nonuniform anchoring,” Appl. Phys. Lett. 97(23), 231120 (2010).
[CrossRef]

2009 (2)

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[CrossRef]

T. Nanba, H. Naito, K. Matsukawa, and A. Sugimura, “Weak anchoring of nematic liquid crystals on photo-induced surface relief gratings of organic polysilane,” Thin Solid Films 518(2), 767–770 (2009).
[CrossRef]

2008 (3)

F. S. Y. Yeung, Y. L. J. Ho, Y. W. Li, and H. S. Kwok, “Liquid crystal alignment layer with controllable anchoring energies,” J Disp. Technol. 4(1), 24–27 (2008).
[CrossRef]

L. Shi, P. F. McManamon, and P. J. Bos, “Liquid crystal optical phase plate with a variable in-plane gradient,” J. Appl. Phys. 104(3), 033109 (2008).
[CrossRef]

A. Muravsky, A. Murauski, V. Chigrinov, and H. S. Kwok, “Light printing of grayscale pixel images on optical rewritable electronic paper,” Jpn. J. Appl. Phys. 47(8), 6347–6353 (2008).
[CrossRef]

2007 (3)

K. E. Vaughn, M. Sousa, D. Kang, and C. Rosenblatt, “Continuous control of liquid crystal pretilt angle from homeotropic to planar,” Appl. Phys. Lett. 90(19), 194102 (2007).
[CrossRef]

J. H. Seo, H. J. Jang, S. R. Lee, T. H. Yoon, J. C. Kim, I. B. Kang, and C. H. Oh, “Wide pretilt angle control of liquid crystal display device by ion beam exposure on the vertical aligning layer,” Jpn. J. Appl. Phys. 46(44), L1074–L1076 (2007).
[CrossRef]

C. Jenkins, R. Bingham, K. Moore, and G. D. Love, “Ray equation for a spatially variable uniaxial crystal and its use in the optical design of liquid-crystal lenses,” J. Opt. Soc. Am. A 24(7), 2089–2096 (2007).
[CrossRef] [PubMed]

2006 (4)

F. S. Yeung, J. Y. Ho, Y. W. Li, F. C. Xie, O. K. Tsui, P. Sheng, and H. S. Kwok, “Variable liquid crystal pretilt angles by nanostructured surfaces,” Appl. Phys. Lett. 88(5), 051910 (2006).
[CrossRef]

M. Ye, Y. Yokoyama, and S. Sato, “Liquid crystal lens prepared utilizing patterned molecular orientations on cell walls,” Appl. Phys. Lett. 89(14), 141112 (2006).
[CrossRef]

B. Bellini, M. A. Geday, N. Bennis, A. Spadlo, X. Quintana, J. M. Oton, and R. Dabrowski, “Design and simulation of single-electrode liquid crystal phased arrays,” Opto-Electron. Rev. 14(4), 269–273 (2006).
[CrossRef]

A. Akatay, C. Ataman, and H. Urey, “High-resolution beam steering using microlens arrays,” Opt. Lett. 31(19), 2861–2863 (2006).
[CrossRef] [PubMed]

2005 (3)

E. Hällstig, T. Martin, L. Sjöqvist, and M. Lindgren, “Polarization properties of a nematic liquid-crystal spatial light modulator for phase modulation,” J. Opt. Soc. Am. A 22(1), 177–184 (2005).
[CrossRef] [PubMed]

X. Wang, B. Wang, P. J. Bos, P. F. Mcmanamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid-crystal optical phased array,” J. Appl. Phys. 98(7), 073101 (2005).
[CrossRef]

A. D. Kiselev, V. Chigrinov, and D. D. Huang, “Photoinduced ordering and anchoring properties of azo-dye films,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(6), 061703 (2005).
[CrossRef] [PubMed]

2004 (3)

B. Apter, U. Efron, and E. Bahat-Treidel, “On the fringing-field effect in liquid-crystal beam-steering devices,” Appl. Opt. 43(1), 11–19 (2004).
[CrossRef] [PubMed]

J. L. D. Bougrenet and D. L. Tocnaye, “A polymer-dispersed liquid crystal-based dynamic gain equalizer,” Liq. Cryst. 31, 241–269 (2004).

S. Gauza, C. H. Wen, S. T. Wu, N. Janarthanan, and C. S. Hsu, “Super high birefringence isothiocyanato biphenyl-bistolane liquid crystals,” Jpn. J. Appl. Phys. 43(11A), 7634–7638 (2004).
[CrossRef]

2001 (1)

2000 (1)

1996 (1)

J. B. Davies, S. Day, F. Di Pasquale, and F. A. Fernandez, “Finite element modelling in 2-D of nematic liquid crystal structures,” Electron. Lett. 32(6), 582–583 (1996).
[CrossRef]

1983 (1)

D. W. Berreman, “Numerical modeling of twisted nematic devices,” Philos. Trans. R. Soc. Lond. A 309(1507), 203–216 (1983).
[CrossRef]

1976 (1)

J. Nehring, A. R. Kmetz, and T. J. Scheffer, “Analysis of weak-boundary-coupling effects in liquid crystal displays,” J. Appl. Phys. 47(3), 850–857 (1976).
[CrossRef]

1972 (1)

1969 (1)

A. Rapini and M. Papoular, “Distorsion d’une lamelle nematique sous champ magnetique conditions d’ancrage aux parois,” J. Phys. (Paris), Colloq. 30, 54–56 (1969).

1941 (1)

Akatay, A.

Anderson, J. A.

Anderson, J. E.

X. Wang, B. Wang, P. J. Bos, P. F. Mcmanamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid-crystal optical phased array,” J. Appl. Phys. 98(7), 073101 (2005).
[CrossRef]

Apter, B.

Arwin, H.

S. Valyukh, I. Valyukh, V. Chigrinov, H. S. Kwok, and H. Arwin, “Liquid crystal light deflecting devices based on nonuniform anchoring,” Appl. Phys. Lett. 97(23), 231120 (2010).
[CrossRef]

Ataman, C.

Bahat-Treidel, E.

Bastiaansen, C. W. M.

Beeckman, J.

J. Beeckman, K. Neyts, and P. J. M. Vanbrabant, “Liquid-crystal photonic applications,” Opt. Eng. 50(8), 081202 (2011).
[CrossRef]

Bellini, B.

B. Bellini, M. A. Geday, N. Bennis, A. Spadlo, X. Quintana, J. M. Oton, and R. Dabrowski, “Design and simulation of single-electrode liquid crystal phased arrays,” Opto-Electron. Rev. 14(4), 269–273 (2006).
[CrossRef]

Bennis, N.

B. Bellini, M. A. Geday, N. Bennis, A. Spadlo, X. Quintana, J. M. Oton, and R. Dabrowski, “Design and simulation of single-electrode liquid crystal phased arrays,” Opto-Electron. Rev. 14(4), 269–273 (2006).
[CrossRef]

Berreman, D. W.

D. W. Berreman, “Numerical modeling of twisted nematic devices,” Philos. Trans. R. Soc. Lond. A 309(1507), 203–216 (1983).
[CrossRef]

D. W. Berreman, “Optics in stratified and anisotropic media: 4x4-matrix formation,” J. Opt. Soc. Am. 62(4), 502–510 (1972).
[CrossRef]

Bingham, R.

Bos, P. J.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[CrossRef]

L. Shi, P. F. McManamon, and P. J. Bos, “Liquid crystal optical phase plate with a variable in-plane gradient,” J. Appl. Phys. 104(3), 033109 (2008).
[CrossRef]

X. Wang, B. Wang, P. J. Bos, P. F. Mcmanamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid-crystal optical phased array,” J. Appl. Phys. 98(7), 073101 (2005).
[CrossRef]

C. M. Titus, J. R. Kelly, E. C. Gartland, S. V. Shiyanovskii, J. A. Anderson, and P. J. Bos, “Asymmetric transmissive behavior of liquid-crystal diffraction gratings,” Opt. Lett. 26(15), 1188–1190 (2001).
[CrossRef] [PubMed]

Bougrenet, J. L. D.

J. L. D. Bougrenet and D. L. Tocnaye, “A polymer-dispersed liquid crystal-based dynamic gain equalizer,” Liq. Cryst. 31, 241–269 (2004).

Chigrinov, V.

M. C. Tseng, F. Fan, C. Y. Lee, A. Murauski, V. Chigrinov, and H. S. Kwok, “Tunable lens by spatially varying liquid crystal pretilt angles,” J. Appl. Phys. 109(8), 083109 (2011).
[CrossRef]

S. Valyukh, I. Valyukh, V. Chigrinov, H. S. Kwok, and H. Arwin, “Liquid crystal light deflecting devices based on nonuniform anchoring,” Appl. Phys. Lett. 97(23), 231120 (2010).
[CrossRef]

A. Muravsky, A. Murauski, V. Chigrinov, and H. S. Kwok, “Light printing of grayscale pixel images on optical rewritable electronic paper,” Jpn. J. Appl. Phys. 47(8), 6347–6353 (2008).
[CrossRef]

A. D. Kiselev, V. Chigrinov, and D. D. Huang, “Photoinduced ordering and anchoring properties of azo-dye films,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(6), 061703 (2005).
[CrossRef] [PubMed]

Chigrinov, V. G.

A. V. Dubtsov, S. V. Pasechnik, A. D. Kiselev, D. V. Shmeliova, and V. G. Chigrinov, “Electrically assisted light-induced azimuthal gliding of the nematic liquid-crystal easy axis on photoaligned substrates,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82(1), 011702 (2010).
[CrossRef] [PubMed]

Dabrowski, R.

S. Gauza, P. Kula, R. Dabrowski, G. Sasnouski, and V. Lapanik, “High optical anisotropy nematic single compounds and mixtures,” Trans. Electr. Electron. Mater. 13(1), 2–5 (2012).
[CrossRef]

B. Bellini, M. A. Geday, N. Bennis, A. Spadlo, X. Quintana, J. M. Oton, and R. Dabrowski, “Design and simulation of single-electrode liquid crystal phased arrays,” Opto-Electron. Rev. 14(4), 269–273 (2006).
[CrossRef]

Davies, J. B.

J. B. Davies, S. Day, F. Di Pasquale, and F. A. Fernandez, “Finite element modelling in 2-D of nematic liquid crystal structures,” Electron. Lett. 32(6), 582–583 (1996).
[CrossRef]

Day, S.

J. B. Davies, S. Day, F. Di Pasquale, and F. A. Fernandez, “Finite element modelling in 2-D of nematic liquid crystal structures,” Electron. Lett. 32(6), 582–583 (1996).
[CrossRef]

de Boer, D. K. G.

de Jong, T. M.

Di Pasquale, F.

J. B. Davies, S. Day, F. Di Pasquale, and F. A. Fernandez, “Finite element modelling in 2-D of nematic liquid crystal structures,” Electron. Lett. 32(6), 582–583 (1996).
[CrossRef]

Dubtsov, A. V.

A. V. Dubtsov, S. V. Pasechnik, A. D. Kiselev, D. V. Shmeliova, and V. G. Chigrinov, “Electrically assisted light-induced azimuthal gliding of the nematic liquid-crystal easy axis on photoaligned substrates,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82(1), 011702 (2010).
[CrossRef] [PubMed]

Efron, U.

Escuti, M. J.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[CrossRef]

Fan, F.

M. C. Tseng, F. Fan, C. Y. Lee, A. Murauski, V. Chigrinov, and H. S. Kwok, “Tunable lens by spatially varying liquid crystal pretilt angles,” J. Appl. Phys. 109(8), 083109 (2011).
[CrossRef]

Fernandez, F. A.

J. B. Davies, S. Day, F. Di Pasquale, and F. A. Fernandez, “Finite element modelling in 2-D of nematic liquid crystal structures,” Electron. Lett. 32(6), 582–583 (1996).
[CrossRef]

Gartland, E. C.

Gauza, S.

S. Gauza, P. Kula, R. Dabrowski, G. Sasnouski, and V. Lapanik, “High optical anisotropy nematic single compounds and mixtures,” Trans. Electr. Electron. Mater. 13(1), 2–5 (2012).
[CrossRef]

S. Gauza, C. H. Wen, S. T. Wu, N. Janarthanan, and C. S. Hsu, “Super high birefringence isothiocyanato biphenyl-bistolane liquid crystals,” Jpn. J. Appl. Phys. 43(11A), 7634–7638 (2004).
[CrossRef]

Geday, M. A.

B. Bellini, M. A. Geday, N. Bennis, A. Spadlo, X. Quintana, J. M. Oton, and R. Dabrowski, “Design and simulation of single-electrode liquid crystal phased arrays,” Opto-Electron. Rev. 14(4), 269–273 (2006).
[CrossRef]

Hällstig, E.

Heikenfeld, J.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[CrossRef]

Ho, J. Y.

F. S. Yeung, J. Y. Ho, Y. W. Li, F. C. Xie, O. K. Tsui, P. Sheng, and H. S. Kwok, “Variable liquid crystal pretilt angles by nanostructured surfaces,” Appl. Phys. Lett. 88(5), 051910 (2006).
[CrossRef]

Ho, Y. L. J.

F. S. Y. Yeung, Y. L. J. Ho, Y. W. Li, and H. S. Kwok, “Liquid crystal alignment layer with controllable anchoring energies,” J Disp. Technol. 4(1), 24–27 (2008).
[CrossRef]

Hsu, C. S.

S. Gauza, C. H. Wen, S. T. Wu, N. Janarthanan, and C. S. Hsu, “Super high birefringence isothiocyanato biphenyl-bistolane liquid crystals,” Jpn. J. Appl. Phys. 43(11A), 7634–7638 (2004).
[CrossRef]

Huang, D. D.

A. D. Kiselev, V. Chigrinov, and D. D. Huang, “Photoinduced ordering and anchoring properties of azo-dye films,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(6), 061703 (2005).
[CrossRef] [PubMed]

Janarthanan, N.

S. Gauza, C. H. Wen, S. T. Wu, N. Janarthanan, and C. S. Hsu, “Super high birefringence isothiocyanato biphenyl-bistolane liquid crystals,” Jpn. J. Appl. Phys. 43(11A), 7634–7638 (2004).
[CrossRef]

Jang, H. J.

J. H. Seo, H. J. Jang, S. R. Lee, T. H. Yoon, J. C. Kim, I. B. Kang, and C. H. Oh, “Wide pretilt angle control of liquid crystal display device by ion beam exposure on the vertical aligning layer,” Jpn. J. Appl. Phys. 46(44), L1074–L1076 (2007).
[CrossRef]

Jenkins, C.

Jones, R. C.

Kang, D.

K. E. Vaughn, M. Sousa, D. Kang, and C. Rosenblatt, “Continuous control of liquid crystal pretilt angle from homeotropic to planar,” Appl. Phys. Lett. 90(19), 194102 (2007).
[CrossRef]

Kang, I. B.

J. H. Seo, H. J. Jang, S. R. Lee, T. H. Yoon, J. C. Kim, I. B. Kang, and C. H. Oh, “Wide pretilt angle control of liquid crystal display device by ion beam exposure on the vertical aligning layer,” Jpn. J. Appl. Phys. 46(44), L1074–L1076 (2007).
[CrossRef]

Kelly, J. R.

Kim, J. C.

J. H. Seo, H. J. Jang, S. R. Lee, T. H. Yoon, J. C. Kim, I. B. Kang, and C. H. Oh, “Wide pretilt angle control of liquid crystal display device by ion beam exposure on the vertical aligning layer,” Jpn. J. Appl. Phys. 46(44), L1074–L1076 (2007).
[CrossRef]

Kiselev, A. D.

A. V. Dubtsov, S. V. Pasechnik, A. D. Kiselev, D. V. Shmeliova, and V. G. Chigrinov, “Electrically assisted light-induced azimuthal gliding of the nematic liquid-crystal easy axis on photoaligned substrates,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82(1), 011702 (2010).
[CrossRef] [PubMed]

A. D. Kiselev, V. Chigrinov, and D. D. Huang, “Photoinduced ordering and anchoring properties of azo-dye films,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(6), 061703 (2005).
[CrossRef] [PubMed]

Kmetz, A. R.

J. Nehring, A. R. Kmetz, and T. J. Scheffer, “Analysis of weak-boundary-coupling effects in liquid crystal displays,” J. Appl. Phys. 47(3), 850–857 (1976).
[CrossRef]

Kula, P.

S. Gauza, P. Kula, R. Dabrowski, G. Sasnouski, and V. Lapanik, “High optical anisotropy nematic single compounds and mixtures,” Trans. Electr. Electron. Mater. 13(1), 2–5 (2012).
[CrossRef]

Kwok, H. S.

M. C. Tseng, F. Fan, C. Y. Lee, A. Murauski, V. Chigrinov, and H. S. Kwok, “Tunable lens by spatially varying liquid crystal pretilt angles,” J. Appl. Phys. 109(8), 083109 (2011).
[CrossRef]

S. Valyukh, I. Valyukh, V. Chigrinov, H. S. Kwok, and H. Arwin, “Liquid crystal light deflecting devices based on nonuniform anchoring,” Appl. Phys. Lett. 97(23), 231120 (2010).
[CrossRef]

A. Muravsky, A. Murauski, V. Chigrinov, and H. S. Kwok, “Light printing of grayscale pixel images on optical rewritable electronic paper,” Jpn. J. Appl. Phys. 47(8), 6347–6353 (2008).
[CrossRef]

F. S. Y. Yeung, Y. L. J. Ho, Y. W. Li, and H. S. Kwok, “Liquid crystal alignment layer with controllable anchoring energies,” J Disp. Technol. 4(1), 24–27 (2008).
[CrossRef]

F. S. Yeung, J. Y. Ho, Y. W. Li, F. C. Xie, O. K. Tsui, P. Sheng, and H. S. Kwok, “Variable liquid crystal pretilt angles by nanostructured surfaces,” Appl. Phys. Lett. 88(5), 051910 (2006).
[CrossRef]

Lapanik, V.

S. Gauza, P. Kula, R. Dabrowski, G. Sasnouski, and V. Lapanik, “High optical anisotropy nematic single compounds and mixtures,” Trans. Electr. Electron. Mater. 13(1), 2–5 (2012).
[CrossRef]

Lee, C. Y.

M. C. Tseng, F. Fan, C. Y. Lee, A. Murauski, V. Chigrinov, and H. S. Kwok, “Tunable lens by spatially varying liquid crystal pretilt angles,” J. Appl. Phys. 109(8), 083109 (2011).
[CrossRef]

Lee, S. R.

J. H. Seo, H. J. Jang, S. R. Lee, T. H. Yoon, J. C. Kim, I. B. Kang, and C. H. Oh, “Wide pretilt angle control of liquid crystal display device by ion beam exposure on the vertical aligning layer,” Jpn. J. Appl. Phys. 46(44), L1074–L1076 (2007).
[CrossRef]

Li, Y. W.

F. S. Y. Yeung, Y. L. J. Ho, Y. W. Li, and H. S. Kwok, “Liquid crystal alignment layer with controllable anchoring energies,” J Disp. Technol. 4(1), 24–27 (2008).
[CrossRef]

F. S. Yeung, J. Y. Ho, Y. W. Li, F. C. Xie, O. K. Tsui, P. Sheng, and H. S. Kwok, “Variable liquid crystal pretilt angles by nanostructured surfaces,” Appl. Phys. Lett. 88(5), 051910 (2006).
[CrossRef]

Lindgren, M.

Love, G. D.

Martin, T.

Matsukawa, K.

T. Nanba, H. Naito, K. Matsukawa, and A. Sugimura, “Weak anchoring of nematic liquid crystals on photo-induced surface relief gratings of organic polysilane,” Thin Solid Films 518(2), 767–770 (2009).
[CrossRef]

McManamon, P. F.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[CrossRef]

L. Shi, P. F. McManamon, and P. J. Bos, “Liquid crystal optical phase plate with a variable in-plane gradient,” J. Appl. Phys. 104(3), 033109 (2008).
[CrossRef]

X. Wang, B. Wang, P. J. Bos, P. F. Mcmanamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid-crystal optical phased array,” J. Appl. Phys. 98(7), 073101 (2005).
[CrossRef]

Miranda, F. A.

X. Wang, B. Wang, P. J. Bos, P. F. Mcmanamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid-crystal optical phased array,” J. Appl. Phys. 98(7), 073101 (2005).
[CrossRef]

Moore, K.

Murauski, A.

M. C. Tseng, F. Fan, C. Y. Lee, A. Murauski, V. Chigrinov, and H. S. Kwok, “Tunable lens by spatially varying liquid crystal pretilt angles,” J. Appl. Phys. 109(8), 083109 (2011).
[CrossRef]

A. Muravsky, A. Murauski, V. Chigrinov, and H. S. Kwok, “Light printing of grayscale pixel images on optical rewritable electronic paper,” Jpn. J. Appl. Phys. 47(8), 6347–6353 (2008).
[CrossRef]

Muravsky, A.

A. Muravsky, A. Murauski, V. Chigrinov, and H. S. Kwok, “Light printing of grayscale pixel images on optical rewritable electronic paper,” Jpn. J. Appl. Phys. 47(8), 6347–6353 (2008).
[CrossRef]

Naito, H.

T. Nanba, H. Naito, K. Matsukawa, and A. Sugimura, “Weak anchoring of nematic liquid crystals on photo-induced surface relief gratings of organic polysilane,” Thin Solid Films 518(2), 767–770 (2009).
[CrossRef]

Nanba, T.

T. Nanba, H. Naito, K. Matsukawa, and A. Sugimura, “Weak anchoring of nematic liquid crystals on photo-induced surface relief gratings of organic polysilane,” Thin Solid Films 518(2), 767–770 (2009).
[CrossRef]

Nehring, J.

J. Nehring, A. R. Kmetz, and T. J. Scheffer, “Analysis of weak-boundary-coupling effects in liquid crystal displays,” J. Appl. Phys. 47(3), 850–857 (1976).
[CrossRef]

Neyts, K.

J. Beeckman, K. Neyts, and P. J. M. Vanbrabant, “Liquid-crystal photonic applications,” Opt. Eng. 50(8), 081202 (2011).
[CrossRef]

Oh, C. H.

J. H. Seo, H. J. Jang, S. R. Lee, T. H. Yoon, J. C. Kim, I. B. Kang, and C. H. Oh, “Wide pretilt angle control of liquid crystal display device by ion beam exposure on the vertical aligning layer,” Jpn. J. Appl. Phys. 46(44), L1074–L1076 (2007).
[CrossRef]

Ostroverkhov, V.

Oton, J. M.

B. Bellini, M. A. Geday, N. Bennis, A. Spadlo, X. Quintana, J. M. Oton, and R. Dabrowski, “Design and simulation of single-electrode liquid crystal phased arrays,” Opto-Electron. Rev. 14(4), 269–273 (2006).
[CrossRef]

Papoular, M.

A. Rapini and M. Papoular, “Distorsion d’une lamelle nematique sous champ magnetique conditions d’ancrage aux parois,” J. Phys. (Paris), Colloq. 30, 54–56 (1969).

Pasechnik, S. V.

A. V. Dubtsov, S. V. Pasechnik, A. D. Kiselev, D. V. Shmeliova, and V. G. Chigrinov, “Electrically assisted light-induced azimuthal gliding of the nematic liquid-crystal easy axis on photoaligned substrates,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82(1), 011702 (2010).
[CrossRef] [PubMed]

Pouch, J. J.

X. Wang, B. Wang, P. J. Bos, P. F. Mcmanamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid-crystal optical phased array,” J. Appl. Phys. 98(7), 073101 (2005).
[CrossRef]

Quintana, X.

B. Bellini, M. A. Geday, N. Bennis, A. Spadlo, X. Quintana, J. M. Oton, and R. Dabrowski, “Design and simulation of single-electrode liquid crystal phased arrays,” Opto-Electron. Rev. 14(4), 269–273 (2006).
[CrossRef]

Rapini, A.

A. Rapini and M. Papoular, “Distorsion d’une lamelle nematique sous champ magnetique conditions d’ancrage aux parois,” J. Phys. (Paris), Colloq. 30, 54–56 (1969).

Reshetnyak, V.

Reznikov, Yu.

Rosenblatt, C.

K. E. Vaughn, M. Sousa, D. Kang, and C. Rosenblatt, “Continuous control of liquid crystal pretilt angle from homeotropic to planar,” Appl. Phys. Lett. 90(19), 194102 (2007).
[CrossRef]

Sasnouski, G.

S. Gauza, P. Kula, R. Dabrowski, G. Sasnouski, and V. Lapanik, “High optical anisotropy nematic single compounds and mixtures,” Trans. Electr. Electron. Mater. 13(1), 2–5 (2012).
[CrossRef]

Sato, S.

M. Ye, Y. Yokoyama, and S. Sato, “Liquid crystal lens prepared utilizing patterned molecular orientations on cell walls,” Appl. Phys. Lett. 89(14), 141112 (2006).
[CrossRef]

Scheffer, T. J.

J. Nehring, A. R. Kmetz, and T. J. Scheffer, “Analysis of weak-boundary-coupling effects in liquid crystal displays,” J. Appl. Phys. 47(3), 850–857 (1976).
[CrossRef]

Seo, J. H.

J. H. Seo, H. J. Jang, S. R. Lee, T. H. Yoon, J. C. Kim, I. B. Kang, and C. H. Oh, “Wide pretilt angle control of liquid crystal display device by ion beam exposure on the vertical aligning layer,” Jpn. J. Appl. Phys. 46(44), L1074–L1076 (2007).
[CrossRef]

Serati, S.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[CrossRef]

Sheng, P.

F. S. Yeung, J. Y. Ho, Y. W. Li, F. C. Xie, O. K. Tsui, P. Sheng, and H. S. Kwok, “Variable liquid crystal pretilt angles by nanostructured surfaces,” Appl. Phys. Lett. 88(5), 051910 (2006).
[CrossRef]

Shi, L.

L. Shi, P. F. McManamon, and P. J. Bos, “Liquid crystal optical phase plate with a variable in-plane gradient,” J. Appl. Phys. 104(3), 033109 (2008).
[CrossRef]

Shiyanovskii, S. V.

Shmeliova, D. V.

A. V. Dubtsov, S. V. Pasechnik, A. D. Kiselev, D. V. Shmeliova, and V. G. Chigrinov, “Electrically assisted light-induced azimuthal gliding of the nematic liquid-crystal easy axis on photoaligned substrates,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82(1), 011702 (2010).
[CrossRef] [PubMed]

Singer, K. D.

Sjöqvist, L.

Sousa, M.

K. E. Vaughn, M. Sousa, D. Kang, and C. Rosenblatt, “Continuous control of liquid crystal pretilt angle from homeotropic to planar,” Appl. Phys. Lett. 90(19), 194102 (2007).
[CrossRef]

Spadlo, A.

B. Bellini, M. A. Geday, N. Bennis, A. Spadlo, X. Quintana, J. M. Oton, and R. Dabrowski, “Design and simulation of single-electrode liquid crystal phased arrays,” Opto-Electron. Rev. 14(4), 269–273 (2006).
[CrossRef]

Sugimura, A.

T. Nanba, H. Naito, K. Matsukawa, and A. Sugimura, “Weak anchoring of nematic liquid crystals on photo-induced surface relief gratings of organic polysilane,” Thin Solid Films 518(2), 767–770 (2009).
[CrossRef]

Titus, C. M.

Tocnaye, D. L.

J. L. D. Bougrenet and D. L. Tocnaye, “A polymer-dispersed liquid crystal-based dynamic gain equalizer,” Liq. Cryst. 31, 241–269 (2004).

Tseng, M. C.

M. C. Tseng, F. Fan, C. Y. Lee, A. Murauski, V. Chigrinov, and H. S. Kwok, “Tunable lens by spatially varying liquid crystal pretilt angles,” J. Appl. Phys. 109(8), 083109 (2011).
[CrossRef]

Tsui, O. K.

F. S. Yeung, J. Y. Ho, Y. W. Li, F. C. Xie, O. K. Tsui, P. Sheng, and H. S. Kwok, “Variable liquid crystal pretilt angles by nanostructured surfaces,” Appl. Phys. Lett. 88(5), 051910 (2006).
[CrossRef]

Urey, H.

Valyukh, I.

S. Valyukh, I. Valyukh, V. Chigrinov, H. S. Kwok, and H. Arwin, “Liquid crystal light deflecting devices based on nonuniform anchoring,” Appl. Phys. Lett. 97(23), 231120 (2010).
[CrossRef]

Valyukh, S.

S. Valyukh, I. Valyukh, V. Chigrinov, H. S. Kwok, and H. Arwin, “Liquid crystal light deflecting devices based on nonuniform anchoring,” Appl. Phys. Lett. 97(23), 231120 (2010).
[CrossRef]

Vanbrabant, P. J. M.

J. Beeckman, K. Neyts, and P. J. M. Vanbrabant, “Liquid-crystal photonic applications,” Opt. Eng. 50(8), 081202 (2011).
[CrossRef]

Vaughn, K. E.

K. E. Vaughn, M. Sousa, D. Kang, and C. Rosenblatt, “Continuous control of liquid crystal pretilt angle from homeotropic to planar,” Appl. Phys. Lett. 90(19), 194102 (2007).
[CrossRef]

Wang, B.

X. Wang, B. Wang, P. J. Bos, P. F. Mcmanamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid-crystal optical phased array,” J. Appl. Phys. 98(7), 073101 (2005).
[CrossRef]

Wang, X.

X. Wang, B. Wang, P. J. Bos, P. F. Mcmanamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid-crystal optical phased array,” J. Appl. Phys. 98(7), 073101 (2005).
[CrossRef]

Watson, E. A.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[CrossRef]

Wen, C. H.

S. Gauza, C. H. Wen, S. T. Wu, N. Janarthanan, and C. S. Hsu, “Super high birefringence isothiocyanato biphenyl-bistolane liquid crystals,” Jpn. J. Appl. Phys. 43(11A), 7634–7638 (2004).
[CrossRef]

Wu, S. T.

S. Gauza, C. H. Wen, S. T. Wu, N. Janarthanan, and C. S. Hsu, “Super high birefringence isothiocyanato biphenyl-bistolane liquid crystals,” Jpn. J. Appl. Phys. 43(11A), 7634–7638 (2004).
[CrossRef]

Xie, F. C.

F. S. Yeung, J. Y. Ho, Y. W. Li, F. C. Xie, O. K. Tsui, P. Sheng, and H. S. Kwok, “Variable liquid crystal pretilt angles by nanostructured surfaces,” Appl. Phys. Lett. 88(5), 051910 (2006).
[CrossRef]

Xie, H.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[CrossRef]

Ye, M.

M. Ye, Y. Yokoyama, and S. Sato, “Liquid crystal lens prepared utilizing patterned molecular orientations on cell walls,” Appl. Phys. Lett. 89(14), 141112 (2006).
[CrossRef]

Yeung, F. S.

F. S. Yeung, J. Y. Ho, Y. W. Li, F. C. Xie, O. K. Tsui, P. Sheng, and H. S. Kwok, “Variable liquid crystal pretilt angles by nanostructured surfaces,” Appl. Phys. Lett. 88(5), 051910 (2006).
[CrossRef]

Yeung, F. S. Y.

F. S. Y. Yeung, Y. L. J. Ho, Y. W. Li, and H. S. Kwok, “Liquid crystal alignment layer with controllable anchoring energies,” J Disp. Technol. 4(1), 24–27 (2008).
[CrossRef]

Yokoyama, Y.

M. Ye, Y. Yokoyama, and S. Sato, “Liquid crystal lens prepared utilizing patterned molecular orientations on cell walls,” Appl. Phys. Lett. 89(14), 141112 (2006).
[CrossRef]

Yoon, T. H.

J. H. Seo, H. J. Jang, S. R. Lee, T. H. Yoon, J. C. Kim, I. B. Kang, and C. H. Oh, “Wide pretilt angle control of liquid crystal display device by ion beam exposure on the vertical aligning layer,” Jpn. J. Appl. Phys. 46(44), L1074–L1076 (2007).
[CrossRef]

Zhang, J.

Appl. Opt. (1)

Appl. Phys. Lett. (4)

M. Ye, Y. Yokoyama, and S. Sato, “Liquid crystal lens prepared utilizing patterned molecular orientations on cell walls,” Appl. Phys. Lett. 89(14), 141112 (2006).
[CrossRef]

S. Valyukh, I. Valyukh, V. Chigrinov, H. S. Kwok, and H. Arwin, “Liquid crystal light deflecting devices based on nonuniform anchoring,” Appl. Phys. Lett. 97(23), 231120 (2010).
[CrossRef]

F. S. Yeung, J. Y. Ho, Y. W. Li, F. C. Xie, O. K. Tsui, P. Sheng, and H. S. Kwok, “Variable liquid crystal pretilt angles by nanostructured surfaces,” Appl. Phys. Lett. 88(5), 051910 (2006).
[CrossRef]

K. E. Vaughn, M. Sousa, D. Kang, and C. Rosenblatt, “Continuous control of liquid crystal pretilt angle from homeotropic to planar,” Appl. Phys. Lett. 90(19), 194102 (2007).
[CrossRef]

Electron. Lett. (1)

J. B. Davies, S. Day, F. Di Pasquale, and F. A. Fernandez, “Finite element modelling in 2-D of nematic liquid crystal structures,” Electron. Lett. 32(6), 582–583 (1996).
[CrossRef]

J Disp. Technol. (1)

F. S. Y. Yeung, Y. L. J. Ho, Y. W. Li, and H. S. Kwok, “Liquid crystal alignment layer with controllable anchoring energies,” J Disp. Technol. 4(1), 24–27 (2008).
[CrossRef]

J. Appl. Phys. (4)

J. Nehring, A. R. Kmetz, and T. J. Scheffer, “Analysis of weak-boundary-coupling effects in liquid crystal displays,” J. Appl. Phys. 47(3), 850–857 (1976).
[CrossRef]

M. C. Tseng, F. Fan, C. Y. Lee, A. Murauski, V. Chigrinov, and H. S. Kwok, “Tunable lens by spatially varying liquid crystal pretilt angles,” J. Appl. Phys. 109(8), 083109 (2011).
[CrossRef]

X. Wang, B. Wang, P. J. Bos, P. F. Mcmanamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid-crystal optical phased array,” J. Appl. Phys. 98(7), 073101 (2005).
[CrossRef]

L. Shi, P. F. McManamon, and P. J. Bos, “Liquid crystal optical phase plate with a variable in-plane gradient,” J. Appl. Phys. 104(3), 033109 (2008).
[CrossRef]

J. Opt. Soc. Am. (2)

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

J. Phys. (Paris), Colloq. (1)

A. Rapini and M. Papoular, “Distorsion d’une lamelle nematique sous champ magnetique conditions d’ancrage aux parois,” J. Phys. (Paris), Colloq. 30, 54–56 (1969).

Jpn. J. Appl. Phys. (3)

S. Gauza, C. H. Wen, S. T. Wu, N. Janarthanan, and C. S. Hsu, “Super high birefringence isothiocyanato biphenyl-bistolane liquid crystals,” Jpn. J. Appl. Phys. 43(11A), 7634–7638 (2004).
[CrossRef]

A. Muravsky, A. Murauski, V. Chigrinov, and H. S. Kwok, “Light printing of grayscale pixel images on optical rewritable electronic paper,” Jpn. J. Appl. Phys. 47(8), 6347–6353 (2008).
[CrossRef]

J. H. Seo, H. J. Jang, S. R. Lee, T. H. Yoon, J. C. Kim, I. B. Kang, and C. H. Oh, “Wide pretilt angle control of liquid crystal display device by ion beam exposure on the vertical aligning layer,” Jpn. J. Appl. Phys. 46(44), L1074–L1076 (2007).
[CrossRef]

Liq. Cryst. (1)

J. L. D. Bougrenet and D. L. Tocnaye, “A polymer-dispersed liquid crystal-based dynamic gain equalizer,” Liq. Cryst. 31, 241–269 (2004).

Opt. Eng. (1)

J. Beeckman, K. Neyts, and P. J. M. Vanbrabant, “Liquid-crystal photonic applications,” Opt. Eng. 50(8), 081202 (2011).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Opto-Electron. Rev. (1)

B. Bellini, M. A. Geday, N. Bennis, A. Spadlo, X. Quintana, J. M. Oton, and R. Dabrowski, “Design and simulation of single-electrode liquid crystal phased arrays,” Opto-Electron. Rev. 14(4), 269–273 (2006).
[CrossRef]

Philos. Trans. R. Soc. Lond. A (1)

D. W. Berreman, “Numerical modeling of twisted nematic devices,” Philos. Trans. R. Soc. Lond. A 309(1507), 203–216 (1983).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

A. V. Dubtsov, S. V. Pasechnik, A. D. Kiselev, D. V. Shmeliova, and V. G. Chigrinov, “Electrically assisted light-induced azimuthal gliding of the nematic liquid-crystal easy axis on photoaligned substrates,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82(1), 011702 (2010).
[CrossRef] [PubMed]

A. D. Kiselev, V. Chigrinov, and D. D. Huang, “Photoinduced ordering and anchoring properties of azo-dye films,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(6), 061703 (2005).
[CrossRef] [PubMed]

Proc. IEEE (1)

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[CrossRef]

Thin Solid Films (1)

T. Nanba, H. Naito, K. Matsukawa, and A. Sugimura, “Weak anchoring of nematic liquid crystals on photo-induced surface relief gratings of organic polysilane,” Thin Solid Films 518(2), 767–770 (2009).
[CrossRef]

Trans. Electr. Electron. Mater. (1)

S. Gauza, P. Kula, R. Dabrowski, G. Sasnouski, and V. Lapanik, “High optical anisotropy nematic single compounds and mixtures,” Trans. Electr. Electron. Mater. 13(1), 2–5 (2012).
[CrossRef]

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I. W. Stewart, The Static and Dynamic Continuum Theory of Liquid Crystals (Taylor & Francis, 2004).

S. Valyukh, V. Chigrinov, and H. S. Kwok, “A liquid crystal lens with non-uniform anchoring energy,” SID Int. Symp. Digest Tech. Papers 39, 659–662 (2008).

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

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Figures (8)

Fig. 1
Fig. 1

Fragment of LC DOE based on non-uniform alignment.

Fig. 2
Fig. 2

η versus reduced voltage V/Vc at (a) different anchoring energy, (b) different pre-tilt angle.

Fig. 3
Fig. 3

Phase retardation versus reduced voltage V/Vc at different thicknesses.

Fig. 4
Fig. 4

Distributions of the anchoring energy within a period in a saw-tooth diffraction grating. The solid curves are results of the computer simulation, the dash curves are obtained according to Eq. (8).

Fig. 5
Fig. 5

η as a function of X/d for different wideness of the “slit”.

Fig. 6
Fig. 6

η as a function of X/Λ for different values of Λ.

Fig. 7
Fig. 7

Δη versus the relative period Λ/d.

Fig. 8
Fig. 8

η versus X/Λ in a saw-tooth diffraction grating with 25V applied for different anchoring energies.

Tables (2)

Tables Icon

Table 1 Values of the Weak Anchoring Energy W2 for Different m and δmax

Tables Icon

Table 2 Diffraction Efficiency of the Grating with the Phase Profiles Shown in Fig. 6

Equations (13)

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φ=η 2π λ dΔn,
f el = 1 2 ( K 11 ( n ) 2 + K 33 [ n × × n ] 2 ),
f diel = 1 2 ε o E ε ^ E ,
f s bottom = f s top = 1 2 W sin 2 ( α α o ),
d ds ( n * ( r ) d r ds )= n * ( r ).
tanδ= ( n e 2 n o 2 )( 1 ( N k ) 2 ) n o 2 + ( N k ) 2 ( n e 2 n o 2 ) .
U o (α)=C Λ 2 Λ 2 ψ(x) e ikxsinβ dx.
U(α)= U o (α) sinNσ sinσ e i(N1)σ ,
δ max =π K 11 Δnρ( 1 W 2 1 W 1 ).
W 2 = π K 11 Δnρ δ max .
W 2 = π K 11 Δnρ(m1) δ max m .
sin 2 ( α(x) )= n o 2 n e 2 n o 2 ( ( n e d n o d+δ(x) ) 2 1 ),
Λ= 1 a ( 0.38λ Δn bd ).

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