Abstract

This article investigates the effect of pretilt angle on disclination lines of liquid crystal (LC) lenses. When the pretilt angle of LCs is higher than 7°, the disclination lines are reduced and are moved to the boundary of the LC lens. The disclination lines at the boundary do not influence the focused beam profile of the LC lens. As the pretilt angle of LCs further increases, the disclination lines at the boundary become almost invisible. However, the interference rings become asymmetrical. The response time of an LC lens with a pretilt angle higher than 7° is 60% of the conventionally homogeneous LC lens. This value is a result of the decrease in the rotation angle of the LCs and the reduced disclination lines.

© 2012 Optical Society of America

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  1. P. Valley, D. L. Mathine, M. R. Dodge, J. Schwiegerling, G. Peyman, and N. Peyghambarian, “Tunable-focus flat liquid-crystal diffractive lens,” Opt. Lett. 35, 336–338 (2010).
    [CrossRef]
  2. S. Suyama, M. Date, and H. Takada, “Three-dimensional display system with dual-frequency liquid-crystal varifocal lens,” Jpn. J. Appl. Phys. 39, 480–484 (2000).
    [CrossRef]
  3. H. C. Lin and Y. H. Lin, “An electrically tunable focusing pico-projector adopting a liquid crystal lens,” Jpn. J. Appl. Phys. 49, 102502 (2010).
    [CrossRef]
  4. S. Sato, “Liquid-crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18, 1679–1684 (1979).
    [CrossRef]
  5. H. Ren, D. W. Fox, B. Wu, and S. T. Wu, “Liquid crystal lens with large focal length tunability and low operating voltage,” Opt. Express 15, 11328–11335 (2007).
    [CrossRef]
  6. Y. Mao and S. Sato, “New method of voltage application for improving response time of a liquid crystal lens,” Mol. Cryst. Liq. Cryst. 433, 229–236 (2005).
    [CrossRef]
  7. M. Ye, B. Wang, and S. Sato, “Liquid-crystal lens with a focal length that is variable in a wide range,” Appl. Opt. 43, 6407–6412 (2004).
    [CrossRef]
  8. T. Nose, S. Masuda, and S. Sato, “Optical properties of a liquid crystal microlens with a symmetric electrode structure,” Jpn. J. Appl. Phys. 30, L2110–L2112 (1991).
    [CrossRef]
  9. T. Nose, S. Masuda, and S. Sato, “A liquid crystal microlens with hole-patterned electrodes on both substrates,” Jpn. J. Appl. Phys. 31, 1643–1646 (1992).
    [CrossRef]
  10. M. Ye, B. Wang, and S. Sato, “Driving of liquid crystal lens without disclination occurring by applying in-plane electric field,” Jpn. J. Appl. Phys. 42, 5086–5089 (2003).
    [CrossRef]
  11. M. Ye and S. Sato, “Optical properties of liquid crystal lens of any size,” Jpn. J. Appl. Phys. 41, L571–L573 (2002).
    [CrossRef]
  12. S. Sato, “Applications of liquid crystals to variable-focusing lenses,” Opt. Rev. 6, 471–485 (1999).
    [CrossRef]
  13. M. Jiao, Z. Ge, Q. Song, and S. T. Wu, “Alignment layer effects on thin liquid crystal cells,” Appl. Phys. Lett. 92, 061102 (2008).
    [CrossRef]
  14. C. J. Hsu and C. R. Sheu, “Preventing occurrence of disclination lines in liquid crystal lenses with a large aperture by means of polymer stabilization,” Opt. Express 19, 14999–15008 (2011).
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  15. O. Pishnyak, S. Sato, and O. D. Lavrentovich, “Electrically tunable lens based on a dual-frequency nematic liquid crystal,” Appl. Opt. 45, 4576–4582 (2006).
    [CrossRef]
  16. T. Nose, S. Masuda, and S. Sato, “Optical properties of a hybrid-aligned liquid crystal microlens,” Mol. Cryst. Liq. Cryst. 199, 27–35 (1991).
    [CrossRef]
  17. 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, 051910 (2006).
    [CrossRef]
  18. P. Yeh and C. Gu, Optics of Liquid Crystal Displays (Wiley, 1999).
  19. T. J. Scheffer, and J. Nehring, “Accurate determination of liquid-crystal tilt bias angles,” J. Appl. Phys. 48, 1783–1792 (1977).
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  20. M. Ye and S. Sato, “Transient properties of a liquid-crystal microlens,” Jpn. J. Appl. Phys. 40, 6012–6016 (2001).
    [CrossRef]
  21. S. Matsumoto, M. Kawamoto, and K. Mizunoya, “Field-induced deformation of hybrid-aligned nematic liquid crystals: new multicolor liquid crystal display,” J. Appl. Phys. 47, 3842–3845 (1976).
    [CrossRef]
  22. Y. Q. Lu, X. Liang, Y. H. Wu, F. Du, and S. T. Wu, “Dual-frequency addressed hybrid-aligned nematic liquid crystal,” Appl. Phys. Lett. 85, 3354–3356 (2004).
    [CrossRef]
  23. H. Wang, T. X. Wu, X. Zhu, and S. T. Wu, “Correlations between liquid crystal director reorientation and optical response time of a homeotropic cell,” J. Appl. Phys. 95, 5502–5508 (2004).
    [CrossRef]
  24. X. Nie, H. Xianyu, R. Lu, T. X. Wu, and S. T. Wu, “Pretilt angle effects on liquid crystal response time,” J. Disp. Tech. 3, 280–283 (2007).
    [CrossRef]
  25. E. J. Acosta, M. J. Towler, and H. G. Walton, “The role of surface tilt in the operation of pi-cell liquid crystal devices,” Liq. Cryst. 27, 977–984 (2000).
    [CrossRef]
  26. A. Bogi, P. Martinot-Lagarde, I. Dozov, and M. Nobili, “Anchoring screening of defects interaction in a nematic liquid crystal,” Phys. Rev. Lett. 89, 225501 (2002).
    [CrossRef]
  27. S. Gauza, H. Wang, C. H. Wen, S. T. Wu, A. J. Seed, and R. Dabrowski, “High birefringence isothiocyanato tolane liquid crystals,” Jpn. J. Appl. Phys. 42, 3463–3466 (2003).
    [CrossRef]
  28. 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, 7634–7638 (2004).
    [CrossRef]
  29. S. T. Wu and C. S. Wu, “Small angle relaxation of highly deformed nematic liquid crystals,” Appl. Phys. Lett. 53, 1794–1796 (1988).
    [CrossRef]
  30. S. T. Wu, “Nematic liquid crystal modulator with response time less than 100 μs at room temperature,” Appl. Phys. Lett. 57, 986–988 (1990).
    [CrossRef]
  31. H. Ren and S. T. Wu, “Tunable electronic lens using a gradient polymer network liquid crystal,” Appl. Phys. Lett. 82, 22–24 (2003).
    [CrossRef]
  32. Y. H. Fan, H. Ren, X. Liang, H. Wang, and S. T. Wu, “Liquid crystal microlens arrays with switchable positive and negative focal lengths,” J. Disp. Tech. 1, 151–156 (2005).
    [CrossRef]

2011 (1)

2010 (2)

P. Valley, D. L. Mathine, M. R. Dodge, J. Schwiegerling, G. Peyman, and N. Peyghambarian, “Tunable-focus flat liquid-crystal diffractive lens,” Opt. Lett. 35, 336–338 (2010).
[CrossRef]

H. C. Lin and Y. H. Lin, “An electrically tunable focusing pico-projector adopting a liquid crystal lens,” Jpn. J. Appl. Phys. 49, 102502 (2010).
[CrossRef]

2008 (1)

M. Jiao, Z. Ge, Q. Song, and S. T. Wu, “Alignment layer effects on thin liquid crystal cells,” Appl. Phys. Lett. 92, 061102 (2008).
[CrossRef]

2007 (2)

H. Ren, D. W. Fox, B. Wu, and S. T. Wu, “Liquid crystal lens with large focal length tunability and low operating voltage,” Opt. Express 15, 11328–11335 (2007).
[CrossRef]

X. Nie, H. Xianyu, R. Lu, T. X. Wu, and S. T. Wu, “Pretilt angle effects on liquid crystal response time,” J. Disp. Tech. 3, 280–283 (2007).
[CrossRef]

2006 (2)

O. Pishnyak, S. Sato, and O. D. Lavrentovich, “Electrically tunable lens based on a dual-frequency nematic liquid crystal,” Appl. Opt. 45, 4576–4582 (2006).
[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, 051910 (2006).
[CrossRef]

2005 (2)

Y. Mao and S. Sato, “New method of voltage application for improving response time of a liquid crystal lens,” Mol. Cryst. Liq. Cryst. 433, 229–236 (2005).
[CrossRef]

Y. H. Fan, H. Ren, X. Liang, H. Wang, and S. T. Wu, “Liquid crystal microlens arrays with switchable positive and negative focal lengths,” J. Disp. Tech. 1, 151–156 (2005).
[CrossRef]

2004 (4)

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, 7634–7638 (2004).
[CrossRef]

Y. Q. Lu, X. Liang, Y. H. Wu, F. Du, and S. T. Wu, “Dual-frequency addressed hybrid-aligned nematic liquid crystal,” Appl. Phys. Lett. 85, 3354–3356 (2004).
[CrossRef]

H. Wang, T. X. Wu, X. Zhu, and S. T. Wu, “Correlations between liquid crystal director reorientation and optical response time of a homeotropic cell,” J. Appl. Phys. 95, 5502–5508 (2004).
[CrossRef]

M. Ye, B. Wang, and S. Sato, “Liquid-crystal lens with a focal length that is variable in a wide range,” Appl. Opt. 43, 6407–6412 (2004).
[CrossRef]

2003 (3)

M. Ye, B. Wang, and S. Sato, “Driving of liquid crystal lens without disclination occurring by applying in-plane electric field,” Jpn. J. Appl. Phys. 42, 5086–5089 (2003).
[CrossRef]

S. Gauza, H. Wang, C. H. Wen, S. T. Wu, A. J. Seed, and R. Dabrowski, “High birefringence isothiocyanato tolane liquid crystals,” Jpn. J. Appl. Phys. 42, 3463–3466 (2003).
[CrossRef]

H. Ren and S. T. Wu, “Tunable electronic lens using a gradient polymer network liquid crystal,” Appl. Phys. Lett. 82, 22–24 (2003).
[CrossRef]

2002 (2)

A. Bogi, P. Martinot-Lagarde, I. Dozov, and M. Nobili, “Anchoring screening of defects interaction in a nematic liquid crystal,” Phys. Rev. Lett. 89, 225501 (2002).
[CrossRef]

M. Ye and S. Sato, “Optical properties of liquid crystal lens of any size,” Jpn. J. Appl. Phys. 41, L571–L573 (2002).
[CrossRef]

2001 (1)

M. Ye and S. Sato, “Transient properties of a liquid-crystal microlens,” Jpn. J. Appl. Phys. 40, 6012–6016 (2001).
[CrossRef]

2000 (2)

E. J. Acosta, M. J. Towler, and H. G. Walton, “The role of surface tilt in the operation of pi-cell liquid crystal devices,” Liq. Cryst. 27, 977–984 (2000).
[CrossRef]

S. Suyama, M. Date, and H. Takada, “Three-dimensional display system with dual-frequency liquid-crystal varifocal lens,” Jpn. J. Appl. Phys. 39, 480–484 (2000).
[CrossRef]

1999 (1)

S. Sato, “Applications of liquid crystals to variable-focusing lenses,” Opt. Rev. 6, 471–485 (1999).
[CrossRef]

1992 (1)

T. Nose, S. Masuda, and S. Sato, “A liquid crystal microlens with hole-patterned electrodes on both substrates,” Jpn. J. Appl. Phys. 31, 1643–1646 (1992).
[CrossRef]

1991 (2)

T. Nose, S. Masuda, and S. Sato, “Optical properties of a hybrid-aligned liquid crystal microlens,” Mol. Cryst. Liq. Cryst. 199, 27–35 (1991).
[CrossRef]

T. Nose, S. Masuda, and S. Sato, “Optical properties of a liquid crystal microlens with a symmetric electrode structure,” Jpn. J. Appl. Phys. 30, L2110–L2112 (1991).
[CrossRef]

1990 (1)

S. T. Wu, “Nematic liquid crystal modulator with response time less than 100 μs at room temperature,” Appl. Phys. Lett. 57, 986–988 (1990).
[CrossRef]

1988 (1)

S. T. Wu and C. S. Wu, “Small angle relaxation of highly deformed nematic liquid crystals,” Appl. Phys. Lett. 53, 1794–1796 (1988).
[CrossRef]

1979 (1)

S. Sato, “Liquid-crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18, 1679–1684 (1979).
[CrossRef]

1977 (1)

T. J. Scheffer, and J. Nehring, “Accurate determination of liquid-crystal tilt bias angles,” J. Appl. Phys. 48, 1783–1792 (1977).
[CrossRef]

1976 (1)

S. Matsumoto, M. Kawamoto, and K. Mizunoya, “Field-induced deformation of hybrid-aligned nematic liquid crystals: new multicolor liquid crystal display,” J. Appl. Phys. 47, 3842–3845 (1976).
[CrossRef]

Acosta, E. J.

E. J. Acosta, M. J. Towler, and H. G. Walton, “The role of surface tilt in the operation of pi-cell liquid crystal devices,” Liq. Cryst. 27, 977–984 (2000).
[CrossRef]

Bogi, A.

A. Bogi, P. Martinot-Lagarde, I. Dozov, and M. Nobili, “Anchoring screening of defects interaction in a nematic liquid crystal,” Phys. Rev. Lett. 89, 225501 (2002).
[CrossRef]

Dabrowski, R.

S. Gauza, H. Wang, C. H. Wen, S. T. Wu, A. J. Seed, and R. Dabrowski, “High birefringence isothiocyanato tolane liquid crystals,” Jpn. J. Appl. Phys. 42, 3463–3466 (2003).
[CrossRef]

Date, M.

S. Suyama, M. Date, and H. Takada, “Three-dimensional display system with dual-frequency liquid-crystal varifocal lens,” Jpn. J. Appl. Phys. 39, 480–484 (2000).
[CrossRef]

Dodge, M. R.

Dozov, I.

A. Bogi, P. Martinot-Lagarde, I. Dozov, and M. Nobili, “Anchoring screening of defects interaction in a nematic liquid crystal,” Phys. Rev. Lett. 89, 225501 (2002).
[CrossRef]

Du, F.

Y. Q. Lu, X. Liang, Y. H. Wu, F. Du, and S. T. Wu, “Dual-frequency addressed hybrid-aligned nematic liquid crystal,” Appl. Phys. Lett. 85, 3354–3356 (2004).
[CrossRef]

Fan, Y. H.

Y. H. Fan, H. Ren, X. Liang, H. Wang, and S. T. Wu, “Liquid crystal microlens arrays with switchable positive and negative focal lengths,” J. Disp. Tech. 1, 151–156 (2005).
[CrossRef]

Fox, D. W.

Gauza, 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, 7634–7638 (2004).
[CrossRef]

S. Gauza, H. Wang, C. H. Wen, S. T. Wu, A. J. Seed, and R. Dabrowski, “High birefringence isothiocyanato tolane liquid crystals,” Jpn. J. Appl. Phys. 42, 3463–3466 (2003).
[CrossRef]

Ge, Z.

M. Jiao, Z. Ge, Q. Song, and S. T. Wu, “Alignment layer effects on thin liquid crystal cells,” Appl. Phys. Lett. 92, 061102 (2008).
[CrossRef]

Gu, C.

P. Yeh and C. Gu, Optics of Liquid Crystal Displays (Wiley, 1999).

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, 051910 (2006).
[CrossRef]

Hsu, C. J.

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, 7634–7638 (2004).
[CrossRef]

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, 7634–7638 (2004).
[CrossRef]

Jiao, M.

M. Jiao, Z. Ge, Q. Song, and S. T. Wu, “Alignment layer effects on thin liquid crystal cells,” Appl. Phys. Lett. 92, 061102 (2008).
[CrossRef]

Kawamoto, M.

S. Matsumoto, M. Kawamoto, and K. Mizunoya, “Field-induced deformation of hybrid-aligned nematic liquid crystals: new multicolor liquid crystal display,” J. Appl. Phys. 47, 3842–3845 (1976).
[CrossRef]

Kwok, H. 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, 051910 (2006).
[CrossRef]

Lavrentovich, O. D.

Li, Y. W.

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, 051910 (2006).
[CrossRef]

Liang, X.

Y. H. Fan, H. Ren, X. Liang, H. Wang, and S. T. Wu, “Liquid crystal microlens arrays with switchable positive and negative focal lengths,” J. Disp. Tech. 1, 151–156 (2005).
[CrossRef]

Y. Q. Lu, X. Liang, Y. H. Wu, F. Du, and S. T. Wu, “Dual-frequency addressed hybrid-aligned nematic liquid crystal,” Appl. Phys. Lett. 85, 3354–3356 (2004).
[CrossRef]

Lin, H. C.

H. C. Lin and Y. H. Lin, “An electrically tunable focusing pico-projector adopting a liquid crystal lens,” Jpn. J. Appl. Phys. 49, 102502 (2010).
[CrossRef]

Lin, Y. H.

H. C. Lin and Y. H. Lin, “An electrically tunable focusing pico-projector adopting a liquid crystal lens,” Jpn. J. Appl. Phys. 49, 102502 (2010).
[CrossRef]

Lu, R.

X. Nie, H. Xianyu, R. Lu, T. X. Wu, and S. T. Wu, “Pretilt angle effects on liquid crystal response time,” J. Disp. Tech. 3, 280–283 (2007).
[CrossRef]

Lu, Y. Q.

Y. Q. Lu, X. Liang, Y. H. Wu, F. Du, and S. T. Wu, “Dual-frequency addressed hybrid-aligned nematic liquid crystal,” Appl. Phys. Lett. 85, 3354–3356 (2004).
[CrossRef]

Mao, Y.

Y. Mao and S. Sato, “New method of voltage application for improving response time of a liquid crystal lens,” Mol. Cryst. Liq. Cryst. 433, 229–236 (2005).
[CrossRef]

Martinot-Lagarde, P.

A. Bogi, P. Martinot-Lagarde, I. Dozov, and M. Nobili, “Anchoring screening of defects interaction in a nematic liquid crystal,” Phys. Rev. Lett. 89, 225501 (2002).
[CrossRef]

Masuda, S.

T. Nose, S. Masuda, and S. Sato, “A liquid crystal microlens with hole-patterned electrodes on both substrates,” Jpn. J. Appl. Phys. 31, 1643–1646 (1992).
[CrossRef]

T. Nose, S. Masuda, and S. Sato, “Optical properties of a liquid crystal microlens with a symmetric electrode structure,” Jpn. J. Appl. Phys. 30, L2110–L2112 (1991).
[CrossRef]

T. Nose, S. Masuda, and S. Sato, “Optical properties of a hybrid-aligned liquid crystal microlens,” Mol. Cryst. Liq. Cryst. 199, 27–35 (1991).
[CrossRef]

Mathine, D. L.

Matsumoto, S.

S. Matsumoto, M. Kawamoto, and K. Mizunoya, “Field-induced deformation of hybrid-aligned nematic liquid crystals: new multicolor liquid crystal display,” J. Appl. Phys. 47, 3842–3845 (1976).
[CrossRef]

Mizunoya, K.

S. Matsumoto, M. Kawamoto, and K. Mizunoya, “Field-induced deformation of hybrid-aligned nematic liquid crystals: new multicolor liquid crystal display,” J. Appl. Phys. 47, 3842–3845 (1976).
[CrossRef]

Nehring, J.

T. J. Scheffer, and J. Nehring, “Accurate determination of liquid-crystal tilt bias angles,” J. Appl. Phys. 48, 1783–1792 (1977).
[CrossRef]

Nie, X.

X. Nie, H. Xianyu, R. Lu, T. X. Wu, and S. T. Wu, “Pretilt angle effects on liquid crystal response time,” J. Disp. Tech. 3, 280–283 (2007).
[CrossRef]

Nobili, M.

A. Bogi, P. Martinot-Lagarde, I. Dozov, and M. Nobili, “Anchoring screening of defects interaction in a nematic liquid crystal,” Phys. Rev. Lett. 89, 225501 (2002).
[CrossRef]

Nose, T.

T. Nose, S. Masuda, and S. Sato, “A liquid crystal microlens with hole-patterned electrodes on both substrates,” Jpn. J. Appl. Phys. 31, 1643–1646 (1992).
[CrossRef]

T. Nose, S. Masuda, and S. Sato, “Optical properties of a liquid crystal microlens with a symmetric electrode structure,” Jpn. J. Appl. Phys. 30, L2110–L2112 (1991).
[CrossRef]

T. Nose, S. Masuda, and S. Sato, “Optical properties of a hybrid-aligned liquid crystal microlens,” Mol. Cryst. Liq. Cryst. 199, 27–35 (1991).
[CrossRef]

Peyghambarian, N.

Peyman, G.

Pishnyak, O.

Ren, H.

H. Ren, D. W. Fox, B. Wu, and S. T. Wu, “Liquid crystal lens with large focal length tunability and low operating voltage,” Opt. Express 15, 11328–11335 (2007).
[CrossRef]

Y. H. Fan, H. Ren, X. Liang, H. Wang, and S. T. Wu, “Liquid crystal microlens arrays with switchable positive and negative focal lengths,” J. Disp. Tech. 1, 151–156 (2005).
[CrossRef]

H. Ren and S. T. Wu, “Tunable electronic lens using a gradient polymer network liquid crystal,” Appl. Phys. Lett. 82, 22–24 (2003).
[CrossRef]

Sato, S.

O. Pishnyak, S. Sato, and O. D. Lavrentovich, “Electrically tunable lens based on a dual-frequency nematic liquid crystal,” Appl. Opt. 45, 4576–4582 (2006).
[CrossRef]

Y. Mao and S. Sato, “New method of voltage application for improving response time of a liquid crystal lens,” Mol. Cryst. Liq. Cryst. 433, 229–236 (2005).
[CrossRef]

M. Ye, B. Wang, and S. Sato, “Liquid-crystal lens with a focal length that is variable in a wide range,” Appl. Opt. 43, 6407–6412 (2004).
[CrossRef]

M. Ye, B. Wang, and S. Sato, “Driving of liquid crystal lens without disclination occurring by applying in-plane electric field,” Jpn. J. Appl. Phys. 42, 5086–5089 (2003).
[CrossRef]

M. Ye and S. Sato, “Optical properties of liquid crystal lens of any size,” Jpn. J. Appl. Phys. 41, L571–L573 (2002).
[CrossRef]

M. Ye and S. Sato, “Transient properties of a liquid-crystal microlens,” Jpn. J. Appl. Phys. 40, 6012–6016 (2001).
[CrossRef]

S. Sato, “Applications of liquid crystals to variable-focusing lenses,” Opt. Rev. 6, 471–485 (1999).
[CrossRef]

T. Nose, S. Masuda, and S. Sato, “A liquid crystal microlens with hole-patterned electrodes on both substrates,” Jpn. J. Appl. Phys. 31, 1643–1646 (1992).
[CrossRef]

T. Nose, S. Masuda, and S. Sato, “Optical properties of a liquid crystal microlens with a symmetric electrode structure,” Jpn. J. Appl. Phys. 30, L2110–L2112 (1991).
[CrossRef]

T. Nose, S. Masuda, and S. Sato, “Optical properties of a hybrid-aligned liquid crystal microlens,” Mol. Cryst. Liq. Cryst. 199, 27–35 (1991).
[CrossRef]

S. Sato, “Liquid-crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18, 1679–1684 (1979).
[CrossRef]

Scheffer, T. J.

T. J. Scheffer, and J. Nehring, “Accurate determination of liquid-crystal tilt bias angles,” J. Appl. Phys. 48, 1783–1792 (1977).
[CrossRef]

Schwiegerling, J.

Seed, A. J.

S. Gauza, H. Wang, C. H. Wen, S. T. Wu, A. J. Seed, and R. Dabrowski, “High birefringence isothiocyanato tolane liquid crystals,” Jpn. J. Appl. Phys. 42, 3463–3466 (2003).
[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, 051910 (2006).
[CrossRef]

Sheu, C. R.

Song, Q.

M. Jiao, Z. Ge, Q. Song, and S. T. Wu, “Alignment layer effects on thin liquid crystal cells,” Appl. Phys. Lett. 92, 061102 (2008).
[CrossRef]

Suyama, S.

S. Suyama, M. Date, and H. Takada, “Three-dimensional display system with dual-frequency liquid-crystal varifocal lens,” Jpn. J. Appl. Phys. 39, 480–484 (2000).
[CrossRef]

Takada, H.

S. Suyama, M. Date, and H. Takada, “Three-dimensional display system with dual-frequency liquid-crystal varifocal lens,” Jpn. J. Appl. Phys. 39, 480–484 (2000).
[CrossRef]

Towler, M. J.

E. J. Acosta, M. J. Towler, and H. G. Walton, “The role of surface tilt in the operation of pi-cell liquid crystal devices,” Liq. Cryst. 27, 977–984 (2000).
[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, 051910 (2006).
[CrossRef]

Valley, P.

Walton, H. G.

E. J. Acosta, M. J. Towler, and H. G. Walton, “The role of surface tilt in the operation of pi-cell liquid crystal devices,” Liq. Cryst. 27, 977–984 (2000).
[CrossRef]

Wang, B.

M. Ye, B. Wang, and S. Sato, “Liquid-crystal lens with a focal length that is variable in a wide range,” Appl. Opt. 43, 6407–6412 (2004).
[CrossRef]

M. Ye, B. Wang, and S. Sato, “Driving of liquid crystal lens without disclination occurring by applying in-plane electric field,” Jpn. J. Appl. Phys. 42, 5086–5089 (2003).
[CrossRef]

Wang, H.

Y. H. Fan, H. Ren, X. Liang, H. Wang, and S. T. Wu, “Liquid crystal microlens arrays with switchable positive and negative focal lengths,” J. Disp. Tech. 1, 151–156 (2005).
[CrossRef]

H. Wang, T. X. Wu, X. Zhu, and S. T. Wu, “Correlations between liquid crystal director reorientation and optical response time of a homeotropic cell,” J. Appl. Phys. 95, 5502–5508 (2004).
[CrossRef]

S. Gauza, H. Wang, C. H. Wen, S. T. Wu, A. J. Seed, and R. Dabrowski, “High birefringence isothiocyanato tolane liquid crystals,” Jpn. J. Appl. Phys. 42, 3463–3466 (2003).
[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, 7634–7638 (2004).
[CrossRef]

S. Gauza, H. Wang, C. H. Wen, S. T. Wu, A. J. Seed, and R. Dabrowski, “High birefringence isothiocyanato tolane liquid crystals,” Jpn. J. Appl. Phys. 42, 3463–3466 (2003).
[CrossRef]

Wu, B.

Wu, C. S.

S. T. Wu and C. S. Wu, “Small angle relaxation of highly deformed nematic liquid crystals,” Appl. Phys. Lett. 53, 1794–1796 (1988).
[CrossRef]

Wu, S. T.

M. Jiao, Z. Ge, Q. Song, and S. T. Wu, “Alignment layer effects on thin liquid crystal cells,” Appl. Phys. Lett. 92, 061102 (2008).
[CrossRef]

H. Ren, D. W. Fox, B. Wu, and S. T. Wu, “Liquid crystal lens with large focal length tunability and low operating voltage,” Opt. Express 15, 11328–11335 (2007).
[CrossRef]

X. Nie, H. Xianyu, R. Lu, T. X. Wu, and S. T. Wu, “Pretilt angle effects on liquid crystal response time,” J. Disp. Tech. 3, 280–283 (2007).
[CrossRef]

Y. H. Fan, H. Ren, X. Liang, H. Wang, and S. T. Wu, “Liquid crystal microlens arrays with switchable positive and negative focal lengths,” J. Disp. Tech. 1, 151–156 (2005).
[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, 7634–7638 (2004).
[CrossRef]

Y. Q. Lu, X. Liang, Y. H. Wu, F. Du, and S. T. Wu, “Dual-frequency addressed hybrid-aligned nematic liquid crystal,” Appl. Phys. Lett. 85, 3354–3356 (2004).
[CrossRef]

H. Wang, T. X. Wu, X. Zhu, and S. T. Wu, “Correlations between liquid crystal director reorientation and optical response time of a homeotropic cell,” J. Appl. Phys. 95, 5502–5508 (2004).
[CrossRef]

S. Gauza, H. Wang, C. H. Wen, S. T. Wu, A. J. Seed, and R. Dabrowski, “High birefringence isothiocyanato tolane liquid crystals,” Jpn. J. Appl. Phys. 42, 3463–3466 (2003).
[CrossRef]

H. Ren and S. T. Wu, “Tunable electronic lens using a gradient polymer network liquid crystal,” Appl. Phys. Lett. 82, 22–24 (2003).
[CrossRef]

S. T. Wu, “Nematic liquid crystal modulator with response time less than 100 μs at room temperature,” Appl. Phys. Lett. 57, 986–988 (1990).
[CrossRef]

S. T. Wu and C. S. Wu, “Small angle relaxation of highly deformed nematic liquid crystals,” Appl. Phys. Lett. 53, 1794–1796 (1988).
[CrossRef]

Wu, T. X.

X. Nie, H. Xianyu, R. Lu, T. X. Wu, and S. T. Wu, “Pretilt angle effects on liquid crystal response time,” J. Disp. Tech. 3, 280–283 (2007).
[CrossRef]

H. Wang, T. X. Wu, X. Zhu, and S. T. Wu, “Correlations between liquid crystal director reorientation and optical response time of a homeotropic cell,” J. Appl. Phys. 95, 5502–5508 (2004).
[CrossRef]

Wu, Y. H.

Y. Q. Lu, X. Liang, Y. H. Wu, F. Du, and S. T. Wu, “Dual-frequency addressed hybrid-aligned nematic liquid crystal,” Appl. Phys. Lett. 85, 3354–3356 (2004).
[CrossRef]

Xianyu, H.

X. Nie, H. Xianyu, R. Lu, T. X. Wu, and S. T. Wu, “Pretilt angle effects on liquid crystal response time,” J. Disp. Tech. 3, 280–283 (2007).
[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, 051910 (2006).
[CrossRef]

Ye, M.

M. Ye, B. Wang, and S. Sato, “Liquid-crystal lens with a focal length that is variable in a wide range,” Appl. Opt. 43, 6407–6412 (2004).
[CrossRef]

M. Ye, B. Wang, and S. Sato, “Driving of liquid crystal lens without disclination occurring by applying in-plane electric field,” Jpn. J. Appl. Phys. 42, 5086–5089 (2003).
[CrossRef]

M. Ye and S. Sato, “Optical properties of liquid crystal lens of any size,” Jpn. J. Appl. Phys. 41, L571–L573 (2002).
[CrossRef]

M. Ye and S. Sato, “Transient properties of a liquid-crystal microlens,” Jpn. J. Appl. Phys. 40, 6012–6016 (2001).
[CrossRef]

Yeh, P.

P. Yeh and C. Gu, Optics of Liquid Crystal Displays (Wiley, 1999).

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, 051910 (2006).
[CrossRef]

Zhu, X.

H. Wang, T. X. Wu, X. Zhu, and S. T. Wu, “Correlations between liquid crystal director reorientation and optical response time of a homeotropic cell,” J. Appl. Phys. 95, 5502–5508 (2004).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (6)

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, 051910 (2006).
[CrossRef]

M. Jiao, Z. Ge, Q. Song, and S. T. Wu, “Alignment layer effects on thin liquid crystal cells,” Appl. Phys. Lett. 92, 061102 (2008).
[CrossRef]

Y. Q. Lu, X. Liang, Y. H. Wu, F. Du, and S. T. Wu, “Dual-frequency addressed hybrid-aligned nematic liquid crystal,” Appl. Phys. Lett. 85, 3354–3356 (2004).
[CrossRef]

S. T. Wu and C. S. Wu, “Small angle relaxation of highly deformed nematic liquid crystals,” Appl. Phys. Lett. 53, 1794–1796 (1988).
[CrossRef]

S. T. Wu, “Nematic liquid crystal modulator with response time less than 100 μs at room temperature,” Appl. Phys. Lett. 57, 986–988 (1990).
[CrossRef]

H. Ren and S. T. Wu, “Tunable electronic lens using a gradient polymer network liquid crystal,” Appl. Phys. Lett. 82, 22–24 (2003).
[CrossRef]

J. Appl. Phys. (3)

S. Matsumoto, M. Kawamoto, and K. Mizunoya, “Field-induced deformation of hybrid-aligned nematic liquid crystals: new multicolor liquid crystal display,” J. Appl. Phys. 47, 3842–3845 (1976).
[CrossRef]

H. Wang, T. X. Wu, X. Zhu, and S. T. Wu, “Correlations between liquid crystal director reorientation and optical response time of a homeotropic cell,” J. Appl. Phys. 95, 5502–5508 (2004).
[CrossRef]

T. J. Scheffer, and J. Nehring, “Accurate determination of liquid-crystal tilt bias angles,” J. Appl. Phys. 48, 1783–1792 (1977).
[CrossRef]

J. Disp. Tech. (2)

X. Nie, H. Xianyu, R. Lu, T. X. Wu, and S. T. Wu, “Pretilt angle effects on liquid crystal response time,” J. Disp. Tech. 3, 280–283 (2007).
[CrossRef]

Y. H. Fan, H. Ren, X. Liang, H. Wang, and S. T. Wu, “Liquid crystal microlens arrays with switchable positive and negative focal lengths,” J. Disp. Tech. 1, 151–156 (2005).
[CrossRef]

Jpn. J. Appl. Phys. (10)

M. Ye and S. Sato, “Transient properties of a liquid-crystal microlens,” Jpn. J. Appl. Phys. 40, 6012–6016 (2001).
[CrossRef]

S. Gauza, H. Wang, C. H. Wen, S. T. Wu, A. J. Seed, and R. Dabrowski, “High birefringence isothiocyanato tolane liquid crystals,” Jpn. J. Appl. Phys. 42, 3463–3466 (2003).
[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, 7634–7638 (2004).
[CrossRef]

T. Nose, S. Masuda, and S. Sato, “Optical properties of a liquid crystal microlens with a symmetric electrode structure,” Jpn. J. Appl. Phys. 30, L2110–L2112 (1991).
[CrossRef]

T. Nose, S. Masuda, and S. Sato, “A liquid crystal microlens with hole-patterned electrodes on both substrates,” Jpn. J. Appl. Phys. 31, 1643–1646 (1992).
[CrossRef]

M. Ye, B. Wang, and S. Sato, “Driving of liquid crystal lens without disclination occurring by applying in-plane electric field,” Jpn. J. Appl. Phys. 42, 5086–5089 (2003).
[CrossRef]

M. Ye and S. Sato, “Optical properties of liquid crystal lens of any size,” Jpn. J. Appl. Phys. 41, L571–L573 (2002).
[CrossRef]

S. Suyama, M. Date, and H. Takada, “Three-dimensional display system with dual-frequency liquid-crystal varifocal lens,” Jpn. J. Appl. Phys. 39, 480–484 (2000).
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H. C. Lin and Y. H. Lin, “An electrically tunable focusing pico-projector adopting a liquid crystal lens,” Jpn. J. Appl. Phys. 49, 102502 (2010).
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[CrossRef]

Liq. Cryst. (1)

E. J. Acosta, M. J. Towler, and H. G. Walton, “The role of surface tilt in the operation of pi-cell liquid crystal devices,” Liq. Cryst. 27, 977–984 (2000).
[CrossRef]

Mol. Cryst. Liq. Cryst. (2)

Y. Mao and S. Sato, “New method of voltage application for improving response time of a liquid crystal lens,” Mol. Cryst. Liq. Cryst. 433, 229–236 (2005).
[CrossRef]

T. Nose, S. Masuda, and S. Sato, “Optical properties of a hybrid-aligned liquid crystal microlens,” Mol. Cryst. Liq. Cryst. 199, 27–35 (1991).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Opt. Rev. (1)

S. Sato, “Applications of liquid crystals to variable-focusing lenses,” Opt. Rev. 6, 471–485 (1999).
[CrossRef]

Phys. Rev. Lett. (1)

A. Bogi, P. Martinot-Lagarde, I. Dozov, and M. Nobili, “Anchoring screening of defects interaction in a nematic liquid crystal,” Phys. Rev. Lett. 89, 225501 (2002).
[CrossRef]

Other (1)

P. Yeh and C. Gu, Optics of Liquid Crystal Displays (Wiley, 1999).

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Figures (5)

Fig. 1.
Fig. 1.

Structure of the hole-patterned LC lens.

Fig. 2.
Fig. 2.

(a) Interference rings of the conventional ECB LC lens; (b) interference rings of the HAN LC lens. In the ECB LC lens, the pretilt angles of the LCs on the top and the bottom substrates are 2°; in the HAN LC lens, the pretilt angles of the LCs on the top and on the bottom substrates are 2° and 89°, respectively. The applied voltage is 1 kHz 60 V.

Fig. 3.
Fig. 3.

Interference rings of the LC lenses with asymmetrical LC alignment. The pretilt angle of the LCs on the top substrate is 2°; the pretilt angles of the LCs on the bottom substrates are (a) 7° and (b) 55°, respectively. The applied voltage is 1 kHz 60 V.

Fig. 4.
Fig. 4.

Focused beam profiles of the LC lenses with asymmetrical LC alignment. The pretilt angle of the LCs on the top substrate is fixed at 2°; the pretilt angle of the LCs on the bottom substrates are (a) 2°; (b) 7°; and (c) 22°, respectively.

Fig. 5.
Fig. 5.

Interference rings of the LC lenses with symmetrical LC alignment. The pretilt angles of LCs are (a) 2°; (b) 5; (c) 9°; (d) 12°; (e) 20°; and (f) 45°. The applied voltage is 1 kHz 40 V.

Tables (2)

Tables Icon

Table 1. Measured Pretilt Angles of the LCs on the Mixed PI-Coated Substrates at Different V-PI Concentrations

Tables Icon

Table 2. Measured Rise times and Fall Times of the LC Lenses with Asymmetrical LC Alignment at Different Pretilt Angles of the LCs on the Bottom Substrates of the LC Lensesa

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

τd=γ1β2K,
τr=γ1ϵ0ΔϵE2β2K,
β=2dcos1(θpθm),

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