Abstract

We report on an electrically controlled liquid-crystal-based variable optical lens filled with a dual-frequency nematic material. The lens design employs a hole-patterned electrode structure in a flat nematic cell. In order to decrease the lens switching time we maximize the dielectric torque by using a dual-frequency nematic material that is aligned at an angle approximately 45° with respect to the bounding plates by obliquely deposited SiOx, and by using an overdrive scheme of electrical switching. Depending on the frequency of the applied field, the director realigns either toward the homeotropic state (perpendicular to the substrates) or toward the planar state (parallel to the substrates), which allows one to control not only the absolute value of the focal length but also its sign. Optical performance of the liquid-crystal lens is close to that of an ideal thin lens.

© 2006 Optical Society of America

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  1. C. Bricot, M. Hareng, and E. Spitz, "Optical projection device and an optical reader incorporating this device," U.S. patent 4,037,929 (26 July 1977).
  2. S. Sato, "Liquid-crystal lens-cells with variable focal length," Jpn. J. Appl. Phys. 18, 1679-1684 (1979).
    [CrossRef]
  3. S. T. Kowel, D. S. Cleverly, and P. G. Kornreich, "Focusing by electrical modulation of refraction in a liquid crystal cell," Appl. Opt. 23, 278-289 (1984).
    [CrossRef] [PubMed]
  4. N. A. Riza and M. C. DeJule, "Three-terminal adaptive nematic liquid-crystal lens device," Opt. Lett. 19, 1013-1015 (1994).
    [CrossRef] [PubMed]
  5. W. W. Chan and S. T. Kowel, "Imaging performance of the liquid-crystal-adaptive lens with conductive ladder meshing," Appl. Opt. 36, 8958-8969 (1997).
    [CrossRef]
  6. S. Sato, A. Sugiyama, and R. Sato, "Variable-focus liquid-crystal Fresnel lens," Jpn. J. Appl. Phys. Part 2 24, L626-L628 (1985).
    [CrossRef]
  7. S. Sato, T. Nose, R. Yamaguchi, and S. Yanase, "Relationship between lens properties and director orientation in a liquid crystal lens," Liq. Cryst. 5, 1435-1442 (1989).
    [CrossRef]
  8. S. Suyama, M. Date, and H. Takada, "Three-dimensional display system with dual-frequency liquid-crystal varifocal lens," Jpn. J. Appl. Phys. Part 1 39, 480-484 (2000).
    [CrossRef]
  9. H. Ren and S.-T. Wu, "Tunable electronic lens using a gradient polymer network liquid crystal," Appl. Phys. Lett. 82, 22-24 (2003).
    [CrossRef]
  10. Y.-H. Fan, H. Ren, and S.-T. Wu, "Switchable Fresnel lens using polymer-stabilized liquid crystals," Opt. Express 11, 3080-3086 (2003).
    [CrossRef] [PubMed]
  11. V. Presnyakov and T. Galstian, "Polymer stabilized liquid crystal lens for electro-optical zoom," in Photonics North 2004: Optical Components and Devices, J. C. Armitage, S. Fafard, R. A. Lessard, G. A. Lampropoulos, eds., Proc. SPIE 5577, 861-869 (2004).
    [CrossRef]
  12. Z. He, T. Nose, and S. Sato, "Optical performance of liquid crystal cells with asymmetric slit-patterned electrodes in various applied field configurations," Jpn. J. Appl. Phys. Part 1 33, 1091-1095 (1994).
    [CrossRef]
  13. H. Ren, Y.-H. Fan, S. Gauza, and S.-T. Wu, "Tunable-focus cylindrical liquid crystal lens," Jpn. J. Appl. Phys. Part 1 43, 652-653 (2004).
    [CrossRef]
  14. T. Nose and S. Sato, "A liquid crystal microlens obtained with a nonuniform electric field," Liq. Cryst. 5, 1425-1433 (1989).
    [CrossRef]
  15. M. Ye and S. Sato, "Optical properties of liquid crystal lens of any size," Jpn. J. Appl. Phys. Part 2 41, L571-L573 (2002).
    [CrossRef]
  16. M. Ye and S. Sato, "Liquid crystal lens with focus movable along and off axis," Opt. Commun. 225, 277-280 (2003).
    [CrossRef]
  17. A. F. Naumov, M. Yu. Loktev, I. R. Guralnik, and G. Vdovin, "Liquid-crystal adaptive lenses with modal control," Opt. Lett. 23, 992-994 (1998).
    [CrossRef]
  18. I. R. Gural'nik and S. A. Samagin, "Optically controlled spherical liquid-crystal lens: theory and experiment," Quantum Electron. 33, 430-424 (2003).
    [CrossRef]
  19. L. M. Blinov and V. G. Chigrinov, Electrooptic Effects in Liquid Crystal Materials (Springer, 1994).
    [CrossRef]
  20. A. B. Golovin, S. V. Shiyanovskii, and O. D. Lavrentovich, "Fast switching dual-frequency liquid crystal optical retarder, driven by an amplitude and frequency modulated voltage," Appl. Phys. Lett. 83, 3864-3866 (2003).
    [CrossRef]
  21. S. Sato, "Applications of liquid crystals to variable-focusing lenses," Opt. Rev. 6, 471-485 (1999).
    [CrossRef]
  22. Y. Yin, M. Gu, A. B. Golovin, S. V. Shiyanovskii, and O. D. Lavrentovich, "Fast switching optical modulator based on dual frequency nematic cell," Mol. Cryst. Liq. Cryst. 421, 133-144 (2004).
    [CrossRef]
  23. 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. Part 1 42, 5086-5089 (2003).
    [CrossRef]
  24. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  25. M. Ye and S. Sato, "Liquid crystal lens with insulator layers for focusing light waves of arbitrary polarizations," Jpn. J. Appl. Phys. Part 1 42, 6439-6440 (2003).
    [CrossRef]
  26. L. G. Commander, S. E. Day, and D. R. Selviah, "Variable focal length microlenses," Opt. Commun. 177, 157-170 (2000).
    [CrossRef]
  27. M. Ye, S. Hayasaka, and S. Sato, "Liquid crystal lens array with hexagonal-hole-patterned electrodes," Jpn. J. Appl. Phys. Part 1 43, 6108-6111 (2004).
    [CrossRef]
  28. H. Ren, Y.-H. Fan, Y.-H. Lin, and S.-T. Wu, "Tunable-focus microlens arrays using nanosized polymer-dispersed liquid crystal droplets," Opt. Commun. 247, 101-106 (2005).
    [CrossRef]
  29. H. Ren, J. R. Wu, Y.-H. Fan, Y.-H. Lin, and S.-T. Wu, "Hermaphroditic liquid-crystal microlens," Opt. Lett. 30, 376-378 (2005).
    [CrossRef] [PubMed]
  30. T. Krupenkin, S. Yang, and P. Mach, "Tunable liquid microlens," Appl. Phys. Lett. 82, 316-318 (2003).
    [CrossRef]
  31. S. Kuiper and B. H. W. Hendriks, "Variable-focus liquid lens for miniature cameras," Appl. Phys. Lett. 85, 1128-1130 (2004).
    [CrossRef]

2005 (2)

H. Ren, Y.-H. Fan, Y.-H. Lin, and S.-T. Wu, "Tunable-focus microlens arrays using nanosized polymer-dispersed liquid crystal droplets," Opt. Commun. 247, 101-106 (2005).
[CrossRef]

H. Ren, J. R. Wu, Y.-H. Fan, Y.-H. Lin, and S.-T. Wu, "Hermaphroditic liquid-crystal microlens," Opt. Lett. 30, 376-378 (2005).
[CrossRef] [PubMed]

2004 (5)

S. Kuiper and B. H. W. Hendriks, "Variable-focus liquid lens for miniature cameras," Appl. Phys. Lett. 85, 1128-1130 (2004).
[CrossRef]

Y. Yin, M. Gu, A. B. Golovin, S. V. Shiyanovskii, and O. D. Lavrentovich, "Fast switching optical modulator based on dual frequency nematic cell," Mol. Cryst. Liq. Cryst. 421, 133-144 (2004).
[CrossRef]

M. Ye, S. Hayasaka, and S. Sato, "Liquid crystal lens array with hexagonal-hole-patterned electrodes," Jpn. J. Appl. Phys. Part 1 43, 6108-6111 (2004).
[CrossRef]

V. Presnyakov and T. Galstian, "Polymer stabilized liquid crystal lens for electro-optical zoom," in Photonics North 2004: Optical Components and Devices, J. C. Armitage, S. Fafard, R. A. Lessard, G. A. Lampropoulos, eds., Proc. SPIE 5577, 861-869 (2004).
[CrossRef]

H. Ren, Y.-H. Fan, S. Gauza, and S.-T. Wu, "Tunable-focus cylindrical liquid crystal lens," Jpn. J. Appl. Phys. Part 1 43, 652-653 (2004).
[CrossRef]

2003 (8)

M. Ye and S. Sato, "Liquid crystal lens with focus movable along and off axis," Opt. Commun. 225, 277-280 (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]

Y.-H. Fan, H. Ren, and S.-T. Wu, "Switchable Fresnel lens using polymer-stabilized liquid crystals," Opt. Express 11, 3080-3086 (2003).
[CrossRef] [PubMed]

I. R. Gural'nik and S. A. Samagin, "Optically controlled spherical liquid-crystal lens: theory and experiment," Quantum Electron. 33, 430-424 (2003).
[CrossRef]

A. B. Golovin, S. V. Shiyanovskii, and O. D. Lavrentovich, "Fast switching dual-frequency liquid crystal optical retarder, driven by an amplitude and frequency modulated voltage," Appl. Phys. Lett. 83, 3864-3866 (2003).
[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. Part 1 42, 5086-5089 (2003).
[CrossRef]

M. Ye and S. Sato, "Liquid crystal lens with insulator layers for focusing light waves of arbitrary polarizations," Jpn. J. Appl. Phys. Part 1 42, 6439-6440 (2003).
[CrossRef]

T. Krupenkin, S. Yang, and P. Mach, "Tunable liquid microlens," Appl. Phys. Lett. 82, 316-318 (2003).
[CrossRef]

2002 (1)

M. Ye and S. Sato, "Optical properties of liquid crystal lens of any size," Jpn. J. Appl. Phys. Part 2 41, L571-L573 (2002).
[CrossRef]

2000 (2)

L. G. Commander, S. E. Day, and D. R. Selviah, "Variable focal length microlenses," Opt. Commun. 177, 157-170 (2000).
[CrossRef]

S. Suyama, M. Date, and H. Takada, "Three-dimensional display system with dual-frequency liquid-crystal varifocal lens," Jpn. J. Appl. Phys. Part 1 39, 480-484 (2000).
[CrossRef]

1999 (1)

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

1998 (1)

1997 (1)

1994 (2)

N. A. Riza and M. C. DeJule, "Three-terminal adaptive nematic liquid-crystal lens device," Opt. Lett. 19, 1013-1015 (1994).
[CrossRef] [PubMed]

Z. He, T. Nose, and S. Sato, "Optical performance of liquid crystal cells with asymmetric slit-patterned electrodes in various applied field configurations," Jpn. J. Appl. Phys. Part 1 33, 1091-1095 (1994).
[CrossRef]

1989 (2)

T. Nose and S. Sato, "A liquid crystal microlens obtained with a nonuniform electric field," Liq. Cryst. 5, 1425-1433 (1989).
[CrossRef]

S. Sato, T. Nose, R. Yamaguchi, and S. Yanase, "Relationship between lens properties and director orientation in a liquid crystal lens," Liq. Cryst. 5, 1435-1442 (1989).
[CrossRef]

1985 (1)

S. Sato, A. Sugiyama, and R. Sato, "Variable-focus liquid-crystal Fresnel lens," Jpn. J. Appl. Phys. Part 2 24, L626-L628 (1985).
[CrossRef]

1984 (1)

1979 (1)

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

1977 (1)

C. Bricot, M. Hareng, and E. Spitz, "Optical projection device and an optical reader incorporating this device," U.S. patent 4,037,929 (26 July 1977).

Blinov, L. M.

L. M. Blinov and V. G. Chigrinov, Electrooptic Effects in Liquid Crystal Materials (Springer, 1994).
[CrossRef]

Bricot, C.

C. Bricot, M. Hareng, and E. Spitz, "Optical projection device and an optical reader incorporating this device," U.S. patent 4,037,929 (26 July 1977).

Chan, W. W.

Chigrinov, V. G.

L. M. Blinov and V. G. Chigrinov, Electrooptic Effects in Liquid Crystal Materials (Springer, 1994).
[CrossRef]

Cleverly, D. S.

Commander, L. G.

L. G. Commander, S. E. Day, and D. R. Selviah, "Variable focal length microlenses," Opt. Commun. 177, 157-170 (2000).
[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. Part 1 39, 480-484 (2000).
[CrossRef]

Day, S. E.

L. G. Commander, S. E. Day, and D. R. Selviah, "Variable focal length microlenses," Opt. Commun. 177, 157-170 (2000).
[CrossRef]

DeJule, M. C.

Fan, Y.-H.

H. Ren, Y.-H. Fan, Y.-H. Lin, and S.-T. Wu, "Tunable-focus microlens arrays using nanosized polymer-dispersed liquid crystal droplets," Opt. Commun. 247, 101-106 (2005).
[CrossRef]

H. Ren, J. R. Wu, Y.-H. Fan, Y.-H. Lin, and S.-T. Wu, "Hermaphroditic liquid-crystal microlens," Opt. Lett. 30, 376-378 (2005).
[CrossRef] [PubMed]

H. Ren, Y.-H. Fan, S. Gauza, and S.-T. Wu, "Tunable-focus cylindrical liquid crystal lens," Jpn. J. Appl. Phys. Part 1 43, 652-653 (2004).
[CrossRef]

Y.-H. Fan, H. Ren, and S.-T. Wu, "Switchable Fresnel lens using polymer-stabilized liquid crystals," Opt. Express 11, 3080-3086 (2003).
[CrossRef] [PubMed]

Galstian, T.

V. Presnyakov and T. Galstian, "Polymer stabilized liquid crystal lens for electro-optical zoom," in Photonics North 2004: Optical Components and Devices, J. C. Armitage, S. Fafard, R. A. Lessard, G. A. Lampropoulos, eds., Proc. SPIE 5577, 861-869 (2004).
[CrossRef]

Gauza, S.

H. Ren, Y.-H. Fan, S. Gauza, and S.-T. Wu, "Tunable-focus cylindrical liquid crystal lens," Jpn. J. Appl. Phys. Part 1 43, 652-653 (2004).
[CrossRef]

Golovin, A. B.

Y. Yin, M. Gu, A. B. Golovin, S. V. Shiyanovskii, and O. D. Lavrentovich, "Fast switching optical modulator based on dual frequency nematic cell," Mol. Cryst. Liq. Cryst. 421, 133-144 (2004).
[CrossRef]

A. B. Golovin, S. V. Shiyanovskii, and O. D. Lavrentovich, "Fast switching dual-frequency liquid crystal optical retarder, driven by an amplitude and frequency modulated voltage," Appl. Phys. Lett. 83, 3864-3866 (2003).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

Gu, M.

Y. Yin, M. Gu, A. B. Golovin, S. V. Shiyanovskii, and O. D. Lavrentovich, "Fast switching optical modulator based on dual frequency nematic cell," Mol. Cryst. Liq. Cryst. 421, 133-144 (2004).
[CrossRef]

Guralnik, I. R.

Gural'nik, I. R.

I. R. Gural'nik and S. A. Samagin, "Optically controlled spherical liquid-crystal lens: theory and experiment," Quantum Electron. 33, 430-424 (2003).
[CrossRef]

Hareng, M.

C. Bricot, M. Hareng, and E. Spitz, "Optical projection device and an optical reader incorporating this device," U.S. patent 4,037,929 (26 July 1977).

Hayasaka, S.

M. Ye, S. Hayasaka, and S. Sato, "Liquid crystal lens array with hexagonal-hole-patterned electrodes," Jpn. J. Appl. Phys. Part 1 43, 6108-6111 (2004).
[CrossRef]

He, Z.

Z. He, T. Nose, and S. Sato, "Optical performance of liquid crystal cells with asymmetric slit-patterned electrodes in various applied field configurations," Jpn. J. Appl. Phys. Part 1 33, 1091-1095 (1994).
[CrossRef]

Hendriks, B. H. W.

S. Kuiper and B. H. W. Hendriks, "Variable-focus liquid lens for miniature cameras," Appl. Phys. Lett. 85, 1128-1130 (2004).
[CrossRef]

Kornreich, P. G.

Kowel, S. T.

Krupenkin, T.

T. Krupenkin, S. Yang, and P. Mach, "Tunable liquid microlens," Appl. Phys. Lett. 82, 316-318 (2003).
[CrossRef]

Kuiper, S.

S. Kuiper and B. H. W. Hendriks, "Variable-focus liquid lens for miniature cameras," Appl. Phys. Lett. 85, 1128-1130 (2004).
[CrossRef]

Lavrentovich, O. D.

Y. Yin, M. Gu, A. B. Golovin, S. V. Shiyanovskii, and O. D. Lavrentovich, "Fast switching optical modulator based on dual frequency nematic cell," Mol. Cryst. Liq. Cryst. 421, 133-144 (2004).
[CrossRef]

A. B. Golovin, S. V. Shiyanovskii, and O. D. Lavrentovich, "Fast switching dual-frequency liquid crystal optical retarder, driven by an amplitude and frequency modulated voltage," Appl. Phys. Lett. 83, 3864-3866 (2003).
[CrossRef]

Lin, Y.-H.

H. Ren, J. R. Wu, Y.-H. Fan, Y.-H. Lin, and S.-T. Wu, "Hermaphroditic liquid-crystal microlens," Opt. Lett. 30, 376-378 (2005).
[CrossRef] [PubMed]

H. Ren, Y.-H. Fan, Y.-H. Lin, and S.-T. Wu, "Tunable-focus microlens arrays using nanosized polymer-dispersed liquid crystal droplets," Opt. Commun. 247, 101-106 (2005).
[CrossRef]

Loktev, M. Yu.

Mach, P.

T. Krupenkin, S. Yang, and P. Mach, "Tunable liquid microlens," Appl. Phys. Lett. 82, 316-318 (2003).
[CrossRef]

Naumov, A. F.

Nose, T.

Z. He, T. Nose, and S. Sato, "Optical performance of liquid crystal cells with asymmetric slit-patterned electrodes in various applied field configurations," Jpn. J. Appl. Phys. Part 1 33, 1091-1095 (1994).
[CrossRef]

T. Nose and S. Sato, "A liquid crystal microlens obtained with a nonuniform electric field," Liq. Cryst. 5, 1425-1433 (1989).
[CrossRef]

S. Sato, T. Nose, R. Yamaguchi, and S. Yanase, "Relationship between lens properties and director orientation in a liquid crystal lens," Liq. Cryst. 5, 1435-1442 (1989).
[CrossRef]

Presnyakov, V.

V. Presnyakov and T. Galstian, "Polymer stabilized liquid crystal lens for electro-optical zoom," in Photonics North 2004: Optical Components and Devices, J. C. Armitage, S. Fafard, R. A. Lessard, G. A. Lampropoulos, eds., Proc. SPIE 5577, 861-869 (2004).
[CrossRef]

Ren, H.

H. Ren, Y.-H. Fan, Y.-H. Lin, and S.-T. Wu, "Tunable-focus microlens arrays using nanosized polymer-dispersed liquid crystal droplets," Opt. Commun. 247, 101-106 (2005).
[CrossRef]

H. Ren, J. R. Wu, Y.-H. Fan, Y.-H. Lin, and S.-T. Wu, "Hermaphroditic liquid-crystal microlens," Opt. Lett. 30, 376-378 (2005).
[CrossRef] [PubMed]

H. Ren, Y.-H. Fan, S. Gauza, and S.-T. Wu, "Tunable-focus cylindrical liquid crystal lens," Jpn. J. Appl. Phys. Part 1 43, 652-653 (2004).
[CrossRef]

Y.-H. Fan, H. Ren, and S.-T. Wu, "Switchable Fresnel lens using polymer-stabilized liquid crystals," Opt. Express 11, 3080-3086 (2003).
[CrossRef] [PubMed]

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

Riza, N. A.

Samagin, S. A.

I. R. Gural'nik and S. A. Samagin, "Optically controlled spherical liquid-crystal lens: theory and experiment," Quantum Electron. 33, 430-424 (2003).
[CrossRef]

Sato, R.

S. Sato, A. Sugiyama, and R. Sato, "Variable-focus liquid-crystal Fresnel lens," Jpn. J. Appl. Phys. Part 2 24, L626-L628 (1985).
[CrossRef]

Sato, S.

M. Ye, S. Hayasaka, and S. Sato, "Liquid crystal lens array with hexagonal-hole-patterned electrodes," Jpn. J. Appl. Phys. Part 1 43, 6108-6111 (2004).
[CrossRef]

M. Ye and S. Sato, "Liquid crystal lens with insulator layers for focusing light waves of arbitrary polarizations," Jpn. J. Appl. Phys. Part 1 42, 6439-6440 (2003).
[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. Part 1 42, 5086-5089 (2003).
[CrossRef]

M. Ye and S. Sato, "Liquid crystal lens with focus movable along and off axis," Opt. Commun. 225, 277-280 (2003).
[CrossRef]

M. Ye and S. Sato, "Optical properties of liquid crystal lens of any size," Jpn. J. Appl. Phys. Part 2 41, L571-L573 (2002).
[CrossRef]

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

Z. He, T. Nose, and S. Sato, "Optical performance of liquid crystal cells with asymmetric slit-patterned electrodes in various applied field configurations," Jpn. J. Appl. Phys. Part 1 33, 1091-1095 (1994).
[CrossRef]

T. Nose and S. Sato, "A liquid crystal microlens obtained with a nonuniform electric field," Liq. Cryst. 5, 1425-1433 (1989).
[CrossRef]

S. Sato, T. Nose, R. Yamaguchi, and S. Yanase, "Relationship between lens properties and director orientation in a liquid crystal lens," Liq. Cryst. 5, 1435-1442 (1989).
[CrossRef]

S. Sato, A. Sugiyama, and R. Sato, "Variable-focus liquid-crystal Fresnel lens," Jpn. J. Appl. Phys. Part 2 24, L626-L628 (1985).
[CrossRef]

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

Selviah, D. R.

L. G. Commander, S. E. Day, and D. R. Selviah, "Variable focal length microlenses," Opt. Commun. 177, 157-170 (2000).
[CrossRef]

Shiyanovskii, S. V.

Y. Yin, M. Gu, A. B. Golovin, S. V. Shiyanovskii, and O. D. Lavrentovich, "Fast switching optical modulator based on dual frequency nematic cell," Mol. Cryst. Liq. Cryst. 421, 133-144 (2004).
[CrossRef]

A. B. Golovin, S. V. Shiyanovskii, and O. D. Lavrentovich, "Fast switching dual-frequency liquid crystal optical retarder, driven by an amplitude and frequency modulated voltage," Appl. Phys. Lett. 83, 3864-3866 (2003).
[CrossRef]

Spitz, E.

C. Bricot, M. Hareng, and E. Spitz, "Optical projection device and an optical reader incorporating this device," U.S. patent 4,037,929 (26 July 1977).

Sugiyama, A.

S. Sato, A. Sugiyama, and R. Sato, "Variable-focus liquid-crystal Fresnel lens," Jpn. J. Appl. Phys. Part 2 24, L626-L628 (1985).
[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. Part 1 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. Part 1 39, 480-484 (2000).
[CrossRef]

Vdovin, G.

Wang, B.

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. Part 1 42, 5086-5089 (2003).
[CrossRef]

Wu, J. R.

Wu, S.-T.

H. Ren, Y.-H. Fan, Y.-H. Lin, and S.-T. Wu, "Tunable-focus microlens arrays using nanosized polymer-dispersed liquid crystal droplets," Opt. Commun. 247, 101-106 (2005).
[CrossRef]

H. Ren, J. R. Wu, Y.-H. Fan, Y.-H. Lin, and S.-T. Wu, "Hermaphroditic liquid-crystal microlens," Opt. Lett. 30, 376-378 (2005).
[CrossRef] [PubMed]

H. Ren, Y.-H. Fan, S. Gauza, and S.-T. Wu, "Tunable-focus cylindrical liquid crystal lens," Jpn. J. Appl. Phys. Part 1 43, 652-653 (2004).
[CrossRef]

Y.-H. Fan, H. Ren, and S.-T. Wu, "Switchable Fresnel lens using polymer-stabilized liquid crystals," Opt. Express 11, 3080-3086 (2003).
[CrossRef] [PubMed]

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

Yamaguchi, R.

S. Sato, T. Nose, R. Yamaguchi, and S. Yanase, "Relationship between lens properties and director orientation in a liquid crystal lens," Liq. Cryst. 5, 1435-1442 (1989).
[CrossRef]

Yanase, S.

S. Sato, T. Nose, R. Yamaguchi, and S. Yanase, "Relationship between lens properties and director orientation in a liquid crystal lens," Liq. Cryst. 5, 1435-1442 (1989).
[CrossRef]

Yang, S.

T. Krupenkin, S. Yang, and P. Mach, "Tunable liquid microlens," Appl. Phys. Lett. 82, 316-318 (2003).
[CrossRef]

Ye, M.

M. Ye, S. Hayasaka, and S. Sato, "Liquid crystal lens array with hexagonal-hole-patterned electrodes," Jpn. J. Appl. Phys. Part 1 43, 6108-6111 (2004).
[CrossRef]

M. Ye and S. Sato, "Liquid crystal lens with insulator layers for focusing light waves of arbitrary polarizations," Jpn. J. Appl. Phys. Part 1 42, 6439-6440 (2003).
[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. Part 1 42, 5086-5089 (2003).
[CrossRef]

M. Ye and S. Sato, "Liquid crystal lens with focus movable along and off axis," Opt. Commun. 225, 277-280 (2003).
[CrossRef]

M. Ye and S. Sato, "Optical properties of liquid crystal lens of any size," Jpn. J. Appl. Phys. Part 2 41, L571-L573 (2002).
[CrossRef]

Yin, Y.

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Figures (7)

Fig. 1
Fig. 1

Design of the dual-frequency nematic lens.

Fig. 2
Fig. 2

Experimental setup for response time measurements.

Fig. 3
Fig. 3

Response time of the 110 μm thick lens. (a) Lens optical response (top trace) under applied voltage (bottom trace). The driving signal (bottom trace) is a sequence of SSP (50 V rms, 1 kHz) followed by a holding voltage (4 V rms, 1 kHz) followed by SSP of 40 V rms at 50 kHz. (b) Transition to the focusing state (top trace). Electric signal applied (bottom trace) is a sequence of SSP (50 V rms) followed by a holding voltage (4 V rms) at 1 kHz. (c) Relaxation from the focusing state to the uniform (nonfocusing) director state (top trace). The transition is triggered by SSP of 40 V rms at 50 kHz (bottom trace).

Fig. 4
Fig. 4

Double lens design. Two hole-patterned NLC lenses are coaxial and oriented in a “head-to-head” fashion. The simplified ray paths and director distribution are shown for the field applied at 1 kHz. Lines of the electric fringe field are shown by thin curves. The off-axis focusing of the light caused by the first lens is corrected by the second lens.

Fig. 5
Fig. 5

Output aperture plane of the double lens illustrating the correction of the off- axis focusing effect based on application of the electric field to both cells. The left and right parts of the picture illustrate positive and negative lenses, respectively. Top row: U 1 = 0, interference fringes are not centered; Bottom row: the electric field is applied to both lenses at 1 and 50 kHz; the interference fringes are centered; the lens focal point is located on the lens axis.

Fig. 6
Fig. 6

Phase retardation measurements (dots) of the double NLC lens and the quadratic fitting curves (the solid curves) at two frequencies of the applied electric field: (a) 50 kHz and (b) 1 kHz.

Fig. 7
Fig. 7

Focal length of the double LC lens versus the applied voltage at two frequencies: (a) 50 kHz and (b) 1 kHz.

Equations (4)

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τ on = γ 1 d 2 π 2 K ( U c     2 U 2 U c     2 ) ,
n eff =     n o n e ( n o     2 cos 2 θ + n e     2 sin 2 θ ) 1 / 2
A L ( x , y ) = exp [ i k n d ] exp [ i k 2 f L ( x 2 + y 2 ) ] ,
ϕ = ϕ 0 2 π λ 1 2 f L x 2 .

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