Abstract

We demonstrate a tunable-focus lens using a spherical glass shell and a homogeneous liquid crystal (LC) cell. The inner surface of the glass shell and the bottom surface of the LC cell are coated with indium tin oxide (ITO) electrodes while the LC layer is sandwiched between the spherical and flat ITO electrodes. When a voltage is applied to the electrodes, a centro-symmetric gradient refractive index is generated within the LC layer and the focusing behavior occurs. Based on our analysis, the focal length tunability of the LC lens depends significantly on the filled material in the sag region. For the air-filled LC lens we designed, its focal length can be tuned from infinity to ~96 cm. A method for reducing the operating voltage is proposed.

© 2006 Optical Society of America

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References

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  1. V. V. Presnyakov, K. E. Asatryan, and T. V. Galstian, "Polymer-stabilized liquid crystal for tunable microlens applications," Opt. Express. 10, 865-870 (2002).
    [PubMed]
  2. H. Ren and S. T. Wu, "Tunable electronic lens using a gradient polymer network liquid crystal," Appl. Phys. Lett. 82, 22-24 (2003).
    [CrossRef]
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  5. M. Ye and S. Sato, "Optical properties of liquid crystal lens of any size," Jpn. J. Appl. Phys.,  41, L571-L573 (2002).
    [CrossRef]
  6. S. Sato, "Liquid-crystal lens-cells with variable focal length," Jpn. J. Appl. Phys. 18, 1679-1684 (1979).
    [CrossRef]
  7. B. Wang, M. Ye, M. Honma, T. Nose, and S. Sato, "Liquid crystal lens with spherical electrode," Jpn. J. Appl. Phys. 41, L1232 -L1233 (2002).
    [CrossRef]
  8. H. Ren, Y. H. Fan, S. Gauza, and S. T. Wu, "Tunable flat liquid crystal spherical lens," Appl. Phys. Lett. 84, 4789-4791(2004).
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    [CrossRef] [PubMed]
  10. 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. Technol. 1, 151 - 156 (2005).
    [CrossRef]
  11. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  12. S. T. Wu and D. K. Yang, Reflective Liquid Crystal Displays (Wiley, New York, 2001).
  13. S. Gauza, H. Wang, C. H. Wen, S. T. Wu, A. J. Seed and R. Dąbrowski, "High birefringence isothiocyanato tolane liquid crystals," Jpn. J. Appl. Phys. Part 1,  42, 3463-3466 (2003).
    [CrossRef]

2005

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. Technol. 1, 151 - 156 (2005).
[CrossRef]

2004

H. Ren, Y. H. Fan, S. Gauza, and S. T. Wu, "Tunable flat liquid crystal spherical lens," Appl. Phys. Lett. 84, 4789-4791(2004).

B. Wang, M. Ye, and S. Sato, "Lens of electrically controllable focal length made by a glass lens and liquid crystal layers," Appl. Opt. 43, 3420-3425 (2004).
[CrossRef] [PubMed]

2003

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. Gauza, H. Wang, C. H. Wen, S. T. Wu, A. J. Seed and R. Dąbrowski, "High birefringence isothiocyanato tolane liquid crystals," Jpn. J. Appl. Phys. Part 1,  42, 3463-3466 (2003).
[CrossRef]

2002

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

V. V. Presnyakov, K. E. Asatryan, and T. V. Galstian, "Polymer-stabilized liquid crystal for tunable microlens applications," Opt. Express. 10, 865-870 (2002).
[PubMed]

B. Wang, M. Ye, M. Honma, T. Nose, and S. Sato, "Liquid crystal lens with spherical electrode," Jpn. J. Appl. Phys. 41, L1232 -L1233 (2002).
[CrossRef]

1999

1994

1979

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

Asatryan, K. E.

V. V. Presnyakov, K. E. Asatryan, and T. V. Galstian, "Polymer-stabilized liquid crystal for tunable microlens applications," Opt. Express. 10, 865-870 (2002).
[PubMed]

Dabrowski, R.

S. Gauza, H. Wang, C. H. Wen, S. T. Wu, A. J. Seed and R. Dąbrowski, "High birefringence isothiocyanato tolane liquid crystals," Jpn. J. Appl. Phys. Part 1,  42, 3463-3466 (2003).
[CrossRef]

DeJule, M. C.

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. Technol. 1, 151 - 156 (2005).
[CrossRef]

H. Ren, Y. H. Fan, S. Gauza, and S. T. Wu, "Tunable flat liquid crystal spherical lens," Appl. Phys. Lett. 84, 4789-4791(2004).

Galstian, T. V.

V. V. Presnyakov, K. E. Asatryan, and T. V. Galstian, "Polymer-stabilized liquid crystal for tunable microlens applications," Opt. Express. 10, 865-870 (2002).
[PubMed]

Gauza, S.

H. Ren, Y. H. Fan, S. Gauza, and S. T. Wu, "Tunable flat liquid crystal spherical lens," Appl. Phys. Lett. 84, 4789-4791(2004).

S. Gauza, H. Wang, C. H. Wen, S. T. Wu, A. J. Seed and R. Dąbrowski, "High birefringence isothiocyanato tolane liquid crystals," Jpn. J. Appl. Phys. Part 1,  42, 3463-3466 (2003).
[CrossRef]

Honma, M.

B. Wang, M. Ye, M. Honma, T. Nose, and S. Sato, "Liquid crystal lens with spherical electrode," Jpn. J. Appl. Phys. 41, L1232 -L1233 (2002).
[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. Technol. 1, 151 - 156 (2005).
[CrossRef]

Loktev, M. Yu.

Love, G. D.

Naumov, A. F.

Nose, T.

B. Wang, M. Ye, M. Honma, T. Nose, and S. Sato, "Liquid crystal lens with spherical electrode," Jpn. J. Appl. Phys. 41, L1232 -L1233 (2002).
[CrossRef]

Presnyakov, V. V.

V. V. Presnyakov, K. E. Asatryan, and T. V. Galstian, "Polymer-stabilized liquid crystal for tunable microlens applications," Opt. Express. 10, 865-870 (2002).
[PubMed]

Ren, 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. Technol. 1, 151 - 156 (2005).
[CrossRef]

H. Ren, Y. H. Fan, S. Gauza, and S. T. Wu, "Tunable flat liquid crystal spherical lens," Appl. Phys. Lett. 84, 4789-4791(2004).

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.

Sato, S.

B. Wang, M. Ye, and S. Sato, "Lens of electrically controllable focal length made by a glass lens and liquid crystal layers," Appl. Opt. 43, 3420-3425 (2004).
[CrossRef] [PubMed]

B. Wang, M. Ye, M. Honma, T. Nose, and S. Sato, "Liquid crystal lens with spherical electrode," Jpn. J. Appl. Phys. 41, L1232 -L1233 (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]

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

Seed, A. J.

S. Gauza, H. Wang, C. H. Wen, S. T. Wu, A. J. Seed and R. Dąbrowski, "High birefringence isothiocyanato tolane liquid crystals," Jpn. J. Appl. Phys. Part 1,  42, 3463-3466 (2003).
[CrossRef]

Vladimirov, F. L.

Wang, B.

B. Wang, M. Ye, and S. Sato, "Lens of electrically controllable focal length made by a glass lens and liquid crystal layers," Appl. Opt. 43, 3420-3425 (2004).
[CrossRef] [PubMed]

B. Wang, M. Ye, M. Honma, T. Nose, and S. Sato, "Liquid crystal lens with spherical electrode," Jpn. J. Appl. Phys. 41, L1232 -L1233 (2002).
[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. Technol. 1, 151 - 156 (2005).
[CrossRef]

S. Gauza, H. Wang, C. H. Wen, S. T. Wu, A. J. Seed and R. Dąbrowski, "High birefringence isothiocyanato tolane liquid crystals," Jpn. J. Appl. Phys. Part 1,  42, 3463-3466 (2003).
[CrossRef]

Wen, C. H.

S. Gauza, H. Wang, C. H. Wen, S. T. Wu, A. J. Seed and R. Dąbrowski, "High birefringence isothiocyanato tolane liquid crystals," Jpn. J. Appl. Phys. Part 1,  42, 3463-3466 (2003).
[CrossRef]

Wu, S. T.

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. Technol. 1, 151 - 156 (2005).
[CrossRef]

H. Ren, Y. H. Fan, S. Gauza, and S. T. Wu, "Tunable flat liquid crystal spherical lens," Appl. Phys. Lett. 84, 4789-4791(2004).

S. Gauza, H. Wang, C. H. Wen, S. T. Wu, A. J. Seed and R. Dąbrowski, "High birefringence isothiocyanato tolane liquid crystals," Jpn. J. Appl. Phys. Part 1,  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]

Ye, M.

B. Wang, M. Ye, and S. Sato, "Lens of electrically controllable focal length made by a glass lens and liquid crystal layers," Appl. Opt. 43, 3420-3425 (2004).
[CrossRef] [PubMed]

B. Wang, M. Ye, M. Honma, T. Nose, and S. Sato, "Liquid crystal lens with spherical electrode," Jpn. J. Appl. Phys. 41, L1232 -L1233 (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]

Appl. Opt.

Appl. Phys. Lett.

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

H. Ren, Y. H. Fan, S. Gauza, and S. T. Wu, "Tunable flat liquid crystal spherical lens," Appl. Phys. Lett. 84, 4789-4791(2004).

J. Disp. Technol.

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. Technol. 1, 151 - 156 (2005).
[CrossRef]

Jpn. J. Appl. Phys

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

S. Gauza, H. Wang, C. H. Wen, S. T. Wu, A. J. Seed and R. Dąbrowski, "High birefringence isothiocyanato tolane liquid crystals," Jpn. J. Appl. Phys. Part 1,  42, 3463-3466 (2003).
[CrossRef]

Jpn. J. Appl. Phys.

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

B. Wang, M. Ye, M. Honma, T. Nose, and S. Sato, "Liquid crystal lens with spherical electrode," Jpn. J. Appl. Phys. 41, L1232 -L1233 (2002).
[CrossRef]

Opt. Express

Opt. Express.

V. V. Presnyakov, K. E. Asatryan, and T. V. Galstian, "Polymer-stabilized liquid crystal for tunable microlens applications," Opt. Express. 10, 865-870 (2002).
[PubMed]

Opt. Lett.

Other

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

S. T. Wu and D. K. Yang, Reflective Liquid Crystal Displays (Wiley, New York, 2001).

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Figures (5)

Fig. 1.
Fig. 1.

Device structure of the proposed surface-relief LC lens.

Fig. 2.
Fig. 2.

Electric field within the LC layer at the lens border and lens center with various voltages applied across the electrodes. The LC cell gap is 25 µm and the sag of the glass shell is 0.72 mm. The filled material is either polymer NOA81 or air.

Fig. 3.
Fig. 3.

Voltage-dependent transmittance of a homogeneous LC cell between crossed polarizers. LC is BL-038, cell gap dLC=25 µm, and λ=633 nm.

Fig. 4.
Fig. 4.

Interference rings of the LC lens at V=140 Vrms. (a) polymer-filled lens and (b) air-filled lens.

Fig. 5.
Fig. 5.

Profiles of phase retardation of the air-filled LC lens at V= 40, 60, and 140 Vrms.

Equations (8)

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

E b = V ε LC ( d LC ε LC + d g ε g ) ,
E c = V ε LC ( d LC ε LC + d g ε g + d s ε m ) ,
E b , p = 1.275 V
E c , p = 0.430 V
E b , air = 1.275 V ,
E c , air = 0.118 V .
f = r 2 2 d LC δ n ,
V th = π K 11 ε 0 Δ ε

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