Abstract

A variable-focus lens is made with one or two liquid-crystal layers and a glass lens. The lens has an aperture near that of the glass lens, and its focal length is electrically changeable from that of the glass lens. The principle is described, and the lens is demonstrated experimentally.

© 2004 Optical Society of America

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References

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  1. S. Sato, “Liquid-crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18, 1679–1684 (1979).
    [CrossRef]
  2. T. Nose, S. Sato, “A liquid crystal microlens obtained with a non-uniform electric field,” Liq. Cryst. 5, 1425–1433 (1989).
    [CrossRef]
  3. N. A. Riza, M. C. DeJule, “Three-terminal adaptive nematic liquid-crystal lens device,” Opt. Lett. 19, 1013–1015 (1994).
    [CrossRef] [PubMed]
  4. A. F. Naumov, M. Yu. Loktev, I. R. Guralnik, G. Vdovin, “Liquid-crystal adaptive lenses with modal control,” Opt. Lett. 23, 992–994 (1998).
    [CrossRef]
  5. L. G. Commander, S. E. Day, D. R. Selviah, “Variable focal length microlenses,” Opt. Commun. 177, 157–170 (2000).
    [CrossRef]
  6. M. Ye, S. Sato, “Optical properties of liquid crystal lens of any size,” Jpn. J. Appl. Phys. 41, L571–L573 (2002).
    [CrossRef]
  7. B. Wang, M. Ye, M. Honma, T. Nose, S. Sato, “Liquid crystal lens with spherical electrode,” Jpn. J. Appl. Phys. 41, L1232–L1233 (2002).
    [CrossRef]
  8. H. Ren, S. T. Wu, “Tunable electronic lens using a gradient polymer network liquid crystal,” Appl. Phys. Lett. 82, 22–24 (2003).
    [CrossRef]
  9. H. Ren, Y. H. Fan, S. T. Wu, “Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals,” Appl. Phys. Lett. 83, 1515–1517 (2003).
    [CrossRef]
  10. M. Ye, S. Sato, “Liquid crystal lens with focus movable along and off axis,” Opt. Commun. 225, 277–280 (2003).
    [CrossRef]
  11. L. M. Blinov, V. G. Chigrinov, Electrooptic Effects in Liquid Crystal Materials (Springer-Verlag, New York, 1996).
  12. P. G. de Gennes, The Physics of Liquid Crystals (Oxford U. Press, London, 1974).
  13. L. D. Landau, E. M. Lifshitz, L. P. Pitaevskii, Electrodynamics of Continuous Media (Butterworth-Heinemann, Oxford, England, 1995).
  14. V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer-Verlag, New York, 1978).
    [CrossRef]
  15. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968).
  16. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, England, 1975).
  17. M. Ye, S. Sato, “Liquid crystal lens with insulator layers for focusing light waves of arbitrary polarizations,” Jpn. J. Appl. Phys. 42, 6439–6440 (2003).
    [CrossRef]

2003 (4)

H. Ren, 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. T. Wu, “Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals,” Appl. Phys. Lett. 83, 1515–1517 (2003).
[CrossRef]

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

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

2002 (2)

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

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

2000 (1)

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

1998 (1)

1994 (1)

1989 (1)

T. Nose, S. Sato, “A liquid crystal microlens obtained with a non-uniform electric field,” Liq. Cryst. 5, 1425–1433 (1989).
[CrossRef]

1979 (1)

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

Arnold, V. I.

V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer-Verlag, New York, 1978).
[CrossRef]

Blinov, L. M.

L. M. Blinov, V. G. Chigrinov, Electrooptic Effects in Liquid Crystal Materials (Springer-Verlag, New York, 1996).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, England, 1975).

Chigrinov, V. G.

L. M. Blinov, V. G. Chigrinov, Electrooptic Effects in Liquid Crystal Materials (Springer-Verlag, New York, 1996).

Commander, L. G.

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

Day, S. E.

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

de Gennes, P. G.

P. G. de Gennes, The Physics of Liquid Crystals (Oxford U. Press, London, 1974).

DeJule, M. C.

Fan, Y. H.

H. Ren, Y. H. Fan, S. T. Wu, “Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals,” Appl. Phys. Lett. 83, 1515–1517 (2003).
[CrossRef]

Goodman, J. W.

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

Guralnik, I. R.

Honma, M.

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

Landau, L. D.

L. D. Landau, E. M. Lifshitz, L. P. Pitaevskii, Electrodynamics of Continuous Media (Butterworth-Heinemann, Oxford, England, 1995).

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, L. P. Pitaevskii, Electrodynamics of Continuous Media (Butterworth-Heinemann, Oxford, England, 1995).

Loktev, M. Yu.

Naumov, A. F.

Nose, T.

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

T. Nose, S. Sato, “A liquid crystal microlens obtained with a non-uniform electric field,” Liq. Cryst. 5, 1425–1433 (1989).
[CrossRef]

Pitaevskii, L. P.

L. D. Landau, E. M. Lifshitz, L. P. Pitaevskii, Electrodynamics of Continuous Media (Butterworth-Heinemann, Oxford, England, 1995).

Ren, H.

H. Ren, Y. H. Fan, S. T. Wu, “Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals,” Appl. Phys. Lett. 83, 1515–1517 (2003).
[CrossRef]

H. Ren, 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.

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

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

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

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

T. Nose, S. Sato, “A liquid crystal microlens obtained with a non-uniform electric field,” Liq. Cryst. 5, 1425–1433 (1989).
[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, D. R. Selviah, “Variable focal length microlenses,” Opt. Commun. 177, 157–170 (2000).
[CrossRef]

Vdovin, G.

Wang, B.

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

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, England, 1975).

Wu, S. T.

H. Ren, Y. H. Fan, S. T. Wu, “Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals,” Appl. Phys. Lett. 83, 1515–1517 (2003).
[CrossRef]

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

Ye, M.

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

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

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

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

Appl. Phys. Lett. (2)

H. Ren, 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. T. Wu, “Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals,” Appl. Phys. Lett. 83, 1515–1517 (2003).
[CrossRef]

Jpn. J. Appl. Phys. (4)

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

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

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

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

Liq. Cryst. (1)

T. Nose, S. Sato, “A liquid crystal microlens obtained with a non-uniform electric field,” Liq. Cryst. 5, 1425–1433 (1989).
[CrossRef]

Opt. Commun. (2)

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

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

Opt. Lett. (2)

Other (6)

L. M. Blinov, V. G. Chigrinov, Electrooptic Effects in Liquid Crystal Materials (Springer-Verlag, New York, 1996).

P. G. de Gennes, The Physics of Liquid Crystals (Oxford U. Press, London, 1974).

L. D. Landau, E. M. Lifshitz, L. P. Pitaevskii, Electrodynamics of Continuous Media (Butterworth-Heinemann, Oxford, England, 1995).

V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer-Verlag, New York, 1978).
[CrossRef]

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

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, England, 1975).

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Figures (9)

Fig. 1
Fig. 1

Combination of a concave GL and a LC cell used in numerical calculation.

Fig. 2
Fig. 2

Equipotential lines between electrodes in the plane x = 0.

Fig. 3
Fig. 3

Equipotential lines in LC layer in the planes (a) x = 0 and (b) z = t LC/2.

Fig. 4
Fig. 4

Phase profiles in the plane x = 0.

Fig. 5
Fig. 5

System structure used in the experiment. ITO, indium tin oxide.

Fig. 6
Fig. 6

Interference patterns at (a) V 0 = 70 Vrms, (b) V 0 = 90 Vrms, and (c) V 0 = 110 Vrms.

Fig. 7
Fig. 7

Distributions of phase retardation in the plane x = 0 at various voltages.

Fig. 8
Fig. 8

Power of the system changes with the applied voltage.

Fig. 9
Fig. 9

Lens system of an electrically tunable focal length used in image formation.

Equations (6)

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

fg=-g8πE2,
fair=-18πE2,
fLC=12K11 · n2+K22n · ×n2+K33n××n2-18πLC · E · E,
-fLCnα+βfLCnαβ=0,
ϕ=2πλ0tLCnonene2 sin2 θ+no2 cos2 θ1/2dz,
1f=1fGL+1fLC.

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