Abstract

We report on a novel approach to the realization of nematic liquid-crystal (LC) phase correctors to form spherical and cylindrical wave fronts. A LC cell with a distributed reactive electrical impedance was driven by an ac voltage applied to the cell boundary to yield the desired spatial distribution of the refractive index. The two-dimensional function of the phase delay introduced into the light beam depends on the frequency of the ac control voltage, the geometry of the boundary electrode surrounding the LC cell, and the electrical parameters of the cell. We realized a cylindrical adaptive lens with a clear aperture of 15 mm×4 mm and a spherical adaptive lens with circular aperture of 6.5 mm. Both devices are capable of focusing collimated light in the range 0.5 m.

© 1998 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

1997

J. Gourlay, G. D. Love, P. M. Birch, R. M. Sharples, and A. Purvis, Opt. Commun. 137, 17 (1997).
[CrossRef]

W. W. Chan and S. T. Kowel, Appl. Opt. 36, 8958 (1997).
[CrossRef]

1996

Y. Takaki and H. Ohzu, Opt. Commun. 126, 123 (1996).
[CrossRef]

1994

1988

S. T. Wu and C. S. Wu, Appl. Phys. Lett. 53, 1794 (1988).
[CrossRef]

1986

Bates, T. D.

Birch, P. M.

J. Gourlay, G. D. Love, P. M. Birch, R. M. Sharples, and A. Purvis, Opt. Commun. 137, 17 (1997).
[CrossRef]

Chan, W. W.

DeJule, M. C.

Efron, U.

Gourlay, J.

J. Gourlay, G. D. Love, P. M. Birch, R. M. Sharples, and A. Purvis, Opt. Commun. 137, 17 (1997).
[CrossRef]

Kowel, S. T.

Love, G. D.

J. Gourlay, G. D. Love, P. M. Birch, R. M. Sharples, and A. Purvis, Opt. Commun. 137, 17 (1997).
[CrossRef]

Matic, R. M.

R. M. Matic, Proc. SPIE 2120, 194 (1994).
[CrossRef]

Ohzu, H.

Y. Takaki and H. Ohzu, Opt. Commun. 126, 123 (1996).
[CrossRef]

Purvis, A.

J. Gourlay, G. D. Love, P. M. Birch, R. M. Sharples, and A. Purvis, Opt. Commun. 137, 17 (1997).
[CrossRef]

Riza, N. A.

Sharples, R. M.

J. Gourlay, G. D. Love, P. M. Birch, R. M. Sharples, and A. Purvis, Opt. Commun. 137, 17 (1997).
[CrossRef]

Takaki, Y.

Y. Takaki and H. Ohzu, Opt. Commun. 126, 123 (1996).
[CrossRef]

Wu, C. S.

S. T. Wu and C. S. Wu, Appl. Phys. Lett. 53, 1794 (1988).
[CrossRef]

Wu, S. T.

Appl. Opt.

Appl. Phys. Lett.

S. T. Wu and C. S. Wu, Appl. Phys. Lett. 53, 1794 (1988).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

J. Gourlay, G. D. Love, P. M. Birch, R. M. Sharples, and A. Purvis, Opt. Commun. 137, 17 (1997).
[CrossRef]

Y. Takaki and H. Ohzu, Opt. Commun. 126, 123 (1996).
[CrossRef]

Opt. Lett.

Proc. SPIE

R. M. Matic, Proc. SPIE 2120, 194 (1994).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Top, geometry of the LC cylindrical adaptive lens and bottom, simplified equivalent circuit, illustrating the distributed nature of the reactive impedance of the LC layer sandwiched between high- and low-resistance electrodes.

Fig. 2
Fig. 2

Control voltage and phase correction across the lens aperture introduced into the transmitted beam.

Fig. 3
Fig. 3

(a) Control frequency, (b) voltage, and (c) rms error of the parabolic approximation as functions of the focal distance.

Fig. 4
Fig. 4

Comparison of the numerically computed and experimentally obtained focal distributions formed by a cylindrical adaptive lens. The registered intensity distribution is shown in the inset.

Fig. 5
Fig. 5

Interference fringe patterns in a spherical LC lens for control frequencies of 22, 70, and 600 kHz (left to right), observed through crossed polarizers. The spherical adaptive lens has a diameter of 6.5 mm and a LC thickness of 25   µ m . The sheet resistance of the control electrode was relatively low, which explains the high working frequencies.

Equations (6)

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

2 U = R C U U t + R G U U ,
C U = 0 I I 2 + I 2 ,   G U = 0 ω I I 2 + I 2 ,
I = - d / 2 d / 2 Θ d z 2 Θ + 2 Θ ,   I = - d / 2 d / 2 Θ d z 2 Θ + 2 Θ ,
=   cos 2   Θ +   sin 2   Θ ,   =   cos 2   Θ +   sin 2   Θ .
z K 11   cos 2   Θ + K 33   sin 2   Θ Θ z - K 33 - K 11 sin   Θ cos   Θ Θ z 2 + - U 2 4 π d 2 sin   Θ cos   Θ = 0 ,
Δ Φ = 2 π λ - d / 2 d / 2 × n n n 2 cos 2   Θ z + n 2   sin 2   Θ z 1 / 2 - n d z ,

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