Abstract

The stylus of an atomic force microscope is used to scribe preferred directions for liquid-crystal alignment on a polyimide-coated substrate. The opposing substrate that comprises the liquid-crystal cell is rubbed unidirectionally, resulting in a twisted nematic structure associated with each micrometer-sized pixel. The polarization of light entering from the uniformly rubbed substrate rotates with the nematic director by a different amount in each pixel, and each of the two emerging polarization eigenmodes interferes separately. Two examples are discussed: a square grating that allows only odd-order diffraction peaks and a grating that combines rotation with optical retardation to simulate a blazed grating for circularly polarized light. The gratings can be electrically switched if used with semitransparent electrodes.

© 2002 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2001 (1)

1999 (1)

1998 (1)

Z. He, T. Nose, S. Sato, “Polarization properties of an amplitude nematic liquid crystal grating,” Opt. Eng. 37, 2885–2898 (1998).
[CrossRef]

1997 (1)

D. Subacius, S. V. Shiyanovskii, Ph. Bos, O. D. Lavrentovich, “Cholesteric gratings with field-controlled period,” Appl. Phys. Lett. 71, 3323–3325 (1997).
[CrossRef]

1996 (1)

Z. He, T. Nose, S. Sato, “Diffraction and polarization properties of a liquid crystal grating,” Jpn. J. Appl. Phys. 35, 3529–3530 (1996).
[CrossRef]

1994 (1)

K. A. Suresh, Y. Sah, P. B. S. Kumar, G. S. Ranganath, “Optical diffraction in chiral smectic-C liquid crystals,” Phys. Rev. Lett. 72, 2863–2866 (1994).
[CrossRef] [PubMed]

1992 (1)

M. Schadt, K. Schmitt, V. Kozenkov, V. Chigrinov, “Surface-induced parallel alignment of liquid-crystals by linearly polymerized photopolymers,” Jpn. J. Appl. Phys. 31, 2155–2164 (1992).
[CrossRef]

Adachi, J.

Bos, Ph.

D. Subacius, S. V. Shiyanovskii, Ph. Bos, O. D. Lavrentovich, “Cholesteric gratings with field-controlled period,” Appl. Phys. Lett. 71, 3323–3325 (1997).
[CrossRef]

Chandarsekhar, S.

S. Chandarsekhar, Liquid Crystals (Cambridge U. Press, Cambridge, UK, 1992).
[CrossRef]

Chigrinov, V.

M. Schadt, K. Schmitt, V. Kozenkov, V. Chigrinov, “Surface-induced parallel alignment of liquid-crystals by linearly polymerized photopolymers,” Jpn. J. Appl. Phys. 31, 2155–2164 (1992).
[CrossRef]

Davis, J. A.

DeGennes, P. G.

P. G. DeGennes, J. Prost, The Physics of Liquid Crystals (Clarendon, Oxford, UK, 1994).

Fernández-Pousa, C. R.

Gori, F.

He, Z.

Z. He, T. Nose, S. Sato, “Polarization properties of an amplitude nematic liquid crystal grating,” Opt. Eng. 37, 2885–2898 (1998).
[CrossRef]

Z. He, T. Nose, S. Sato, “Diffraction and polarization properties of a liquid crystal grating,” Jpn. J. Appl. Phys. 35, 3529–3530 (1996).
[CrossRef]

Kozenkov, V.

M. Schadt, K. Schmitt, V. Kozenkov, V. Chigrinov, “Surface-induced parallel alignment of liquid-crystals by linearly polymerized photopolymers,” Jpn. J. Appl. Phys. 31, 2155–2164 (1992).
[CrossRef]

Kumar, P. B. S.

K. A. Suresh, Y. Sah, P. B. S. Kumar, G. S. Ranganath, “Optical diffraction in chiral smectic-C liquid crystals,” Phys. Rev. Lett. 72, 2863–2866 (1994).
[CrossRef] [PubMed]

Lavrentovich, O. D.

D. Subacius, S. V. Shiyanovskii, Ph. Bos, O. D. Lavrentovich, “Cholesteric gratings with field-controlled period,” Appl. Phys. Lett. 71, 3323–3325 (1997).
[CrossRef]

Moreno, I.

Nose, T.

Z. He, T. Nose, S. Sato, “Polarization properties of an amplitude nematic liquid crystal grating,” Opt. Eng. 37, 2885–2898 (1998).
[CrossRef]

Z. He, T. Nose, S. Sato, “Diffraction and polarization properties of a liquid crystal grating,” Jpn. J. Appl. Phys. 35, 3529–3530 (1996).
[CrossRef]

Owechko, Y.

Y. Owechko, B. H. Soffer, “Optical intensity-to-position mapping and light deflector apparatus and method,” U.S. patent4,958,914 (25September1990).

Prost, J.

P. G. DeGennes, J. Prost, The Physics of Liquid Crystals (Clarendon, Oxford, UK, 1994).

Ranganath, G. S.

K. A. Suresh, Y. Sah, P. B. S. Kumar, G. S. Ranganath, “Optical diffraction in chiral smectic-C liquid crystals,” Phys. Rev. Lett. 72, 2863–2866 (1994).
[CrossRef] [PubMed]

Sah, Y.

K. A. Suresh, Y. Sah, P. B. S. Kumar, G. S. Ranganath, “Optical diffraction in chiral smectic-C liquid crystals,” Phys. Rev. Lett. 72, 2863–2866 (1994).
[CrossRef] [PubMed]

Sato, S.

Z. He, T. Nose, S. Sato, “Polarization properties of an amplitude nematic liquid crystal grating,” Opt. Eng. 37, 2885–2898 (1998).
[CrossRef]

Z. He, T. Nose, S. Sato, “Diffraction and polarization properties of a liquid crystal grating,” Jpn. J. Appl. Phys. 35, 3529–3530 (1996).
[CrossRef]

Schadt, M.

M. Schadt, K. Schmitt, V. Kozenkov, V. Chigrinov, “Surface-induced parallel alignment of liquid-crystals by linearly polymerized photopolymers,” Jpn. J. Appl. Phys. 31, 2155–2164 (1992).
[CrossRef]

Schmitt, K.

M. Schadt, K. Schmitt, V. Kozenkov, V. Chigrinov, “Surface-induced parallel alignment of liquid-crystals by linearly polymerized photopolymers,” Jpn. J. Appl. Phys. 31, 2155–2164 (1992).
[CrossRef]

Shiyanovskii, S. V.

D. Subacius, S. V. Shiyanovskii, Ph. Bos, O. D. Lavrentovich, “Cholesteric gratings with field-controlled period,” Appl. Phys. Lett. 71, 3323–3325 (1997).
[CrossRef]

Soffer, B. H.

Y. Owechko, B. H. Soffer, “Optical intensity-to-position mapping and light deflector apparatus and method,” U.S. patent4,958,914 (25September1990).

Subacius, D.

D. Subacius, S. V. Shiyanovskii, Ph. Bos, O. D. Lavrentovich, “Cholesteric gratings with field-controlled period,” Appl. Phys. Lett. 71, 3323–3325 (1997).
[CrossRef]

Suresh, K. A.

K. A. Suresh, Y. Sah, P. B. S. Kumar, G. S. Ranganath, “Optical diffraction in chiral smectic-C liquid crystals,” Phys. Rev. Lett. 72, 2863–2866 (1994).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

D. Subacius, S. V. Shiyanovskii, Ph. Bos, O. D. Lavrentovich, “Cholesteric gratings with field-controlled period,” Appl. Phys. Lett. 71, 3323–3325 (1997).
[CrossRef]

Jpn. J. Appl. Phys. (2)

Z. He, T. Nose, S. Sato, “Diffraction and polarization properties of a liquid crystal grating,” Jpn. J. Appl. Phys. 35, 3529–3530 (1996).
[CrossRef]

M. Schadt, K. Schmitt, V. Kozenkov, V. Chigrinov, “Surface-induced parallel alignment of liquid-crystals by linearly polymerized photopolymers,” Jpn. J. Appl. Phys. 31, 2155–2164 (1992).
[CrossRef]

Opt. Eng. (1)

Z. He, T. Nose, S. Sato, “Polarization properties of an amplitude nematic liquid crystal grating,” Opt. Eng. 37, 2885–2898 (1998).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

K. A. Suresh, Y. Sah, P. B. S. Kumar, G. S. Ranganath, “Optical diffraction in chiral smectic-C liquid crystals,” Phys. Rev. Lett. 72, 2863–2866 (1994).
[CrossRef] [PubMed]

Other (3)

P. G. DeGennes, J. Prost, The Physics of Liquid Crystals (Clarendon, Oxford, UK, 1994).

Y. Owechko, B. H. Soffer, “Optical intensity-to-position mapping and light deflector apparatus and method,” U.S. patent4,958,914 (25September1990).

S. Chandarsekhar, Liquid Crystals (Cambridge U. Press, Cambridge, UK, 1992).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Idealized polarization grating. Heavy lines show director orientations at lower and upper substrates for pixels j and j + 1. Solid arrows at the upper substrate show the polarization exiting from the cell, and dotted arrows show the x and y components of the polarization.

Fig. 2
Fig. 2

AFM image of a polyimide-coated substrate scribed with a square grating pattern.

Fig. 3
Fig. 3

Intensity versus diffraction angle for the x component of polarization emerging from the square grating.

Fig. 4
Fig. 4

AFM image of a polyimide-coated substrate scribed with a pattern used for a blazed grating for circular polarization.

Fig. 5
Fig. 5

Intensity versus diffraction angle for light emerging from the grating in Fig. 4. Upper panel, right-circular polarization (θ = +45°); lower panel, left-circular polarization (θ = -45°).

Equations (5)

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

Ein=AxAy.
Ejout=cos βjsin βj-sin βjcos βjexp-iα001AxAy=Ax exp-iαcos βj+Ay sin βj-Ax exp-iαsin βj+Ay cos βj.
Ejout=Asinβ0-1jA cos β0.
Ej,xout=4Aπm=1,3,5,1msinmπxw.
Ejout=A2-i cos βj+sin βji sin βj+cos βj=A expiβj2-i1,

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