Abstract

We show how to two dimensionally encode the polarization state of an incident light beam using a parallel-aligned liquid-crystal spatial light modulator (LCSLM). Each pixel of the LCSLM acts as a voltage-controlled wave plate and can be programmed over a 2π phase range at a wavelength of 514.5 nm. Techniques are reviewed for either rotating the major axis of elliptically polarized light or for converting an input linearly polarized beam into an arbitrary elliptically polarized beam. Experimental results are demonstrated in which we generate various two-dimensional spatial patterns of polarized light. Several potential applications are suggested. We also report an unexpected edge-enhancement effect that might be useful in image processing applications.

© 2000 Optical Society of America

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    [CrossRef] [PubMed]
  2. R. Fontana, R. H. Pantell, “A high-energy laser accelerator for electrons using the inverse Cerenkov effect,” J. Appl. Phys. 54, 4285–4288 (1983).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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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]
  14. C. Ye, “Construction of an optical rotator using quarter-wave plates and an optical retarder,” Opt. Eng. 34, 3031–3035 (1995).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]

1999

1998

S. Sanyal, P. Bandyopadhyay, A. Ghosh, “Vector wave imagery using a birefringent lens,” Opt. Eng. 37, 592–599 (1998).
[CrossRef]

1996

1995

C. Ye, “Construction of an optical rotator using quarter-wave plates and an optical retarder,” Opt. Eng. 34, 3031–3035 (1995).
[CrossRef]

1993

1992

S. C. Tidwell, D. H. Ford, W. D. Kimura, “Transporting and focusing radially polarized laser beams,” Opt. Eng. 31, 1527–1530 (1992).
[CrossRef]

1990

1989

R. Yamaguchi, T. Nose, S. Sato, “Liquid crystal polarizers with axially symmetrical properties,” Jpn. J. Appl. Phys. 28, 1730–1731 (1989).
[CrossRef]

T. H. Chao, “Real time optical edge enhancement using a Hughes liquid crystal light valve,” Appl. Opt. 28, 4727–4731 (1989).
[CrossRef] [PubMed]

1983

R. Fontana, R. H. Pantell, “A high-energy laser accelerator for electrons using the inverse Cerenkov effect,” J. Appl. Phys. 54, 4285–4288 (1983).
[CrossRef]

1982

Amako, J.

J. A. Davis, P. S. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
[CrossRef]

T. Sonehara, J. Amako, “Phase modulated liquid crystal spatial light modulator with VGA resolution,” in Spatial Light Modulators, G. Burdge, S. Esener, eds., Vol. 14 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1997), pp. 165–168.

Armitage, D.

D. Armitage, J. I. Thackara, “Liquid crystal differentiating spatial light modulators,” in Nonlinear Optics and Applications, P. Yeh, ed., Proc. SPIE613, 165–170 (1986).
[CrossRef]

Bandyopadhyay, P.

S. Sanyal, P. Bandyopadhyay, A. Ghosh, “Vector wave imagery using a birefringent lens,” Opt. Eng. 37, 592–599 (1998).
[CrossRef]

Caimi, F.

Casasent, D.

Chao, T. H.

Cottrell, D. M.

J. A. Davis, P. S. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
[CrossRef]

Davis, J. A.

J. A. Davis, P. S. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
[CrossRef]

Fainman, Y.

Fontana, R.

R. Fontana, R. H. Pantell, “A high-energy laser accelerator for electrons using the inverse Cerenkov effect,” J. Appl. Phys. 54, 4285–4288 (1983).
[CrossRef]

Ford, D. H.

S. C. Tidwell, D. H. Ford, W. D. Kimura, “Transporting and focusing radially polarized laser beams,” Opt. Eng. 31, 1527–1530 (1992).
[CrossRef]

S. C. Tidwell, D. H. Ford, W. D. Kimura, “Generating radially polarized beams interferometrically,” Appl. Opt. 29, 2234–2239 (1990).
[CrossRef] [PubMed]

Ford, J. E.

Ghosh, A.

S. Sanyal, P. Bandyopadhyay, A. Ghosh, “Vector wave imagery using a birefringent lens,” Opt. Eng. 37, 592–599 (1998).
[CrossRef]

Gori, F.

Khomenko, A.

Kimura, W. D.

S. C. Tidwell, D. H. Ford, W. D. Kimura, “Transporting and focusing radially polarized laser beams,” Opt. Eng. 31, 1527–1530 (1992).
[CrossRef]

S. C. Tidwell, D. H. Ford, W. D. Kimura, “Generating radially polarized beams interferometrically,” Appl. Opt. 29, 2234–2239 (1990).
[CrossRef] [PubMed]

Kley, E.-B.

Nose, T.

R. Yamaguchi, T. Nose, S. Sato, “Liquid crystal polarizers with axially symmetrical properties,” Jpn. J. Appl. Phys. 28, 1730–1731 (1989).
[CrossRef]

Pantell, R. H.

R. Fontana, R. H. Pantell, “A high-energy laser accelerator for electrons using the inverse Cerenkov effect,” J. Appl. Phys. 54, 4285–4288 (1983).
[CrossRef]

Patel, J. S.

Petronb, M.

Sanyal, S.

S. Sanyal, P. Bandyopadhyay, A. Ghosh, “Vector wave imagery using a birefringent lens,” Opt. Eng. 37, 592–599 (1998).
[CrossRef]

Sato, S.

R. Yamaguchi, T. Nose, S. Sato, “Liquid crystal polarizers with axially symmetrical properties,” Jpn. J. Appl. Phys. 28, 1730–1731 (1989).
[CrossRef]

Schadt, M.

Schnabel, B.

Sonehara, T.

J. A. Davis, P. S. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
[CrossRef]

T. Sonehara, J. Amako, “Phase modulated liquid crystal spatial light modulator with VGA resolution,” in Spatial Light Modulators, G. Burdge, S. Esener, eds., Vol. 14 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1997), pp. 165–168.

Stalder, M.

Suh, S.-W.

Thackara, J. I.

D. Armitage, J. I. Thackara, “Liquid crystal differentiating spatial light modulators,” in Nonlinear Optics and Applications, P. Yeh, ed., Proc. SPIE613, 165–170 (1986).
[CrossRef]

Tidwell, S. C.

S. C. Tidwell, D. H. Ford, W. D. Kimura, “Transporting and focusing radially polarized laser beams,” Opt. Eng. 31, 1527–1530 (1992).
[CrossRef]

S. C. Tidwell, D. H. Ford, W. D. Kimura, “Generating radially polarized beams interferometrically,” Appl. Opt. 29, 2234–2239 (1990).
[CrossRef] [PubMed]

Tsai, P. S.

J. A. Davis, P. S. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
[CrossRef]

Urquhart, K.

Wang, L. V.

Wyrowski, F.

Yamaguchi, R.

R. Yamaguchi, T. Nose, S. Sato, “Liquid crystal polarizers with axially symmetrical properties,” Jpn. J. Appl. Phys. 28, 1730–1731 (1989).
[CrossRef]

Yao, G.

Yariv, A.

A. Yariv, Optical Electronics, 4th ed. (Saunders, Philadelphia, Pa., 1991), Chap. 9.2, p. 326.

Ye, C.

C. Ye, “Photopolarimetric measurement of single, intact pulp fibers by Mueller matrix imaging polarimetry,” Appl. Opt. 38, 1975–1985 (1999).
[CrossRef]

C. Ye, “Construction of an optical rotator using quarter-wave plates and an optical retarder,” Opt. Eng. 34, 3031–3035 (1995).
[CrossRef]

Yu, F.

Zeitner, U. D.

Zhuang, Z.

Appl. Opt.

J. Appl. Phys.

R. Fontana, R. H. Pantell, “A high-energy laser accelerator for electrons using the inverse Cerenkov effect,” J. Appl. Phys. 54, 4285–4288 (1983).
[CrossRef]

Jpn. J. Appl. Phys.

R. Yamaguchi, T. Nose, S. Sato, “Liquid crystal polarizers with axially symmetrical properties,” Jpn. J. Appl. Phys. 28, 1730–1731 (1989).
[CrossRef]

Opt. Eng.

S. C. Tidwell, D. H. Ford, W. D. Kimura, “Transporting and focusing radially polarized laser beams,” Opt. Eng. 31, 1527–1530 (1992).
[CrossRef]

S. Sanyal, P. Bandyopadhyay, A. Ghosh, “Vector wave imagery using a birefringent lens,” Opt. Eng. 37, 592–599 (1998).
[CrossRef]

J. A. Davis, P. S. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
[CrossRef]

C. Ye, “Construction of an optical rotator using quarter-wave plates and an optical retarder,” Opt. Eng. 34, 3031–3035 (1995).
[CrossRef]

Opt. Lett.

Other

See, for example, Polarization Solutions, Meadowlark Optics 1997–1998 Catalog (Meadowlark, Optics, Longmont, Colorado 80504-9470), p. 44.

D. Armitage, J. I. Thackara, “Liquid crystal differentiating spatial light modulators,” in Nonlinear Optics and Applications, P. Yeh, ed., Proc. SPIE613, 165–170 (1986).
[CrossRef]

A. Yariv, Optical Electronics, 4th ed. (Saunders, Philadelphia, Pa., 1991), Chap. 9.2, p. 326.

T. Sonehara, J. Amako, “Phase modulated liquid crystal spatial light modulator with VGA resolution,” in Spatial Light Modulators, G. Burdge, S. Esener, eds., Vol. 14 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1997), pp. 165–168.

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Figures (7)

Fig. 1
Fig. 1

Optical system for rotating the principal axis of elliptically polarized light by an arbitrary angle. The lines denote the extraordinary axes of the wave plates.

Fig. 2
Fig. 2

Experimental results showing the rotation of the plane of polarization as a function of phase level encoded onto the LCSLM. Experiments show transmission through the analyzer polarizer as a function of orientation angle.

Fig. 3
Fig. 3

(a) Phase pattern for generating a radially polarized beam for P = 2. (b) Expected polarization of a radially polarized beam for P = 2. (c) Intensity pattern with the analyzer polarizer parallel to the input polarizer. (d) Intensity pattern with the analyzer polarizer perpendicular to the input polarizer.

Fig. 4
Fig. 4

Optical system for converting incident linearly polarized (LP) light to an arbitrary state of elliptically polarized light. The lines designate the transmission axis of the polarizer and the extraordinary axis of the LCSLM, respectively.

Fig. 5
Fig. 5

Experimental results showing the ellipticity of the transmitted beam as a function of phase level encoded onto the LCSLM. Experiments show transmission through the analyzer polarizer as a function of orientation angle.

Fig. 6
Fig. 6

Pattern used for the experiment. Different gray levels correspond to different phase retardations as discussed in the text.

Fig. 7
Fig. 7

(a) Intensity pattern with the analyzer polarizer perpendicular to the input polarizer. (b) Intensity pattern with the analyzer polarizer parallel to the input polarizer. (c) Intensity pattern with the analyzer polarizer parallel to the ordinary axis of the LCSLM. (d) Intensity pattern with the analyzer polarizer parallel to the extraordinary axis of the LCSLM.

Equations (5)

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ϕV=2π neV-no dλ
M=i001cosϕ/2i sinϕ/2i sinϕ/2cosϕ/2-i001=cosϕ/2sinϕ/2-sinϕ/2cosϕ/2.
θρ, ψ=Pψ+θ0.
Eoutρ, ψ=cosPψ+θ0sinPψ+θ0.
Eout=cosϕ/2i sinϕ/2i sinϕ/2cosϕ/210=cosϕ/2i sinϕ/2.

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