Abstract

Using both direct mathematical analysis and numerical modeling based on the predictions by Jones [1] it is shown that if the director in a liquid crystal cell is in a plane which lies at 45° to the incident polarization, then, for normally incident light, the transmission signal which conserves polarization will always have a phase difference of π/2 from the transmission signal of the orthogonal polarization. This is independent of the director profile in the plane, the cell thickness, the anisotropy of the liquid crystal refractive index and the optical parameters of other isotropic layers in the cell. Based on this realization a hybrid aligned nematic liquid crystal cell has been tested as a thresholdless voltage-controlled polarization rotator. By using a quarter-wave plate to compensate for the phase difference between the two orthogonal output polarizations a simple liquid crystal spatial light modulator has been realized.

© 2007 Optical Society of America

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References

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  1. R. C. Jones, "A new calculation for the treatment of optical systems, III. The Sohncke theory of optical activity," J. Opt. Soc. Am. 31, 500-503 (1941).
    [CrossRef]
  2. J. L. Horner and P. D. Gianino, "Phase-only matched filtering," Appl. Opt. 23, 812-816 (1984).
    [CrossRef] [PubMed]
  3. J. A. Davis, D. E. McNamara and D. M. Cottrell, "Encoding complex diffractive optical elements onto a phase-only liquid-crystal spatial light modulator," Opt. Eng. 40, 327-329 (2001).
    [CrossRef]
  4. L. Hu, L. Xuan, Y. Liu, Z. Cao, D. Li, and Q. Mu, "Phase-only liquid crystal spatial light modulator for wavefront correction with high precision," Opt. Express 12, 6403-6409 (2004).
    [CrossRef] [PubMed]
  5. V. Arrizon, G. Mendez and D. Sanchez-de-La-Llave, "Accurate encoding of arbitrary complex fields with amplitude-only liquid crystal spatial light modulator," Opt. Express 13, 7913-7927 (2005).
    [CrossRef] [PubMed]
  6. M. Stalder and M. Schadt, "Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters," Opt. Lett. 21, 1948-1950 (1996).
    [CrossRef] [PubMed]
  7. Z. Zhuang, S.-W. Suh and J. S. Patel, "Polarization controller using nematic liquid crystals," Opt. Lett. 24, 694-696 (1999).
    [CrossRef]
  8. YuT-C  and LoY-L , "Using a new liquid-crystal polarization modulator for a polarimetric glucose sensor," Proc. SPIE  5852, 21-27 (2005).
    [CrossRef]
  9. J. Remenyi, P. Varhegyi, L. Domjan, P. Koppa and E. Lorincz, "Amplitude, phase, and hybrid ternary modulation modes of a twisted-nematic liquid-crystal display at ~400 nm," Appl. Opt. 42, 3428-3434 (2003).
    [CrossRef] [PubMed]
  10. J. S. Jang and D. H. Shin, "Optical representation of binary data based on both intensity and phase modulation with a twisted-nematic liquid-crystal display for holographic digital data storage," Opt. Lett. 26, 1797-1799 (2001).
    [CrossRef]
  11. J. A. Davis, D. E. McNamara, D. M. Cottrell and T. Sonehara, "Two-dimentional Polarization Encoding with a Phase-only Liquid Crystal Light Modulator," Appl. Opt,  39, 1549-1554 (2000).
    [CrossRef]
  12. J. Nicolas, J. Campos and M. J. Yzuel, "Phase and amplitude modulation of elliptic polarization states bynonabsorbing anisotropic elements: application to liquid-crystal devices," J. Opt. Soc. Am. A 19, 1013-1020 (2002).
    [CrossRef]

2005 (2)

2004 (1)

2003 (1)

2002 (1)

2001 (2)

J. S. Jang and D. H. Shin, "Optical representation of binary data based on both intensity and phase modulation with a twisted-nematic liquid-crystal display for holographic digital data storage," Opt. Lett. 26, 1797-1799 (2001).
[CrossRef]

J. A. Davis, D. E. McNamara and D. M. Cottrell, "Encoding complex diffractive optical elements onto a phase-only liquid-crystal spatial light modulator," Opt. Eng. 40, 327-329 (2001).
[CrossRef]

2000 (1)

J. A. Davis, D. E. McNamara, D. M. Cottrell and T. Sonehara, "Two-dimentional Polarization Encoding with a Phase-only Liquid Crystal Light Modulator," Appl. Opt,  39, 1549-1554 (2000).
[CrossRef]

1999 (1)

1996 (1)

1984 (1)

1941 (1)

Arrizon, V.

Campos, J.

Cao, Z.

Cottrell, D. M.

J. A. Davis, D. E. McNamara and D. M. Cottrell, "Encoding complex diffractive optical elements onto a phase-only liquid-crystal spatial light modulator," Opt. Eng. 40, 327-329 (2001).
[CrossRef]

J. A. Davis, D. E. McNamara, D. M. Cottrell and T. Sonehara, "Two-dimentional Polarization Encoding with a Phase-only Liquid Crystal Light Modulator," Appl. Opt,  39, 1549-1554 (2000).
[CrossRef]

Davis, J. A.

J. A. Davis, D. E. McNamara and D. M. Cottrell, "Encoding complex diffractive optical elements onto a phase-only liquid-crystal spatial light modulator," Opt. Eng. 40, 327-329 (2001).
[CrossRef]

J. A. Davis, D. E. McNamara, D. M. Cottrell and T. Sonehara, "Two-dimentional Polarization Encoding with a Phase-only Liquid Crystal Light Modulator," Appl. Opt,  39, 1549-1554 (2000).
[CrossRef]

Domjan, L.

Gianino, P. D.

Horner, J. L.

Hu, L.

Jang, J. S.

Jones, R. C.

Koppa, P.

Li, D.

Liu, Y.

Lo, T-C

YuT-C  and LoY-L , "Using a new liquid-crystal polarization modulator for a polarimetric glucose sensor," Proc. SPIE  5852, 21-27 (2005).
[CrossRef]

Lorincz, E.

McNamara, D. E.

J. A. Davis, D. E. McNamara and D. M. Cottrell, "Encoding complex diffractive optical elements onto a phase-only liquid-crystal spatial light modulator," Opt. Eng. 40, 327-329 (2001).
[CrossRef]

J. A. Davis, D. E. McNamara, D. M. Cottrell and T. Sonehara, "Two-dimentional Polarization Encoding with a Phase-only Liquid Crystal Light Modulator," Appl. Opt,  39, 1549-1554 (2000).
[CrossRef]

Mendez, G.

Mu, Q.

Nicolas, J.

Patel, J. S.

Remenyi, J.

Sanchez-de-La-Llave, D.

Schadt, M.

Shin, D. H.

Sonehara, T.

J. A. Davis, D. E. McNamara, D. M. Cottrell and T. Sonehara, "Two-dimentional Polarization Encoding with a Phase-only Liquid Crystal Light Modulator," Appl. Opt,  39, 1549-1554 (2000).
[CrossRef]

Stalder, M.

Suh, S.-W.

Varhegyi, P.

Xuan, L.

Yu,

YuT-C  and LoY-L , "Using a new liquid-crystal polarization modulator for a polarimetric glucose sensor," Proc. SPIE  5852, 21-27 (2005).
[CrossRef]

Yzuel, M. J.

Zhuang, Z.

Appl. Opt (1)

J. A. Davis, D. E. McNamara, D. M. Cottrell and T. Sonehara, "Two-dimentional Polarization Encoding with a Phase-only Liquid Crystal Light Modulator," Appl. Opt,  39, 1549-1554 (2000).
[CrossRef]

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Eng. (1)

J. A. Davis, D. E. McNamara and D. M. Cottrell, "Encoding complex diffractive optical elements onto a phase-only liquid-crystal spatial light modulator," Opt. Eng. 40, 327-329 (2001).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

SPIE (1)

YuT-C  and LoY-L , "Using a new liquid-crystal polarization modulator for a polarimetric glucose sensor," Proc. SPIE  5852, 21-27 (2005).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

The director in the lab-system, O-XYZ.

Fig. 2.
Fig. 2.

The model results for a HAN cell under an applied voltage. The liquid crystal layer has ne = 1.7400, no = 1.5200 and d = 6.00 μm. (a) The transmission intensities, Txx and Txy against voltage. (b) The transmission phases, Φx and Φy , against voltage.

Fig. 3
Fig. 3

The model results of a HAN cell under an applied voltage. The transmission phases, Φx and Φy , against voltage when the liquid crystal layer has (a) ne = 1.7400, no = 1.5200 and d = 8.00 μm and (b) ne = 1.7400, no = 1.5800 and d = 6.00 μm.

Fig. 4.
Fig. 4.

The experimental set-up.

Fig. 5.
Fig. 5.

The polarization direction of the output beam against applied voltage for (a) a parallel aligned cell and (b) a HAN cell.

Fig. 6.
Fig. 6.

Sum of transmissivities against applied voltage for (a) a parallel cell and (b) a HAN cell.

Equations (8)

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n e = n e n o n e 2 cos 2 θ + n o 2 sin 2 θ
x 1 = 1 2 [ e i 2 π λ n e ( 1 ) d 1 + e i 2 π λ n o d 1 ] = cos [ π λ ( n e ( 1 ) n o ) d 1 ] e i [ π λ ( n e ( 1 ) + n o ) d 1 ] = A x 1 e x 1 ,
y 1 = 1 2 [ e i 2 π λ n e ( 1 ) d 1 e i 2 π λ n o d 1 ] = sin [ π λ ( n e ( 1 ) n o ) d 1 ] e i [ π λ ( n e ( 1 ) + n o ) d 1 + π 2 ] = A y 1 e y 1
x 1 = A x 1 , y 1 = A y 1 e i π 2 and A y 1 = 1 A x 1 2 . It follows that
x 2 = 1 2 [ ( x 1 + y 1 ) e i 2 π λ n e ( 2 ) d 2 + ( x 1 y 1 ) e i 2 π λ n o d 2 ] = A x 2 e x 2 ,
y 2 = 1 2 [ ( x 1 + y 1 ) e i 2 π λ n e ( 2 ) d 2 ( x 1 y 1 ) e i 2 π λ n o d 2 = A y 2 e i Φ y 2 ] with A y 2 = 1 A x 2 2 and
Φ x 2 = π λ [ n e ( 2 ) + n o ] d 2 , Φ y 2 = π λ [ n e ( 2 ) + n o ] d 2 + π 2 .
Φ = π λ n o [ d + n e o d dz n e 2 cos 2 θ ( z ) + n o 2 sin 2 θ ( z ) ]

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