Abstract

A new approach to a polarization-independent twisted liquid-crystal (LC) structure, where phase difference between orthogonal eigenmodes is tuned to be an integer multiple of 2π, is demonstrated with a numerical model. For select wavelengths, polarization-independent operation can be achieved by tuning the twist rate and thickness of the LC cavity. Applications can be found in polarization- independent switches and field sequential wavelength selection devices.

© 2008 Optical Society of America

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References

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  1. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon, 1993).
  2. J. S. Patel, M. A. Saifi, D. W. Berreman, C. Lin, N. Andreadakis, and S. D. Lee, “Electrically tunable optical filter for infrared wavelength using liquid crystals in a Fabry-Perot etalon,” Appl. Phys. Lett. 57, 1718-1720 (1990).
    [CrossRef]
  3. M. Born and E. Wolf, Principles of Optics (Pergamon, 1965).
  4. J. S. Patel and S. D. Lee, “Electrically tunable and polarization insensitive Fabry-Perot etalon with a liquid-crystal film,” Appl. Phys. Lett. 58, 2491-2493 (1991).
    [CrossRef]
  5. Y. Morita and K. M. Johnson, “Polarization-insensitive tunable liquid crystal Fabry-Perot filter incorporating polymer liquid crystal waveplates,” Proc. SPIE 3475, 152-162 (1998).
    [CrossRef]
  6. J. H. Lee, H. R. Kim, and S. D. Lee, “Polarization-insensitive wavelength selection in an axially symmetric liquid-crystal Fabry-Perot filter,” Appl. Phys. Lett. 75, 859-861 (1999).
    [CrossRef]
  7. C. Mauguin, “Sur la représentation gémoétrique de Poincaré relative aux propriétés optiques des piles de lames,” Bull. Soc. Fr. Mineral. 34, 6-15 (1911).
  8. J. H. Poincaré, Theorie Mathematique de la Lumiere (Saint-Andre-des-Arts, 1892), Vol. 2, p. 105.
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  13. D. W. Berreman, “Optics in smoothly varying anisotropic planar structures: application to liquid-crystal twist cells,” J. Opt. Soc. Am. 63, 1374-1380 (1973).
    [CrossRef]
  14. D. W. Berreman, “Liquid crystal twist cell dynamics and backflow,” J. Appl. Phys. 46, 3746-3751 (1975).
    [CrossRef]
  15. H. de Vries, “Rotatory power and other optical properties of certain liquid crystals,” Acta Crystallogr. 4, 219-226 (1951).
    [CrossRef]

1999

J. H. Lee, H. R. Kim, and S. D. Lee, “Polarization-insensitive wavelength selection in an axially symmetric liquid-crystal Fabry-Perot filter,” Appl. Phys. Lett. 75, 859-861 (1999).
[CrossRef]

1998

Y. Morita and K. M. Johnson, “Polarization-insensitive tunable liquid crystal Fabry-Perot filter incorporating polymer liquid crystal waveplates,” Proc. SPIE 3475, 152-162 (1998).
[CrossRef]

1991

J. S. Patel and S. D. Lee, “Electrically tunable and polarization insensitive Fabry-Perot etalon with a liquid-crystal film,” Appl. Phys. Lett. 58, 2491-2493 (1991).
[CrossRef]

1990

J. S. Patel, M. A. Saifi, D. W. Berreman, C. Lin, N. Andreadakis, and S. D. Lee, “Electrically tunable optical filter for infrared wavelength using liquid crystals in a Fabry-Perot etalon,” Appl. Phys. Lett. 57, 1718-1720 (1990).
[CrossRef]

1977

1975

D. W. Berreman, “Liquid crystal twist cell dynamics and backflow,” J. Appl. Phys. 46, 3746-3751 (1975).
[CrossRef]

1973

1972

1951

H. de Vries, “Rotatory power and other optical properties of certain liquid crystals,” Acta Crystallogr. 4, 219-226 (1951).
[CrossRef]

1941

1911

C. Mauguin, “Sur la représentation gémoétrique de Poincaré relative aux propriétés optiques des piles de lames,” Bull. Soc. Fr. Mineral. 34, 6-15 (1911).

Andreadakis, N.

J. S. Patel, M. A. Saifi, D. W. Berreman, C. Lin, N. Andreadakis, and S. D. Lee, “Electrically tunable optical filter for infrared wavelength using liquid crystals in a Fabry-Perot etalon,” Appl. Phys. Lett. 57, 1718-1720 (1990).
[CrossRef]

Berreman, D. W.

J. S. Patel, M. A. Saifi, D. W. Berreman, C. Lin, N. Andreadakis, and S. D. Lee, “Electrically tunable optical filter for infrared wavelength using liquid crystals in a Fabry-Perot etalon,” Appl. Phys. Lett. 57, 1718-1720 (1990).
[CrossRef]

D. W. Berreman, “Liquid crystal twist cell dynamics and backflow,” J. Appl. Phys. 46, 3746-3751 (1975).
[CrossRef]

D. W. Berreman, “Optics in smoothly varying anisotropic planar structures: application to liquid-crystal twist cells,” J. Opt. Soc. Am. 63, 1374-1380 (1973).
[CrossRef]

D. W. Berreman, “Optics in stratified and anisotropic media: 4×4-formulation,” J. Opt. Soc. Am. 62, 502-510 (1972).
[CrossRef]

Bigelow, J. E.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1965).

de Gennes, P. G.

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon, 1993).

de Vries, H.

H. de Vries, “Rotatory power and other optical properties of certain liquid crystals,” Acta Crystallogr. 4, 219-226 (1951).
[CrossRef]

Gu, C.

P. Yeh and C. Gu, Optics of Liquid Crystal Displays (Wiley, 1999).

Johnson, K. M.

Y. Morita and K. M. Johnson, “Polarization-insensitive tunable liquid crystal Fabry-Perot filter incorporating polymer liquid crystal waveplates,” Proc. SPIE 3475, 152-162 (1998).
[CrossRef]

Jones, R. C.

Kashnow, R. A.

Kim, H. R.

J. H. Lee, H. R. Kim, and S. D. Lee, “Polarization-insensitive wavelength selection in an axially symmetric liquid-crystal Fabry-Perot filter,” Appl. Phys. Lett. 75, 859-861 (1999).
[CrossRef]

Lee, J. H.

J. H. Lee, H. R. Kim, and S. D. Lee, “Polarization-insensitive wavelength selection in an axially symmetric liquid-crystal Fabry-Perot filter,” Appl. Phys. Lett. 75, 859-861 (1999).
[CrossRef]

Lee, S. D.

J. H. Lee, H. R. Kim, and S. D. Lee, “Polarization-insensitive wavelength selection in an axially symmetric liquid-crystal Fabry-Perot filter,” Appl. Phys. Lett. 75, 859-861 (1999).
[CrossRef]

J. S. Patel and S. D. Lee, “Electrically tunable and polarization insensitive Fabry-Perot etalon with a liquid-crystal film,” Appl. Phys. Lett. 58, 2491-2493 (1991).
[CrossRef]

J. S. Patel, M. A. Saifi, D. W. Berreman, C. Lin, N. Andreadakis, and S. D. Lee, “Electrically tunable optical filter for infrared wavelength using liquid crystals in a Fabry-Perot etalon,” Appl. Phys. Lett. 57, 1718-1720 (1990).
[CrossRef]

Lin, C.

J. S. Patel, M. A. Saifi, D. W. Berreman, C. Lin, N. Andreadakis, and S. D. Lee, “Electrically tunable optical filter for infrared wavelength using liquid crystals in a Fabry-Perot etalon,” Appl. Phys. Lett. 57, 1718-1720 (1990).
[CrossRef]

Mauguin, C.

C. Mauguin, “Sur la représentation gémoétrique de Poincaré relative aux propriétés optiques des piles de lames,” Bull. Soc. Fr. Mineral. 34, 6-15 (1911).

Morita, Y.

Y. Morita and K. M. Johnson, “Polarization-insensitive tunable liquid crystal Fabry-Perot filter incorporating polymer liquid crystal waveplates,” Proc. SPIE 3475, 152-162 (1998).
[CrossRef]

Patel, J. S.

J. S. Patel and S. D. Lee, “Electrically tunable and polarization insensitive Fabry-Perot etalon with a liquid-crystal film,” Appl. Phys. Lett. 58, 2491-2493 (1991).
[CrossRef]

J. S. Patel, M. A. Saifi, D. W. Berreman, C. Lin, N. Andreadakis, and S. D. Lee, “Electrically tunable optical filter for infrared wavelength using liquid crystals in a Fabry-Perot etalon,” Appl. Phys. Lett. 57, 1718-1720 (1990).
[CrossRef]

Poincaré, J. H.

J. H. Poincaré, Theorie Mathematique de la Lumiere (Saint-Andre-des-Arts, 1892), Vol. 2, p. 105.

Prost, J.

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon, 1993).

Saifi, M. A.

J. S. Patel, M. A. Saifi, D. W. Berreman, C. Lin, N. Andreadakis, and S. D. Lee, “Electrically tunable optical filter for infrared wavelength using liquid crystals in a Fabry-Perot etalon,” Appl. Phys. Lett. 57, 1718-1720 (1990).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1965).

Yeh, P.

P. Yeh and C. Gu, Optics of Liquid Crystal Displays (Wiley, 1999).

Acta Crystallogr.

H. de Vries, “Rotatory power and other optical properties of certain liquid crystals,” Acta Crystallogr. 4, 219-226 (1951).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

J. S. Patel, M. A. Saifi, D. W. Berreman, C. Lin, N. Andreadakis, and S. D. Lee, “Electrically tunable optical filter for infrared wavelength using liquid crystals in a Fabry-Perot etalon,” Appl. Phys. Lett. 57, 1718-1720 (1990).
[CrossRef]

J. S. Patel and S. D. Lee, “Electrically tunable and polarization insensitive Fabry-Perot etalon with a liquid-crystal film,” Appl. Phys. Lett. 58, 2491-2493 (1991).
[CrossRef]

J. H. Lee, H. R. Kim, and S. D. Lee, “Polarization-insensitive wavelength selection in an axially symmetric liquid-crystal Fabry-Perot filter,” Appl. Phys. Lett. 75, 859-861 (1999).
[CrossRef]

Bull. Soc. Fr. Mineral.

C. Mauguin, “Sur la représentation gémoétrique de Poincaré relative aux propriétés optiques des piles de lames,” Bull. Soc. Fr. Mineral. 34, 6-15 (1911).

J. Appl. Phys.

D. W. Berreman, “Liquid crystal twist cell dynamics and backflow,” J. Appl. Phys. 46, 3746-3751 (1975).
[CrossRef]

J. Opt. Soc. Am.

Proc. SPIE

Y. Morita and K. M. Johnson, “Polarization-insensitive tunable liquid crystal Fabry-Perot filter incorporating polymer liquid crystal waveplates,” Proc. SPIE 3475, 152-162 (1998).
[CrossRef]

Other

M. Born and E. Wolf, Principles of Optics (Pergamon, 1965).

J. H. Poincaré, Theorie Mathematique de la Lumiere (Saint-Andre-des-Arts, 1892), Vol. 2, p. 105.

P. Yeh and C. Gu, Optics of Liquid Crystal Displays (Wiley, 1999).

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon, 1993).

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Figures (8)

Fig. 1
Fig. 1

Diagram of acquired phases of eigenmodes upon reflection from the mirrors.

Fig. 2
Fig. 2

Transmittance of a nontwist LC FPI (optical structure: ( n L n H ) 3 n LC ( n H n L ) 3 , where n L = 1.38 , n H = 2.27 , n LC = 1.5 / 1.9 , d L 95 nm , d H 57 nm , d LC = 0.45 μm , and twist   angle = 0 ).

Fig. 3
Fig. 3

Transmittance of a highly twisted LC FPI ( d LC = 0.45 μm , n LC = 1.5 / 1.9 , and twist   angle = 3600 ° ).

Fig. 4
Fig. 4

Plot of relative phase difference between the eigenmodes as a function of twist angle for a 525 nm wave ( d LC = 0.45 μm and n LC = 1.5 / 1.9 ). Note that the phase difference reaches 2 π at a 169 ° twist angle.

Fig. 5
Fig. 5

Phases of the eigenmodes in the local frame and the transmitted intensity of the twisted LC FPI ( d LC = 0.45 μm , n LC = 1.5 / 1.9 , λ phase = 525 nm , and twist   angle = 169 ° ).

Fig. 6
Fig. 6

Transmitted intensity of the twisted LC FPI ( d LC = 0.23 μm , n LC = 1.5 / 1.9 , and twist   angle = 86 ° ).

Fig. 7
Fig. 7

Phases of the eigenmodes in the local frame and the transmitted intensity of the twisted LC FPI ( d LC = 0.45 μm , n LC = 1.5 / 1.9 , λ phase = 525 nm , and twist   angle = 340 ° ).

Fig. 8
Fig. 8

Transmitted intensity of the twisted LC FPI as a function of applied voltage ( d LC = 0.45 μm , n LC = 1.5 / 1.9 , and twist   angle = 169 ° ).

Equations (6)

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

M = [ exp ( i Γ e ) 0 0 exp ( i Γ o ) ] .
R ( ϕ ) = [ cos ( ϕ / N ) sin ( ϕ / N ) sin ( ϕ / N ) cos ( ϕ / N ) ] .
( E ) out 1 , 2 = ( M ) N E in 1 , 2 .
( E ) out 1 , 2 = R ( φ ) ( E ) out 1 , 2 .
Δ θ 1 , 2 = θ out 1 , 2 θ in 1 , 2 .
Δ θ = θ out 1 θ out 2 .

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