Abstract

We analyze the optical effects associated with an adiabatic rotation of a plane of polarization in a twisted nematic liquid crystal. The experimental verification was performed with a cell with linear rubbing of a front surface and circular rubbing of a rear surface. The expectations of the liquid crystal’s orientation defect origin along the line of the maximum tension and a polarization conflict caused by geometrical phase are confirmed.

© 2011 Optical Society of America

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References

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  1. N. V. Tabiryan, S. R. Nersisyan, D. M. Steeves, and B. R. Kimball, Opt. Photonics News 2140 (2010).
  2. M. C. Mauguin, Bull. Soc. Fr. Mineral. 34, 71 (1911).
  3. C. H. Gooch and H. A. Tarry, J. Phys. D 8, 1575 (1975).
    [CrossRef]
  4. S. Pancharatnam, Proc. Indian Acad. Sci., Sect. A 44, 247 (1956).
  5. M. V. Berry, Proc. R. Soc. A 392, 45 (1984).
    [CrossRef]
  6. M. Stalder and M. Schadt, Opt. Lett. 21, 1948 (1996).
    [CrossRef] [PubMed]
  7. J. F. Nye and M. V. Berry, Proc. R. Soc. A 336, 165 (1974).
    [CrossRef]
  8. I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 119, 604 (1995).
    [CrossRef]
  9. D. V. Petrov, Opt. Quantum Electron. 34, 759 (2002).
    [CrossRef]
  10. A. E. Siegman, Lasers (University Science Books, 1986).
  11. Q. Zhan and J. R. Leger, Opt. Commun. 213, 241 (2002).
    [CrossRef]
  12. Z. Bomzon, V. Kleiner, and E. Hasman, Opt. Lett. 26, 1424 (2001).
    [CrossRef]
  13. L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
    [CrossRef] [PubMed]

2010

N. V. Tabiryan, S. R. Nersisyan, D. M. Steeves, and B. R. Kimball, Opt. Photonics News 2140 (2010).

2006

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef] [PubMed]

2002

D. V. Petrov, Opt. Quantum Electron. 34, 759 (2002).
[CrossRef]

Q. Zhan and J. R. Leger, Opt. Commun. 213, 241 (2002).
[CrossRef]

2001

1996

1995

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 119, 604 (1995).
[CrossRef]

1984

M. V. Berry, Proc. R. Soc. A 392, 45 (1984).
[CrossRef]

1975

C. H. Gooch and H. A. Tarry, J. Phys. D 8, 1575 (1975).
[CrossRef]

1974

J. F. Nye and M. V. Berry, Proc. R. Soc. A 336, 165 (1974).
[CrossRef]

1956

S. Pancharatnam, Proc. Indian Acad. Sci., Sect. A 44, 247 (1956).

1911

M. C. Mauguin, Bull. Soc. Fr. Mineral. 34, 71 (1911).

Basistiy, I. V.

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 119, 604 (1995).
[CrossRef]

Berry, M. V.

M. V. Berry, Proc. R. Soc. A 392, 45 (1984).
[CrossRef]

J. F. Nye and M. V. Berry, Proc. R. Soc. A 336, 165 (1974).
[CrossRef]

Bomzon, Z.

Gooch, C. H.

C. H. Gooch and H. A. Tarry, J. Phys. D 8, 1575 (1975).
[CrossRef]

Hasman, E.

Kimball, B. R.

N. V. Tabiryan, S. R. Nersisyan, D. M. Steeves, and B. R. Kimball, Opt. Photonics News 2140 (2010).

Kleiner, V.

Leger, J. R.

Q. Zhan and J. R. Leger, Opt. Commun. 213, 241 (2002).
[CrossRef]

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef] [PubMed]

Marrucci, L.

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef] [PubMed]

Mauguin, M. C.

M. C. Mauguin, Bull. Soc. Fr. Mineral. 34, 71 (1911).

Nersisyan, S. R.

N. V. Tabiryan, S. R. Nersisyan, D. M. Steeves, and B. R. Kimball, Opt. Photonics News 2140 (2010).

Nye, J. F.

J. F. Nye and M. V. Berry, Proc. R. Soc. A 336, 165 (1974).
[CrossRef]

Pancharatnam, S.

S. Pancharatnam, Proc. Indian Acad. Sci., Sect. A 44, 247 (1956).

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef] [PubMed]

Petrov, D. V.

D. V. Petrov, Opt. Quantum Electron. 34, 759 (2002).
[CrossRef]

Schadt, M.

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986).

Soskin, M. S.

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 119, 604 (1995).
[CrossRef]

Stalder, M.

Steeves, D. M.

N. V. Tabiryan, S. R. Nersisyan, D. M. Steeves, and B. R. Kimball, Opt. Photonics News 2140 (2010).

Tabiryan, N. V.

N. V. Tabiryan, S. R. Nersisyan, D. M. Steeves, and B. R. Kimball, Opt. Photonics News 2140 (2010).

Tarry, H. A.

C. H. Gooch and H. A. Tarry, J. Phys. D 8, 1575 (1975).
[CrossRef]

Vasnetsov, M. V.

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 119, 604 (1995).
[CrossRef]

Zhan, Q.

Q. Zhan and J. R. Leger, Opt. Commun. 213, 241 (2002).
[CrossRef]

Bull. Soc. Fr. Mineral.

M. C. Mauguin, Bull. Soc. Fr. Mineral. 34, 71 (1911).

J. Phys. D

C. H. Gooch and H. A. Tarry, J. Phys. D 8, 1575 (1975).
[CrossRef]

Opt. Commun.

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 119, 604 (1995).
[CrossRef]

Q. Zhan and J. R. Leger, Opt. Commun. 213, 241 (2002).
[CrossRef]

Opt. Lett.

Opt. Photonics News

N. V. Tabiryan, S. R. Nersisyan, D. M. Steeves, and B. R. Kimball, Opt. Photonics News 2140 (2010).

Opt. Quantum Electron.

D. V. Petrov, Opt. Quantum Electron. 34, 759 (2002).
[CrossRef]

Phys. Rev. Lett.

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef] [PubMed]

Proc. Indian Acad. Sci., Sect. A

S. Pancharatnam, Proc. Indian Acad. Sci., Sect. A 44, 247 (1956).

Proc. R. Soc. A

M. V. Berry, Proc. R. Soc. A 392, 45 (1984).
[CrossRef]

J. F. Nye and M. V. Berry, Proc. R. Soc. A 336, 165 (1974).
[CrossRef]

Other

A. E. Siegman, Lasers (University Science Books, 1986).

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic view of a cell prepared with rubbing of a front face parallel to the x axis and circular rubbing of a rear face. The origin of the x and y axes is placed at the center of the circular rubbing. The LC orientation is planar ( x y plane). There is not any twist of LC director in the cell for the azimuth θ = ± π / 2 and the twist reaches ± π / 2 for θ = 0 , π. (b) Inner circle shows the polarization distribution in the cross section of the output wave by the tangent arrows. The outer circle shows momentary field direction at y > 0 by solid arrows and at y < 0 by dotted arrows. Polarization conflict is seen as the opposite directions of the field vectors along the x axis.

Fig. 2
Fig. 2

Calculated Fourier transform of the amplitude functions (Eqs. (1, 2)): (a) x-polarized component, (b) y- polarized component. (c) Calculated far-field structure of the whole beam. The parameters used are k = 10 4 mm 1 , w = 1 mm , and R = 670 mm .

Fig. 3
Fig. 3

The view of a twist cell placed between crossed polarizers: (a) calculated transmittance, (b) experimental picture. (c), (d) The same for parallel polarizers. The width of the experimental pictures is 10 mm .

Fig. 4
Fig. 4

Microscopic view of the twist LC cell in crossed polarizers. The defect lines are indicated by arrows. The direction of the defect line is close to the horizontal axis (parallel to the input surface rubbing). The imperfections of circular rubbing are detectable. The width of the picture is 1 mm .

Fig. 5
Fig. 5

Experimental pictures of the far-field intensity distribution (Fourier plane) of an optical beam passed through the cell. (a) x-polarized lobes are oriented along the y axis. (b) y- polarized lobes are separated by phase dislocation lines. (c) The whole beam in the far field. The angular measure 10 mrad is shown in (a).

Equations (3)

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E x ( out ) = E x ( in ) | sin θ | ,
E y ( out ) = { E x ( in ) cos θ , y > 0 E x ( in ) cos θ , y < 0 ,
E x ( in ) = exp ( x 2 + y 2 w 2 + i k x 2 + y 2 2 R ) .

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