Abstract

By using a pure operatorial (nonmatrix) approach to some of the variable composite polarization devices, we show that for some values of the variable internal parameters, these devices lose their anisotropy. Their principal axes, or more generally their eigenvectors, become undetermined, i.e., in this sense, the anisotropic devices get “disorientated.”

© 2011 Optical Society of America

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  1. M. V. Berry and M. R. Dennis, Proc. R. Soc. A 459, 1261(2003).
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  2. M. V. Berry and M. R. Dennis, Proc. R. Soc. A 457, 141(2001).
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    [CrossRef]
  4. O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. Soskin, Phys. Rev. E 65, 036602 (2002).
    [CrossRef]
  5. M. V. Berry, R. Bhandary, and S. Klein, Eur. J. Phys. 20, 1 (1999).
    [CrossRef]
  6. M. V. Berry and M. R. Dennis, J. Opt. A 6, S24 (2004).
    [CrossRef]
  7. O. Sydoruk and S. N. Savenkov, J. Opt. 12, 035702, (2010).
    [CrossRef]
  8. R. Bhandari, Phys. Lett., Sect. A 157, 221 (1991).
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  9. R. Bhandari, Phys. Lett., Sect. A 171, 262 (1992).
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  10. R. Bhandari, Phys. Lett., Sect. A 171, 267 (1992).
    [CrossRef]
  11. G. D. Love and R. Bhandari, Opt. Commun. 110, 475 (1994).
    [CrossRef]
  12. R. Bhandari and G. D.Love, Opt. Commun. 110, 479 (1994).
    [CrossRef]
  13. R. Bhandari, Phys. Lett., Sect. A 204, 188 (1995).
    [CrossRef]
  14. R. Bhandari, Phys. Lett., Sect. A 88, 100403(2002).
  15. P. A. M. Dirac, Proc. R. Soc. A 133, 60 (1931).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  21. W. A. Shurcliff, Polarized Light (Harvard University, 1962).
  22. M. Richartz and H.-Y. Hsü, J. Opt. Soc. Am. 39, 136 (1949).
    [CrossRef]

2010 (1)

O. Sydoruk and S. N. Savenkov, J. Opt. 12, 035702, (2010).
[CrossRef]

2006 (1)

O. V. Angelsky, A. G. Ushenko, Y. A. Ushenko, and Ye. G. Ushenko, J. Phys. D 39, 3547 (2006).
[CrossRef]

2004 (1)

M. V. Berry and M. R. Dennis, J. Opt. A 6, S24 (2004).
[CrossRef]

2003 (1)

M. V. Berry and M. R. Dennis, Proc. R. Soc. A 459, 1261(2003).
[CrossRef]

2002 (2)

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. Soskin, Phys. Rev. E 65, 036602 (2002).
[CrossRef]

R. Bhandari, Phys. Lett., Sect. A 88, 100403(2002).

2001 (2)

M. V. Berry and M. R. Dennis, Proc. R. Soc. A 457, 141(2001).
[CrossRef]

T. Tudor, J. Opt. Soc. Am. A 18, 926 (2001).
[CrossRef]

1999 (1)

M. V. Berry, R. Bhandary, and S. Klein, Eur. J. Phys. 20, 1 (1999).
[CrossRef]

1997 (1)

R. Bhandari, Phys. Rep. 281, 1 (1997).
[CrossRef]

1996 (1)

M. V. Berry and S. Klein, J. Mod. Opt. 43, 165 (1996).
[CrossRef]

1995 (1)

R. Bhandari, Phys. Lett., Sect. A 204, 188 (1995).
[CrossRef]

1994 (2)

G. D. Love and R. Bhandari, Opt. Commun. 110, 475 (1994).
[CrossRef]

R. Bhandari and G. D.Love, Opt. Commun. 110, 479 (1994).
[CrossRef]

1992 (2)

R. Bhandari, Phys. Lett., Sect. A 171, 262 (1992).
[CrossRef]

R. Bhandari, Phys. Lett., Sect. A 171, 267 (1992).
[CrossRef]

1991 (1)

R. Bhandari, Phys. Lett., Sect. A 157, 221 (1991).
[CrossRef]

1949 (1)

1931 (1)

P. A. M. Dirac, Proc. R. Soc. A 133, 60 (1931).
[CrossRef]

Angelsky, O. V.

O. V. Angelsky, A. G. Ushenko, Y. A. Ushenko, and Ye. G. Ushenko, J. Phys. D 39, 3547 (2006).
[CrossRef]

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. Soskin, Phys. Rev. E 65, 036602 (2002).
[CrossRef]

Berry, M. V.

M. V. Berry and M. R. Dennis, J. Opt. A 6, S24 (2004).
[CrossRef]

M. V. Berry and M. R. Dennis, Proc. R. Soc. A 459, 1261(2003).
[CrossRef]

M. V. Berry and M. R. Dennis, Proc. R. Soc. A 457, 141(2001).
[CrossRef]

M. V. Berry, R. Bhandary, and S. Klein, Eur. J. Phys. 20, 1 (1999).
[CrossRef]

M. V. Berry and S. Klein, J. Mod. Opt. 43, 165 (1996).
[CrossRef]

Bhandari, R.

R. Bhandari, Phys. Lett., Sect. A 88, 100403(2002).

R. Bhandari, Phys. Rep. 281, 1 (1997).
[CrossRef]

R. Bhandari, Phys. Lett., Sect. A 204, 188 (1995).
[CrossRef]

G. D. Love and R. Bhandari, Opt. Commun. 110, 475 (1994).
[CrossRef]

R. Bhandari and G. D.Love, Opt. Commun. 110, 479 (1994).
[CrossRef]

R. Bhandari, Phys. Lett., Sect. A 171, 262 (1992).
[CrossRef]

R. Bhandari, Phys. Lett., Sect. A 171, 267 (1992).
[CrossRef]

R. Bhandari, Phys. Lett., Sect. A 157, 221 (1991).
[CrossRef]

Bhandary, R.

M. V. Berry, R. Bhandary, and S. Klein, Eur. J. Phys. 20, 1 (1999).
[CrossRef]

Dennis, M. R.

M. V. Berry and M. R. Dennis, J. Opt. A 6, S24 (2004).
[CrossRef]

M. V. Berry and M. R. Dennis, Proc. R. Soc. A 459, 1261(2003).
[CrossRef]

M. V. Berry and M. R. Dennis, Proc. R. Soc. A 457, 141(2001).
[CrossRef]

Dirac, P. A. M.

P. A. M. Dirac, Proc. R. Soc. A 133, 60 (1931).
[CrossRef]

P. A. M. Dirac, The Principles of Quantum Mechanics, 3rd ed. (Clarendon, 1947).

Hsü, H.-Y.

Klein, S.

M. V. Berry, R. Bhandary, and S. Klein, Eur. J. Phys. 20, 1 (1999).
[CrossRef]

M. V. Berry and S. Klein, J. Mod. Opt. 43, 165 (1996).
[CrossRef]

Love, G. D.

R. Bhandari and G. D.Love, Opt. Commun. 110, 479 (1994).
[CrossRef]

G. D. Love and R. Bhandari, Opt. Commun. 110, 475 (1994).
[CrossRef]

Mokhun, A. I.

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. Soskin, Phys. Rev. E 65, 036602 (2002).
[CrossRef]

Mokhun, I. I.

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. Soskin, Phys. Rev. E 65, 036602 (2002).
[CrossRef]

Pancharatnam, S.

S. Pancharatnam, in Proceedings of the Indiana Academy of Science (1955), pp. 137.

Richartz, M.

Savenkov, S. N.

O. Sydoruk and S. N. Savenkov, J. Opt. 12, 035702, (2010).
[CrossRef]

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light (Harvard University, 1962).

Soskin, M.

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. Soskin, Phys. Rev. E 65, 036602 (2002).
[CrossRef]

Sydoruk, O.

O. Sydoruk and S. N. Savenkov, J. Opt. 12, 035702, (2010).
[CrossRef]

Tudor, T.

Ushenko, A. G.

O. V. Angelsky, A. G. Ushenko, Y. A. Ushenko, and Ye. G. Ushenko, J. Phys. D 39, 3547 (2006).
[CrossRef]

Ushenko, Y. A.

O. V. Angelsky, A. G. Ushenko, Y. A. Ushenko, and Ye. G. Ushenko, J. Phys. D 39, 3547 (2006).
[CrossRef]

Ushenko, Ye. G.

O. V. Angelsky, A. G. Ushenko, Y. A. Ushenko, and Ye. G. Ushenko, J. Phys. D 39, 3547 (2006).
[CrossRef]

Eur. J. Phys. (1)

M. V. Berry, R. Bhandary, and S. Klein, Eur. J. Phys. 20, 1 (1999).
[CrossRef]

J. Mod. Opt. (1)

M. V. Berry and S. Klein, J. Mod. Opt. 43, 165 (1996).
[CrossRef]

J. Opt. (1)

O. Sydoruk and S. N. Savenkov, J. Opt. 12, 035702, (2010).
[CrossRef]

J. Opt. A (1)

M. V. Berry and M. R. Dennis, J. Opt. A 6, S24 (2004).
[CrossRef]

J. Opt. Soc. Am. (1)

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

J. Phys. D (1)

O. V. Angelsky, A. G. Ushenko, Y. A. Ushenko, and Ye. G. Ushenko, J. Phys. D 39, 3547 (2006).
[CrossRef]

Opt. Commun. (2)

G. D. Love and R. Bhandari, Opt. Commun. 110, 475 (1994).
[CrossRef]

R. Bhandari and G. D.Love, Opt. Commun. 110, 479 (1994).
[CrossRef]

Phys. Lett., Sect. A (5)

R. Bhandari, Phys. Lett., Sect. A 204, 188 (1995).
[CrossRef]

R. Bhandari, Phys. Lett., Sect. A 88, 100403(2002).

R. Bhandari, Phys. Lett., Sect. A 157, 221 (1991).
[CrossRef]

R. Bhandari, Phys. Lett., Sect. A 171, 262 (1992).
[CrossRef]

R. Bhandari, Phys. Lett., Sect. A 171, 267 (1992).
[CrossRef]

Phys. Rep. (1)

R. Bhandari, Phys. Rep. 281, 1 (1997).
[CrossRef]

Phys. Rev. E (1)

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. Soskin, Phys. Rev. E 65, 036602 (2002).
[CrossRef]

Proc. R. Soc. A (3)

M. V. Berry and M. R. Dennis, Proc. R. Soc. A 459, 1261(2003).
[CrossRef]

M. V. Berry and M. R. Dennis, Proc. R. Soc. A 457, 141(2001).
[CrossRef]

P. A. M. Dirac, Proc. R. Soc. A 133, 60 (1931).
[CrossRef]

Other (3)

P. A. M. Dirac, The Principles of Quantum Mechanics, 3rd ed. (Clarendon, 1947).

S. Pancharatnam, in Proceedings of the Indiana Academy of Science (1955), pp. 137.

W. A. Shurcliff, Polarized Light (Harvard University, 1962).

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Equations (21)

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D = λ 1 | S 1 > < S 1 | + λ | 2 S 2 > < S 2 | ,
D = i = 1 2 j = 1 2 < S i | D | S j > | S i > < S j | ,
R | P θ > ( δ ) = e i δ / 2 | P θ > < P θ | + e i δ / 2 | P θ + 90 0 > < P θ + 90 0 | ,
R | R > ( δ ) = e i δ / 2 | R > < R | + e i δ / 2 | L > < L | ,
R | P θ > ( δ ) = e i δ 2 [ cos θ | P x > + sin θ | P y > ] · [ cos θ < P x | + sin θ < P y | ] + e i δ 2 [ sin θ | P x > cos θ | P y > ] · [ sin θ < P x | cos θ < P y | ] = [ cos δ 2 + i cos 2 θ sin δ 2 ] | P x > < P x | + i sin 2 θ sin δ 2 [ | P x > < P y | + | P y > < P x | ] + [ cos δ 2 i cos 2 θ sin δ 2 ] | P y > < P y | ,
R | R > ( δ ) = 1 2 { e i δ 2 [ | P x > + i | P y > ] [ < P x | i < P y ] } + 1 2 { e i δ 2 [ | P x > i | P y > ] [ < P x | + i < P y ] } = cos δ 2 + sin δ 2 [ | P x > < P y | | P y > < P x | ] .
R P = R | P x > ( π / 2 ) R | P θ > ( π ) R | P x > ( π / 2 ) ,
R P = ( e i π 4 | P x > < P x | + e i π 4 | P y > < P y | ) · ( i cos 2 θ | P x > < P x | + i sin 2 θ | P x > < P y | + i sin 2 θ | P y > < P x | i cos 2 θ | P y > < P y | ) · ( e i π 4 | P x > < P x | + e i π 4 | P y > < P y | ) = cos 2 θ | P x > < P x | + i sin 2 θ | ( P x > < P y | + | P y > < P x | ) cos 2 θ | P y > < P y | .
R | P 45 0 > ( 4 θ ) = cos 2 θ | P x > < P x | i sin 2 θ ( | P x > < P y | + | P y > < P x | ) + cos 2 θ | P y > < P y | .
R | P x > ( π / 2 ) R | P θ > ( π ) R | P x > ( π / 2 ) = R | P 45 0 > ( 4 θ ) ,
R P = I cos 2 θ + i S sin 2 θ ,
θ = k π R P = I ,
θ = ( 2 k + 1 ) π 4 R P = ± i S ,
θ = ( 2 k + 1 ) π 2 R P = I .
R P = ( 1 ) n + 1 I ,
R T = R | P θ > ( π ) R | P x > ( π ) .
R T = ( i cos 2 θ | P x > < P x | + i sin 2 θ | P x > < P y | + i sin 2 θ | P y > < P x | i cos 2 θ | P y > < P y ) · ( i | P x > < P x | i | P y > < | ) = cos 2 θ + sin 2 θ ( | P x > < P y | | P y > < P x | ) .
R T = R | R > ( 4 θ ) = R | L > ( 4 θ ) .
| P x > < P y | | P y > < P x | = R | R > ( π ) ,
R T = I cos 2 θ + i R | R > ( π ) sin 2 θ .
R I P n π / 2 > ( π ) R I P x > ( π ) = ( 1 ) n + 1 I ,

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