Abstract

The spectral Stokes singularities are introduced to describe the polarization singularities of stochastic electromagnetic beams. The motion and annihilation, as well as the changes in the polarization of spectral Stokes singularities, take place in the free-space propagation. The results are illustrated by numerical examples.

© 2009 Optical Society of America

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References

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  1. J. F. Nye, Natural Focusing and the Fine Structure of Light (IOP Publishing, 1999).
  2. M. V. Berry and M. R. Dennis, Proc. R. Soc. London, Ser. A 457, 141 (2001).
    [CrossRef]
  3. A. I. Konukhov and L. A. Melnikov, J. Opt. B 3, S139 (2001).
  4. I. Freund, Opt. Commun. 201, 251 (2002).
    [CrossRef]
  5. F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, Phys. Rev. Lett. 95, 253901 (2005).
    [CrossRef] [PubMed]
  6. R. W. Schoonover and T. D. Visser, Opt. Express 14, 5733 (2006).
    [CrossRef] [PubMed]
  7. I. Freund, Opt. Lett. 26, 1996 (2001).
    [CrossRef]
  8. M. R. Dennis, Opt. Lett. 33, 2572 (2008).
    [CrossRef] [PubMed]
  9. A. I. Mokhun, M. S. Soskin, and I. Freund, Opt. Lett. 27, 995 (2002).
    [CrossRef]
  10. M. S. Soskin, V. Denisenko, and I. Freund, Opt. Lett. 28, 1475 (2003).
    [CrossRef] [PubMed]
  11. I. Freund, A. I. Mokhun, M. S. Soskin, O. V. Angelsky, and I. I. Mokhun, Opt. Lett. 27, 545 (2002).
    [CrossRef]
  12. O. Angelsky, A. Mokhun, I. Mokhun, and M. Soskin, Opt. Commun. 207, 57 (2002).
    [CrossRef]
  13. O. Korotkova and E. Wolf, Opt. Lett. 30, 198 (2005).
    [CrossRef] [PubMed]
  14. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge U. Press, 2007).
  15. M. Lahiri and E. Wolf, Opt. Lett. 34, 557 (2009).
    [CrossRef] [PubMed]
  16. I. Freund and N. Shvartsman, Phys. Rev. A 50, 5164 (1994).
    [CrossRef] [PubMed]

2009 (1)

2008 (1)

2006 (1)

2005 (2)

O. Korotkova and E. Wolf, Opt. Lett. 30, 198 (2005).
[CrossRef] [PubMed]

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, Phys. Rev. Lett. 95, 253901 (2005).
[CrossRef] [PubMed]

2003 (1)

2002 (4)

2001 (3)

I. Freund, Opt. Lett. 26, 1996 (2001).
[CrossRef]

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

A. I. Konukhov and L. A. Melnikov, J. Opt. B 3, S139 (2001).

1994 (1)

I. Freund and N. Shvartsman, Phys. Rev. A 50, 5164 (1994).
[CrossRef] [PubMed]

Angelsky, O.

O. Angelsky, A. Mokhun, I. Mokhun, and M. Soskin, Opt. Commun. 207, 57 (2002).
[CrossRef]

Angelsky, O. V.

Berry, M. V.

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

Denisenko, V.

Dennis, M. R.

M. R. Dennis, Opt. Lett. 33, 2572 (2008).
[CrossRef] [PubMed]

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, Phys. Rev. Lett. 95, 253901 (2005).
[CrossRef] [PubMed]

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

Flossmann, F.

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, Phys. Rev. Lett. 95, 253901 (2005).
[CrossRef] [PubMed]

Freund, I.

Konukhov, A. I.

A. I. Konukhov and L. A. Melnikov, J. Opt. B 3, S139 (2001).

Korotkova, O.

Lahiri, M.

Maier, M.

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, Phys. Rev. Lett. 95, 253901 (2005).
[CrossRef] [PubMed]

Melnikov, L. A.

A. I. Konukhov and L. A. Melnikov, J. Opt. B 3, S139 (2001).

Mokhun, A.

O. Angelsky, A. Mokhun, I. Mokhun, and M. Soskin, Opt. Commun. 207, 57 (2002).
[CrossRef]

Mokhun, A. I.

Mokhun, I.

O. Angelsky, A. Mokhun, I. Mokhun, and M. Soskin, Opt. Commun. 207, 57 (2002).
[CrossRef]

Mokhun, I. I.

Nye, J. F.

J. F. Nye, Natural Focusing and the Fine Structure of Light (IOP Publishing, 1999).

Schoonover, R. W.

Schwarz, U. T.

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, Phys. Rev. Lett. 95, 253901 (2005).
[CrossRef] [PubMed]

Shvartsman, N.

I. Freund and N. Shvartsman, Phys. Rev. A 50, 5164 (1994).
[CrossRef] [PubMed]

Soskin, M.

O. Angelsky, A. Mokhun, I. Mokhun, and M. Soskin, Opt. Commun. 207, 57 (2002).
[CrossRef]

Soskin, M. S.

Visser, T. D.

Wolf, E.

M. Lahiri and E. Wolf, Opt. Lett. 34, 557 (2009).
[CrossRef] [PubMed]

O. Korotkova and E. Wolf, Opt. Lett. 30, 198 (2005).
[CrossRef] [PubMed]

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge U. Press, 2007).

J. Opt. B (1)

A. I. Konukhov and L. A. Melnikov, J. Opt. B 3, S139 (2001).

Opt. Commun. (2)

I. Freund, Opt. Commun. 201, 251 (2002).
[CrossRef]

O. Angelsky, A. Mokhun, I. Mokhun, and M. Soskin, Opt. Commun. 207, 57 (2002).
[CrossRef]

Opt. Express (1)

Opt. Lett. (7)

Phys. Rev. A (1)

I. Freund and N. Shvartsman, Phys. Rev. A 50, 5164 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, Phys. Rev. Lett. 95, 253901 (2005).
[CrossRef] [PubMed]

Proc. R. Soc. London, Ser. A (1)

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

Other (2)

J. F. Nye, Natural Focusing and the Fine Structure of Light (IOP Publishing, 1999).

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge U. Press, 2007).

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Figures (2)

Fig. 1
Fig. 1

Spectral Stokes vortices of an electromagnetic GSM vortex beam in the source plane z = 0 .

Fig. 2
Fig. 2

Evolution of spectral Stokes vortices of an electromagnetic GSM vortex beam in the free-space propagation: (a) z = 0.4978 z R , (b) z = 1.2 z R .

Equations (15)

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W ( x 01 , y 01 , x 02 , y 02 , ω , 0 ) = [ W u v ( x 01 , y 01 , x 02 , y 02 , ω , 0 ) ] = E u * ( x 01 , y 01 , ω , 0 ) E v ( x 02 , y 02 , ω , 0 )
( u , v = x , y , unless otherwise stated ) ,
s 0 ( x 01 , y 01 , x 02 , y 02 , 0 ) = W x x ( x 01 , y 01 , x 02 , y 02 , 0 ) + W y y ( x 01 , y 01 , x 02 , y 02 , 0 ) ,
s 1 ( x 01 , y 01 , x 02 , y 02 , 0 ) = W x x ( x 01 , y 01 , x 02 , y 02 , 0 ) W y y ( x 01 , y 01 , x 02 , y 02 , 0 ) ,
s 2 ( x 01 , y 01 , x 02 , y 02 , 0 ) = W x y ( x 01 , y 01 , x 02 , y 02 , 0 ) + W y x ( x 01 , y 01 , x 02 , y 02 , 0 ) ,
s 3 ( x 01 , y 01 , x 02 , y 02 , 0 ) = i W y x ( x 01 , y 01 , x 02 , y 02 , 0 ) W x y ( x 01 , y 01 , x 02 , y 02 , 0 ) .
S 1 ( x 0 , y 0 , 0 ) = s 0 1 [ W x x ( x 0 , y 0 , 0 ) W y y ( x 0 , y 0 , 0 ) ] ,
S 2 ( x 0 , y 0 , 0 ) = s 0 1 [ W x y ( x 0 , y 0 , 0 ) + W y x ( x 0 , y 0 , 0 ) ] ,
S 3 ( x 0 , y 0 , 0 ) = i s 0 1 [ W y x ( x 0 , y 0 , 0 ) W x y ( x 0 , y 0 , 0 ) ] ,
      P = S 1 2 + S 2 2 + S 3 2 ,
θ = 1 2 arctan S 2 S 1 ,
ε = A minor A major = S 1 2 + S 2 2 + S 3 2 S 1 2 + S 2 2 S 1 2 + S 2 2 + S 3 2 + S 1 2 + S 2 2 ,
S 12 = S 1 + i S 2 , S 23 = S 2 + i S 3 , S 31 = S 3 + i S 1 .
W u v ( x 01 , y 01 , x 02 , y 02 , 0 ) = A u A v B u v [ x 01 + ( 1 ) u d i y 01 w 0 ] exp [ x 01 2 + y 01 2 w 0 2 ] [ x 02 + ( 1 ) v d + i y 02 w 0 ] exp [ x 02 2 + y 02 2 w 0 2 ] exp [ ( x 01 x 02 ) 2 + ( y 01 y 02 ) 2 2 δ u v 2 ] ,
2 σ k ( k ) m i j = ( k ) σ i m j k = ( k ) σ j m i k ( i , j , k = 1 , 2 , 3 )

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