Abstract

A new classification of circular polarization C points in three-dimensional polarization ellipse fields is proposed. The classification type depends on the out-of-plane variation of the polarization ellipse axis, in particular, whether the ellipse axes are in the plane of circular polarization one or three times. A minimal set of parameters for this classification is derived and discussed in the context of the familiar in-plane C point classification into lemon, star, and monstar types. This new geometric classification is related to the Möbius index of polarization singularities recently introduced by Freund.

© 2011 Optical Society of America

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References

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  1. J. F. Nye and J. V. Hajnal, Proc. R. Soc. A 409, 21 (1987).
    [CrossRef]
  2. J. F. Nye, Natural Focusing and Fine Structure of Light (IoPP, 1999).
  3. M. R. Dennis, K. O’Holleran, and M. J. Padgett, Prog. Opt. 53, 293 (2009).
    [CrossRef]
  4. V. G. Denisenko, R. I. Egorov, and M. S. Soskin, JETP Lett. 80, 17 (2004).
    [CrossRef]
  5. F. Flossmann, K. O’Holleran, M. R. Dennis, and M. J. Padgett, Phys. Rev. Lett. 100, 203902 (2008).
    [CrossRef] [PubMed]
  6. J. F. Nye, Proc. R. Soc. A 389, 279 (1983).
    [CrossRef]
  7. M. V. Berry and J. H. Hannay, J. Phys. A 10, 1809 (1977).
    [CrossRef]
  8. M. R. Dennis, Opt. Lett. 33, 2572 (2008).
    [CrossRef] [PubMed]
  9. I. Freund, Opt. Commun. 283, 1 (2010).
    [CrossRef]
  10. I. Freund, Opt. Lett. 26, 1996 (2001).
    [CrossRef]
  11. M. R. Dennis, Opt. Commun. 213, 201 (2002).
    [CrossRef]
  12. Y. Y. Schechner and J. Shamir, J. Opt. Soc. Am. A 13, 967 (1996).
    [CrossRef]
  13. M. V. Berry and M. R. Dennis, Proc. R. Soc. A 456, 2059(2000).
    [CrossRef]
  14. F. S. RouxJ. Opt. Soc. Am. B 21, 664 (2004).
    [CrossRef]
  15. M. V. Berry and M. R. Dennis, Proc. R. Soc. A 457, 141(2001).
    [CrossRef]
  16. M. V. Berry, J. Opt. A 6, 675 (2004).
    [CrossRef]
  17. I. Freund, Opt. Commun. 283, 16 (2010).
    [CrossRef]
  18. I. Freund, Opt. Lett. 35, 148 (2010).
    [CrossRef] [PubMed]
  19. F. C. Frank, Faraday Soc. Disc. 25, 19 (1958).
    [CrossRef]

2010 (3)

I. Freund, Opt. Commun. 283, 1 (2010).
[CrossRef]

I. Freund, Opt. Commun. 283, 16 (2010).
[CrossRef]

I. Freund, Opt. Lett. 35, 148 (2010).
[CrossRef] [PubMed]

2009 (1)

M. R. Dennis, K. O’Holleran, and M. J. Padgett, Prog. Opt. 53, 293 (2009).
[CrossRef]

2008 (2)

F. Flossmann, K. O’Holleran, M. R. Dennis, and M. J. Padgett, Phys. Rev. Lett. 100, 203902 (2008).
[CrossRef] [PubMed]

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

2004 (3)

V. G. Denisenko, R. I. Egorov, and M. S. Soskin, JETP Lett. 80, 17 (2004).
[CrossRef]

M. V. Berry, J. Opt. A 6, 675 (2004).
[CrossRef]

F. S. RouxJ. Opt. Soc. Am. B 21, 664 (2004).
[CrossRef]

2002 (1)

M. R. Dennis, Opt. Commun. 213, 201 (2002).
[CrossRef]

2001 (2)

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

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

2000 (1)

M. V. Berry and M. R. Dennis, Proc. R. Soc. A 456, 2059(2000).
[CrossRef]

1996 (1)

1987 (1)

J. F. Nye and J. V. Hajnal, Proc. R. Soc. A 409, 21 (1987).
[CrossRef]

1983 (1)

J. F. Nye, Proc. R. Soc. A 389, 279 (1983).
[CrossRef]

1977 (1)

M. V. Berry and J. H. Hannay, J. Phys. A 10, 1809 (1977).
[CrossRef]

1958 (1)

F. C. Frank, Faraday Soc. Disc. 25, 19 (1958).
[CrossRef]

Berry, M. V.

M. V. Berry, J. Opt. A 6, 675 (2004).
[CrossRef]

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

M. V. Berry and M. R. Dennis, Proc. R. Soc. A 456, 2059(2000).
[CrossRef]

M. V. Berry and J. H. Hannay, J. Phys. A 10, 1809 (1977).
[CrossRef]

Denisenko, V. G.

V. G. Denisenko, R. I. Egorov, and M. S. Soskin, JETP Lett. 80, 17 (2004).
[CrossRef]

Dennis, M. R.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, Prog. Opt. 53, 293 (2009).
[CrossRef]

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

F. Flossmann, K. O’Holleran, M. R. Dennis, and M. J. Padgett, Phys. Rev. Lett. 100, 203902 (2008).
[CrossRef] [PubMed]

M. R. Dennis, Opt. Commun. 213, 201 (2002).
[CrossRef]

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

M. V. Berry and M. R. Dennis, Proc. R. Soc. A 456, 2059(2000).
[CrossRef]

Egorov, R. I.

V. G. Denisenko, R. I. Egorov, and M. S. Soskin, JETP Lett. 80, 17 (2004).
[CrossRef]

Flossmann, F.

F. Flossmann, K. O’Holleran, M. R. Dennis, and M. J. Padgett, Phys. Rev. Lett. 100, 203902 (2008).
[CrossRef] [PubMed]

Frank, F. C.

F. C. Frank, Faraday Soc. Disc. 25, 19 (1958).
[CrossRef]

Freund, I.

Hajnal, J. V.

J. F. Nye and J. V. Hajnal, Proc. R. Soc. A 409, 21 (1987).
[CrossRef]

Hannay, J. H.

M. V. Berry and J. H. Hannay, J. Phys. A 10, 1809 (1977).
[CrossRef]

Nye, J. F.

J. F. Nye and J. V. Hajnal, Proc. R. Soc. A 409, 21 (1987).
[CrossRef]

J. F. Nye, Proc. R. Soc. A 389, 279 (1983).
[CrossRef]

J. F. Nye, Natural Focusing and Fine Structure of Light (IoPP, 1999).

O’Holleran, K.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, Prog. Opt. 53, 293 (2009).
[CrossRef]

F. Flossmann, K. O’Holleran, M. R. Dennis, and M. J. Padgett, Phys. Rev. Lett. 100, 203902 (2008).
[CrossRef] [PubMed]

Padgett, M. J.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, Prog. Opt. 53, 293 (2009).
[CrossRef]

F. Flossmann, K. O’Holleran, M. R. Dennis, and M. J. Padgett, Phys. Rev. Lett. 100, 203902 (2008).
[CrossRef] [PubMed]

Roux, F. S.

Schechner, Y. Y.

Shamir, J.

Soskin, M. S.

V. G. Denisenko, R. I. Egorov, and M. S. Soskin, JETP Lett. 80, 17 (2004).
[CrossRef]

Faraday Soc. Disc. (1)

F. C. Frank, Faraday Soc. Disc. 25, 19 (1958).
[CrossRef]

J. Opt. A (1)

M. V. Berry, J. Opt. A 6, 675 (2004).
[CrossRef]

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

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

J. Phys. A (1)

M. V. Berry and J. H. Hannay, J. Phys. A 10, 1809 (1977).
[CrossRef]

JETP Lett. (1)

V. G. Denisenko, R. I. Egorov, and M. S. Soskin, JETP Lett. 80, 17 (2004).
[CrossRef]

Opt. Commun. (3)

I. Freund, Opt. Commun. 283, 1 (2010).
[CrossRef]

I. Freund, Opt. Commun. 283, 16 (2010).
[CrossRef]

M. R. Dennis, Opt. Commun. 213, 201 (2002).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. Lett. (1)

F. Flossmann, K. O’Holleran, M. R. Dennis, and M. J. Padgett, Phys. Rev. Lett. 100, 203902 (2008).
[CrossRef] [PubMed]

Proc. R. Soc. A (4)

J. F. Nye, Proc. R. Soc. A 389, 279 (1983).
[CrossRef]

J. F. Nye and J. V. Hajnal, Proc. R. Soc. A 409, 21 (1987).
[CrossRef]

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

M. V. Berry and M. R. Dennis, Proc. R. Soc. A 456, 2059(2000).
[CrossRef]

Prog. Opt. (1)

M. R. Dennis, K. O’Holleran, and M. J. Padgett, Prog. Opt. 53, 293 (2009).
[CrossRef]

Other (1)

J. F. Nye, Natural Focusing and Fine Structure of Light (IoPP, 1999).

Supplementary Material (1)

» Media 1: MOV (686 KB)     

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Figures (2)

Fig. 1
Fig. 1

Representation of polarization axes close to C points. (a)  E = ( 2 + x + i y , i 2 i x + y , ( 1.40 . 18 i ) x + ( 1.40 + . 18 i ) y ) . (b)  E = ( 1. 0.98 x + 0.20 i y , i + 0.98 i x + 0.20 y , 0.63 ( x 2 i y ) ) . In each frame, the black lines represent the ellipse axes around the C point (sphere) in its plane of polarization. The lighter (darker) gray ellipse is the anisotropy ellipse for E ( E z ) , and the blue surface above represents ± a z around the C point, with either three zeros (a) or one zero (b), resembling a two-sheet Riemann surface.

Fig. 2
Fig. 2

Surface D O = 0 for alignment θ = 0 in ( γ , γ z , χ ) space, where D O > 0 on the red side. The surface is periodic in χ, and, in the four faces where γ , γ z = ± 1 , the line D O = 0 resembles the L classification locus [8]. Media 1 shows the variation of the surface with θ.

Equations (4)

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a = ± Re E * · E * E .
a z ± Re E + * E * ( x , y , 0 ) · E z ,
a z ± Re | E + | 1 / 2 e i β u x x i v y y ( x , y , 0 ) · E z .
D O = 2 ( 3 ϒ 2 14 ϒ ϒ z ϒ z 2 + 12 ϒ 2 ϒ z 2 ) ( 1 + ϒ ) 1 ϒ 2 ( 1 + ϒ z ) 2 cos 4 ( χ θ ) + 2 ( 2 ϒ ) ( 1 + ϒ ) ( 1 + ϒ z ) 1 ϒ z 2 cos 2 ( 2 χ θ ) 4 1 ϒ 2 ( 2 7 ϒ ϒ z ) 1 ϒ z 2 cos 2 θ + 2 ( 1 ϒ 2 ) ( 1 ϒ z 2 ) cos 4 θ 6 1 ϒ 2 ( 1 ϒ z 2 ) cos 4 χ + 2 ( 1 ϒ ) ( 2 + ϒ ) ( 1 ϒ z ) 1 ϒ z 2 cos 2 ( 2 χ + θ ) ( 1 ϒ ) 1 ϒ 2 ( 1 ϒ z ) 2 cos 4 ( χ + θ ) ,

Metrics