Abstract

The canonical point singularity of elliptically polarized light is a C point, an isolated point of circular polarization surrounded by a field of polarization ellipses. The defining singular property of a C point is that the surrounding ellipses rotate about the point. It is shown that this rotation is seen only for a particular line of sight (LOS) and, conversely, that there exists a unique LOS for every ellipse along which the ellipse is seen as a singularity. It is also shown that changes in LOS can turn singularities into stationary points and vice versa. The democratic behavior of polarization singularities and stationary points is a consequence of the fundamental “what you see is what you get” property of ellipse fields. Simple experiments are proposed for observing this unusual property of elliptically polarized light.

© 2004 Optical Society of America

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References

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  1. S. H. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley, Reading, Mass., 1994), Chap. 6.
  2. J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
    [CrossRef]
  3. M. S. Soskin and M. V. Vasnetsov, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 2001), Vol. 43, pp. 219–276.
    [CrossRef]
  4. J. F. Nye, Natural Focusing and the Fine Structure of Light (Institute of Physics, Bristol, England, 1999).
  5. J. F. Nye and J. V. Hajnal, Proc. R. Soc. London Ser. A 409, 21 (1987).
    [CrossRef]
  6. I. Freund, M. S. Soskin, and A. I. Mokhun, Opt. Commun. 208, 223 (2002).
    [CrossRef]
  7. M. S. Soskin, V. Denisenko, and I. Freund, Opt. Lett. 28, 1475 (2003).
    [CrossRef] [PubMed]
  8. J. F. Nye, Proc. R. Soc. London Ser. A 389, 279 (1983).
    [CrossRef]
  9. M. Born and E. W. Wolf, Principles of Optics (Pergamon, Oxford, England, 1959).
  10. A. I. Konukhov and L. A. Melnikov, J. Opt. B 3, S139 (2001).
    [CrossRef]
  11. I. Freund, Opt. Lett. 26, 1996 (2001).
    [CrossRef]

2003 (1)

2002 (1)

I. Freund, M. S. Soskin, and A. I. Mokhun, Opt. Commun. 208, 223 (2002).
[CrossRef]

2001 (2)

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

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

1987 (1)

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

1983 (1)

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

1974 (1)

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

Berry, M. V.

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

Born, M.

M. Born and E. W. Wolf, Principles of Optics (Pergamon, Oxford, England, 1959).

Denisenko, V.

Freund, I.

Hajnal, J. V.

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

Konukhov, A. I.

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

Melnikov, L. A.

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

Mokhun, A. I.

I. Freund, M. S. Soskin, and A. I. Mokhun, Opt. Commun. 208, 223 (2002).
[CrossRef]

Nye, J. F.

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

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

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

J. F. Nye, Natural Focusing and the Fine Structure of Light (Institute of Physics, Bristol, England, 1999).

Soskin, M. S.

M. S. Soskin, V. Denisenko, and I. Freund, Opt. Lett. 28, 1475 (2003).
[CrossRef] [PubMed]

I. Freund, M. S. Soskin, and A. I. Mokhun, Opt. Commun. 208, 223 (2002).
[CrossRef]

M. S. Soskin and M. V. Vasnetsov, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 2001), Vol. 43, pp. 219–276.
[CrossRef]

Strogatz, S. H.

S. H. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley, Reading, Mass., 1994), Chap. 6.

Vasnetsov, M. V.

M. S. Soskin and M. V. Vasnetsov, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 2001), Vol. 43, pp. 219–276.
[CrossRef]

Wolf, E. W.

M. Born and E. W. Wolf, Principles of Optics (Pergamon, Oxford, England, 1959).

J. Opt. B (1)

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

Opt. Commun. (1)

I. Freund, M. S. Soskin, and A. I. Mokhun, Opt. Commun. 208, 223 (2002).
[CrossRef]

Opt. Lett. (2)

Proc. R. Soc. London Ser. A (3)

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

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

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

Other (4)

S. H. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley, Reading, Mass., 1994), Chap. 6.

M. S. Soskin and M. V. Vasnetsov, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 2001), Vol. 43, pp. 219–276.
[CrossRef]

J. F. Nye, Natural Focusing and the Fine Structure of Light (Institute of Physics, Bristol, England, 1999).

M. Born and E. W. Wolf, Principles of Optics (Pergamon, Oxford, England, 1959).

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Figures (4)

Fig. 1
Fig. 1

Geometry of the LOS vector Λ.

Fig. 2
Fig. 2

Targeted translation of a C point under change in LOS. (a) Ellipse field for Λ parallel to Z (θ=0). The central, positive C point is shown by the filled gray circle; the targeted ellipse, by the filled black figure. (b) Ellipse field for φ=63°, θ=77°. (a′), (b′) Phase Φ12 of the complex Stokes field S12 coded -π to +π black to white, corresponding to (a) and (b). Here and throughout positive (negative) singularities are shown by white circles with black rims (black circles with white rims), and L lines are shown by thin white curves.

Fig. 3
Fig. 3

LOS transformations. (a) Conversion of paired extrema into (b) paired C points. The targeted ellipse is at the center. (c) Conversion of a region free of singularities and stationary points into (d) C points and saddles (black dots). The targeted ellipse is at the positive C point in (d). (e) Conversion of paired C points into (f) paired extrema. The targeted ellipse is at the center.

Fig. 4
Fig. 4

LOS transformations in a random field. Shown is a contour map of a segment of the field. The two thick curves are α contours (bifurcation lines6) chosen because they pass through an α saddle point (black diamond with white border). The thin curves are contours of constant . The position of the single initial positive (IC=+1/2) C point is shown by a white circle with a black rim, whereas the positions of two initial negative (IC=-1/2) C points are shown by black circles with white rims. All three initial C points correspond to =1. The positions of positive (negative) LOS generated C points are shown by light gray circles with dark gray rims (dark gray circles with light gray rims). The closed, roughly circular contour =0 is an L line that separates right-handed (h=+1) ellipses from left-handed (h=-1) ones: ellipses inside (outside) the line are right handed (left handed).

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