Abstract

In generic three-dimensional optical fields the canonical point polarization singularities are points of circular polarization, C points on C lines, and points of linear polarization, L points on L lines. These special points are surrounded by a sea of ordinary points. In planes oriented normal to the principle axes of the polarization ellipse at the point, every ordinary point is also a singularity, here an ordinary polarization singularity, or O point. Interactions between O points, between O points and C points, and between O points and L points are described that highlight the fact that a consistent description of optical fields containing C and L lines must include O points.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2011 (2)

G. H. Yuan, S. B. Wei, and X.-C. Yuan, Opt. Lett. 36, 3499 (2011).

I. Freund, Opt. Lett. 36, 4506 (2011).
[CrossRef]

2010 (3)

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

Y. Luo and B. Lü, J. Opt. Soc. Am. A 27, 578 (2010).
[CrossRef]

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

2009 (2)

M. Burresi, R. J. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902(2009).
[CrossRef]

J. S. Ahn, H. W. Kihm, J. E. Kihm, D. S. Kim, and K. G. Lee, Opt. Express 17, 2280 (2009).
[CrossRef]

2008 (3)

V. Vasil’ev and M. Soskin, Opt. Commun. 281, 5527 (2008).
[CrossRef]

V. I. Vasil’ev and M. S. Soskin, JETP Lett. 88, 418 (2008).
[CrossRef]

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

2007 (1)

S. Zhang, B. Hu, Y. Lockerman, P. Sebbah, and A. Z. Genack, J. Opt. Soc. Am. A 24, 35 (2007).

2006 (2)

Y. F. Chen, T. H. Lu, and K. F. Huang, Phys. Rev. Lett. 96, 033901 (2006).
[CrossRef]

R. W. Schoonover and T. D. Visser, Opt. Express 14, 5733 (2006).
[CrossRef]

2005 (2)

I. Freund, Opt. Commun. 249, 7 (2005).
[CrossRef]

I. Freund, Opt. Commun. 256, 220 (2005).
[CrossRef]

2004 (1)

I. Freund, Opt. Commun. 242, 65 (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. Lond. A 457, 141 (2001).
[CrossRef]

I. Freund and D. A. Kessler, Opt. Commun. 187, 71 (2001).
[CrossRef]

1998 (1)

M. Berry, Proc. SPIE 3487, 1 (1998).
[CrossRef]

1987 (1)

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

1983 (1)

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

Ahn, J. S.

Baba, T.

M. Burresi, R. J. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902(2009).
[CrossRef]

Berry, M.

M. Berry, Proc. SPIE 3487, 1 (1998).
[CrossRef]

Berry, M. V.

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

Burresi, M.

M. Burresi, R. J. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902(2009).
[CrossRef]

Chen, Y. F.

Y. F. Chen, T. H. Lu, and K. F. Huang, Phys. Rev. Lett. 96, 033901 (2006).
[CrossRef]

Dennis, M. R.

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

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

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

Engelen, R. J.

M. Burresi, R. J. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902(2009).
[CrossRef]

Freund, I.

I. Freund, Opt. Lett. 36, 4506 (2011).
[CrossRef]

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

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

I. Freund, Opt. Commun. 249, 7 (2005).
[CrossRef]

I. Freund, Opt. Commun. 256, 220 (2005).
[CrossRef]

I. Freund, Opt. Commun. 242, 65 (2004).
[CrossRef]

I. Freund and D. A. Kessler, Opt. Commun. 187, 71 (2001).
[CrossRef]

Genack, A. Z.

S. Zhang, B. Hu, Y. Lockerman, P. Sebbah, and A. Z. Genack, J. Opt. Soc. Am. A 24, 35 (2007).

Hajnal, J. V.

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

Hu, B.

S. Zhang, B. Hu, Y. Lockerman, P. Sebbah, and A. Z. Genack, J. Opt. Soc. Am. A 24, 35 (2007).

Huang, K. F.

Y. F. Chen, T. H. Lu, and K. F. Huang, Phys. Rev. Lett. 96, 033901 (2006).
[CrossRef]

Kessler, D. A.

I. Freund and D. A. Kessler, Opt. Commun. 187, 71 (2001).
[CrossRef]

Kihm, H. W.

Kihm, J. E.

Kim, D. S.

Kuipers, L.

M. Burresi, R. J. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902(2009).
[CrossRef]

Lee, K. G.

Lockerman, Y.

S. Zhang, B. Hu, Y. Lockerman, P. Sebbah, and A. Z. Genack, J. Opt. Soc. Am. A 24, 35 (2007).

Lu, T. H.

Y. F. Chen, T. H. Lu, and K. F. Huang, Phys. Rev. Lett. 96, 033901 (2006).
[CrossRef]

Lü, B.

Luo, Y.

Mori, D.

M. Burresi, R. J. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902(2009).
[CrossRef]

Nye, J. F.

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

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

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

Opheij, A.

M. Burresi, R. J. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902(2009).
[CrossRef]

Schoonover, R. W.

Sebbah, P.

S. Zhang, B. Hu, Y. Lockerman, P. Sebbah, and A. Z. Genack, J. Opt. Soc. Am. A 24, 35 (2007).

Soskin, M.

V. Vasil’ev and M. Soskin, Opt. Commun. 281, 5527 (2008).
[CrossRef]

Soskin, M. S.

V. I. Vasil’ev and M. S. Soskin, JETP Lett. 88, 418 (2008).
[CrossRef]

van Oosten, D.

M. Burresi, R. J. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902(2009).
[CrossRef]

Vasil’ev, V.

V. Vasil’ev and M. Soskin, Opt. Commun. 281, 5527 (2008).
[CrossRef]

Vasil’ev, V. I.

V. I. Vasil’ev and M. S. Soskin, JETP Lett. 88, 418 (2008).
[CrossRef]

Visser, T. D.

Wei, S. B.

G. H. Yuan, S. B. Wei, and X.-C. Yuan, Opt. Lett. 36, 3499 (2011).

Yuan, G. H.

G. H. Yuan, S. B. Wei, and X.-C. Yuan, Opt. Lett. 36, 3499 (2011).

Yuan, X.-C.

G. H. Yuan, S. B. Wei, and X.-C. Yuan, Opt. Lett. 36, 3499 (2011).

Zhang, S.

S. Zhang, B. Hu, Y. Lockerman, P. Sebbah, and A. Z. Genack, J. Opt. Soc. Am. A 24, 35 (2007).

J. Opt. Soc. Am. A (2)

S. Zhang, B. Hu, Y. Lockerman, P. Sebbah, and A. Z. Genack, J. Opt. Soc. Am. A 24, 35 (2007).

Y. Luo and B. Lü, J. Opt. Soc. Am. A 27, 578 (2010).
[CrossRef]

JETP Lett. (1)

V. I. Vasil’ev and M. S. Soskin, JETP Lett. 88, 418 (2008).
[CrossRef]

Opt. Commun. (8)

I. Freund, Opt. Commun. 242, 65 (2004).
[CrossRef]

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

I. Freund, Opt. Commun. 249, 7 (2005).
[CrossRef]

I. Freund, Opt. Commun. 256, 220 (2005).
[CrossRef]

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

V. Vasil’ev and M. Soskin, Opt. Commun. 281, 5527 (2008).
[CrossRef]

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

I. Freund and D. A. Kessler, Opt. Commun. 187, 71 (2001).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

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

I. Freund, Opt. Lett. 36, 4506 (2011).
[CrossRef]

G. H. Yuan, S. B. Wei, and X.-C. Yuan, Opt. Lett. 36, 3499 (2011).

Phys. Rev. Lett. (2)

M. Burresi, R. J. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902(2009).
[CrossRef]

Y. F. Chen, T. H. Lu, and K. F. Huang, Phys. Rev. Lett. 96, 033901 (2006).
[CrossRef]

Proc. R. Soc. Lond. A (3)

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

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

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

Proc. SPIE (1)

M. Berry, Proc. SPIE 3487, 1 (1998).
[CrossRef]

Other (1)

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

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Figures (5)

Fig. 1.
Fig. 1.

Streamline patterns. (a)–(c) αO, βO, γO points, and L points, (d)–(f) C points. (a) Spiral, I=+1, NΛ=0. (b) Sink, I=+1, NΛ=4. (c) Saddle, I=1, NΛ=4. (d) Lemon, I=+1/2, NΛ=1. (e) Monstar, I=+1/2, NΛ=3. (f) Star, I=1/2, NΛ=3. Winding number I can be found by moving, say, counterclockwise along the figure boundary while noting the net signed rotation, positive counterclockwise, negative clockwise, of the surrounding axes (tangents to the streamlines). NΛ can be found by counting Λ lines, the straight streamlines (separatixes) shown by dotted lines that terminate on the central singularity.

Fig. 2.
Fig. 2.

Apparent motion of a γO point in a random field simulation. The winding angle in P of axis γ is gray scale coded 0 to π black to white. The colors go through two black-to-white cycles in the negative clockwise direction, the net signed winding angle in P is 2π, and IγO=1. This “vortex” representation is used throughout.

Fig. 3.
Fig. 3.

Sign inversion of the γO point in Fig. 2 versus rotation angle χ in increments of 0.01°. (a) IγO. (b) Ellipticity ε. Qualitatively similar results are obtained as the orientation of rotation axis A varies over a swath of 60°.

Fig. 4.
Fig. 4.

L points, γO track, and charge exchange collisions. (a) Winding angle of axis γ in the region surrounding the γO point in Fig. 2, coded as in that figure. Positive sinks (negative saddles) are shown by white (black) filled circles. The γO point is the uppermost negative vortex; the other vortices are shown in (b) to be L points. (b) L point discriminant DL [18] coded 0 to 1 black to white; DL0 at the three L points labeled 1 to 3. (c) Schematic track of the γO point in Fig. 3. χ increases counterclockwise (decreases clockwise) from the dotted line labeled 0. Positive (negative) L points numbered as in (b) are shown by white (black) circles, and track segments with positive (negative) IγO are shown by white (black) arcs. The track diverges at the points labeled . (d)–(f) Charge exchange collision between the γO point and an L point on L line 3. (d) The negative γO point approaches the central positive L point. (e) The points collide and exchange charge. (f) The now positive γO point leaves the now negative L point behind and continues on to the next collision.

Fig. 5.
Fig. 5.

αO point reactions. (a) Upper panel, vortex representation of the initial, χ=0, field. Positive (negative) singularities are shown by white (black) circles. Lower panel, streamline pattern of the field in (a). The dotted lines are separatixes. (b) Inelastic charge exchange reaction of an αO point with a C point. (c) Annihilation of two αO points. In (b) [in (c)] χ increases positively (decreases negatively) top to bottom. Please see the text for additional details.

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