Abstract

Multiple vortices with different topological charges are formed by the use of two sequential geometric phase elements. These elements are realized by quasi-periodic subwavelength gratings. The first element is a spiral phase element and the second element is a spherical phase element. We provide a theoretical analysis and an experimental demonstration of the formation of the multiple vortices that comprise scalar vortices and a vectorial vortex.

© 2006 Optical Society of America

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References

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2005

2004

K. Ladavac and D. G. Grier, Opt. Express 12, 1144 (2004).
[CrossRef] [PubMed]

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, Nature 432, 165 (2004).
[CrossRef] [PubMed]

2003

E. Hasman, V. Kleiner, G. Biener, and A. Niv, Appl. Phys. Lett. 82, 328 (2003).
[CrossRef]

1997

1996

Allen, L.

Biener, G.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 30, 2933 (2005).
[CrossRef] [PubMed]

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Commun. 251, 306 (2005).
[CrossRef]

Y. Gorodetski, G. Biener, A. Niv, V. Kleiner, and E. Hasman, Opt. Lett. 30, 2245 (2005).
[CrossRef] [PubMed]

E. Hasman, V. Kleiner, G. Biener, and A. Niv, Appl. Phys. Lett. 82, 328 (2003).
[CrossRef]

E. Hasman, G. Biener, A. Niv, and V. Kleiner, in Progress in Optics, Vol. 47, E.Wolf, ed. (Elsevier, 2005), p. 215.
[CrossRef]

Brosseau, C.

C. Brosseau, Fundamentals of Polarized Light; A Statistical Optics Approach (Wiley, 1998).
[PubMed]

Courtial, J.

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, Nature 432, 165 (2004).
[CrossRef] [PubMed]

Dennis, M. R.

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, Nature 432, 165 (2004).
[CrossRef] [PubMed]

Dholakia, K.

Gahagan, K. T.

Gorodetski, Y.

Grier, D. G.

Hasman, E.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 30, 2933 (2005).
[CrossRef] [PubMed]

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Commun. 251, 306 (2005).
[CrossRef]

Y. Gorodetski, G. Biener, A. Niv, V. Kleiner, and E. Hasman, Opt. Lett. 30, 2245 (2005).
[CrossRef] [PubMed]

E. Hasman, V. Kleiner, G. Biener, and A. Niv, Appl. Phys. Lett. 82, 328 (2003).
[CrossRef]

E. Hasman, G. Biener, A. Niv, and V. Kleiner, in Progress in Optics, Vol. 47, E.Wolf, ed. (Elsevier, 2005), p. 215.
[CrossRef]

Kleiner, V.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Commun. 251, 306 (2005).
[CrossRef]

Y. Gorodetski, G. Biener, A. Niv, V. Kleiner, and E. Hasman, Opt. Lett. 30, 2245 (2005).
[CrossRef] [PubMed]

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 30, 2933 (2005).
[CrossRef] [PubMed]

E. Hasman, V. Kleiner, G. Biener, and A. Niv, Appl. Phys. Lett. 82, 328 (2003).
[CrossRef]

E. Hasman, G. Biener, A. Niv, and V. Kleiner, in Progress in Optics, Vol. 47, E.Wolf, ed. (Elsevier, 2005), p. 215.
[CrossRef]

Ladavac, K.

Leach, J.

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, Nature 432, 165 (2004).
[CrossRef] [PubMed]

Niv, A.

Y. Gorodetski, G. Biener, A. Niv, V. Kleiner, and E. Hasman, Opt. Lett. 30, 2245 (2005).
[CrossRef] [PubMed]

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 30, 2933 (2005).
[CrossRef] [PubMed]

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Commun. 251, 306 (2005).
[CrossRef]

E. Hasman, V. Kleiner, G. Biener, and A. Niv, Appl. Phys. Lett. 82, 328 (2003).
[CrossRef]

E. Hasman, G. Biener, A. Niv, and V. Kleiner, in Progress in Optics, Vol. 47, E.Wolf, ed. (Elsevier, 2005), p. 215.
[CrossRef]

Padgett, M. J.

Simpson, N. B.

Swartzlander, G. A.

Appl. Phys. Lett.

E. Hasman, V. Kleiner, G. Biener, and A. Niv, Appl. Phys. Lett. 82, 328 (2003).
[CrossRef]

Nature

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, Nature 432, 165 (2004).
[CrossRef] [PubMed]

Opt. Commun.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Commun. 251, 306 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Other

E. Hasman, G. Biener, A. Niv, and V. Kleiner, in Progress in Optics, Vol. 47, E.Wolf, ed. (Elsevier, 2005), p. 215.
[CrossRef]

C. Brosseau, Fundamentals of Polarized Light; A Statistical Optics Approach (Wiley, 1998).
[PubMed]

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Figures (3)

Fig. 1
Fig. 1

(a) Concept of the manipulation of a polarization-dependent multivortex beam with quasi-periodic subwavelength gratings. The rounded arrows in the near and far focal planes describe the LCP and RCP states of the focused beams, whereas the inset at the central focal plane depicts the measured orientation angles of the space-variant polarization ellipses. (b) Measured intensity distributions in the three focal planes. (c) Measured intensity distributions in the three focal planes transmitted through a polarizer oriented at 0 ° .

Fig. 2
Fig. 2

(a) Magnified geometry of a region on the spherical phase PBOE mask with N = 4 . (b) and (c) SEM images taken from a small region of the spherical phase PBOE. (d) SEM image of the central part of the spiral phase PBOE. (e) Measured local azimuthal angles of the beam emerging from the spiral phase PBOE.

Fig. 3
Fig. 3

Normalized intensity at different focuses of the spherical phase PBOE followed by the refractive lens as a function of the orientation of the QWP used as a polarization state generator. Triangles are the measurements in the RCP focal plane, circles are the measurements in the LCP focal plane, and diamonds are the measurements in the focal plane of the first polarization order. The dotted, dashed–dotted, and dashed curves are the theoretical calculations for each order.

Equations (2)

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T = t x + t y e i ϕ 2 [ 1 0 0 1 ] + t x t y e i ϕ 2 [ 0 e i 2 θ ( ρ ) e i 2 θ ( ρ ) 0 ] ,
E out = T rl T sp T s E in = 1 2 [ exp ( i π ρ 2 λ f r ) E l + R E in exp ( i l ω i π ρ 2 λ f R ) R ) [ + L E in exp ( i l ω i π ρ 2 λ f L ) L ] ,

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