Abstract

We propose the use of a geometric phase, obtained by spatial polarization state manipulations, for the formation of polychromatic vectorial vortices. Experimental demonstration is obtained by using Pancharatnam–Berry phase optical elements formed by a space-variant subwavelength grating etched on a GaAs wafer. We further demonstrate formation of scalar and unpolarized polychromatic vortices.

© 2007 Optical Society of America

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References

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  1. G. Gbur, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 88, 013901 (2002).
    [CrossRef] [PubMed]
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  4. D. Mawet, P. Riaud, O. Absil, and J. Surdej, Astrophys. J. 633, 1191 (2005).
    [CrossRef]
  5. G. Foo, D. M. Palacios, and G. A. Swartzlander, Jr., Opt. Lett. 30, 3308 (2005).
    [CrossRef]
  6. A. V. Volyar and T. A. Fadeeva, Opt. Spectrosc. 94, 235 (2003).
    [CrossRef]
  7. J. Leach and M. J. Padgett, New J. Phys. 5, 154 (2003).
    [CrossRef]
  8. I. G. Mariyenko, J. Strohaber, and C. J. G. J. Uiterwaal, Opt. Express 13, 7599 (2005).
    [CrossRef] [PubMed]
  9. G. A. Swartzlander, Jr., Opt. Lett. 31, 2042 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  11. Q. Zhan and J. R. Leger, Opt. Commun. 213, 241 (2002).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. N. Bokor, R. Shechter, N. Davidson, A. A. Friesem, and E. Hasman, Appl. Opt. 40, 2076 (2001).
    [CrossRef]
  18. H. Kikuta, Y. Ohira, and K. Iwata, Appl. Opt. 36, 1566 (1997).
    [CrossRef] [PubMed]
  19. M. V. Berry, J. Opt. A, Pure Appl. Opt. 6, 259 (2004).
    [CrossRef]

2006 (3)

2005 (4)

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

D. Mawet, P. Riaud, O. Absil, and J. Surdej, Astrophys. J. 633, 1191 (2005).
[CrossRef]

G. Foo, D. M. Palacios, and G. A. Swartzlander, Jr., Opt. Lett. 30, 3308 (2005).
[CrossRef]

I. G. Mariyenko, J. Strohaber, and C. J. G. J. Uiterwaal, Opt. Express 13, 7599 (2005).
[CrossRef] [PubMed]

2004 (3)

2003 (2)

A. V. Volyar and T. A. Fadeeva, Opt. Spectrosc. 94, 235 (2003).
[CrossRef]

J. Leach and M. J. Padgett, New J. Phys. 5, 154 (2003).
[CrossRef]

2002 (3)

G. Gbur, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 88, 013901 (2002).
[CrossRef] [PubMed]

M. V. Berry, New J. Phys. 4, 66 (2002).
[CrossRef]

Q. Zhan and J. R. Leger, Opt. Commun. 213, 241 (2002).
[CrossRef]

2001 (1)

1997 (1)

1993 (1)

Absil, O.

D. Mawet, P. Riaud, O. Absil, and J. Surdej, Astrophys. J. 633, 1191 (2005).
[CrossRef]

Berry, M. V.

M. V. Berry, J. Opt. A, Pure Appl. Opt. 6, 259 (2004).
[CrossRef]

M. V. Berry, New J. Phys. 4, 66 (2002).
[CrossRef]

Bezuhanov, K.

Biener, G.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Express 14, 4208 (2006).
[CrossRef] [PubMed]

Y. Yirmiyahu, A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 31, 3252 (2006).
[CrossRef] [PubMed]

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

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

Bokor, N.

Davidson, N.

Dreischuh, A.

Fadeeva, T. A.

A. V. Volyar and T. A. Fadeeva, Opt. Spectrosc. 94, 235 (2003).
[CrossRef]

Foo, G.

Friesem, A. A.

Gbur, G.

G. Gbur, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 88, 013901 (2002).
[CrossRef] [PubMed]

Hasman, E.

Honkanen, S.

Iwata, K.

Kikuta, H.

Kim, G. H.

Kimura, W. D.

Kleiner, V.

Y. Yirmiyahu, A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 31, 3252 (2006).
[CrossRef] [PubMed]

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Express 14, 4208 (2006).
[CrossRef] [PubMed]

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

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

Leach, J.

J. Leach and M. J. Padgett, New J. Phys. 5, 154 (2003).
[CrossRef]

Leger, J. R.

Q. Zhan and J. R. Leger, Opt. Commun. 213, 241 (2002).
[CrossRef]

Mansuripur, M.

Mariyenko, I. G.

Mawet, D.

D. Mawet, P. Riaud, O. Absil, and J. Surdej, Astrophys. J. 633, 1191 (2005).
[CrossRef]

Niv, A.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Express 14, 4208 (2006).
[CrossRef] [PubMed]

Y. Yirmiyahu, A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 31, 3252 (2006).
[CrossRef] [PubMed]

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

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

Ohira, Y.

Padgett, M. J.

J. Leach and M. J. Padgett, New J. Phys. 5, 154 (2003).
[CrossRef]

Palacios, D. M.

Paulus, G. G.

Riaud, P.

D. Mawet, P. Riaud, O. Absil, and J. Surdej, Astrophys. J. 633, 1191 (2005).
[CrossRef]

Schätzel, M. G.

Shechter, R.

Strohaber, J.

Surdej, J.

D. Mawet, P. Riaud, O. Absil, and J. Surdej, Astrophys. J. 633, 1191 (2005).
[CrossRef]

Swartzlander, G. A.

Tidwell, S. C.

Turunen, J.

Uiterwaal, C. J. G. J.

Vallius, T.

Visser, T. D.

G. Gbur, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 88, 013901 (2002).
[CrossRef] [PubMed]

Volyar, A. V.

A. V. Volyar and T. A. Fadeeva, Opt. Spectrosc. 94, 235 (2003).
[CrossRef]

Walther, H.

Wolf, E.

G. Gbur, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 88, 013901 (2002).
[CrossRef] [PubMed]

Yirmiyahu, Y.

Zhan, Q.

Q. Zhan and J. R. Leger, Opt. Commun. 213, 241 (2002).
[CrossRef]

Appl. Opt. (3)

Astrophys. J. (1)

D. Mawet, P. Riaud, O. Absil, and J. Surdej, Astrophys. J. 633, 1191 (2005).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

M. V. Berry, J. Opt. A, Pure Appl. Opt. 6, 259 (2004).
[CrossRef]

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

New J. Phys. (2)

M. V. Berry, New J. Phys. 4, 66 (2002).
[CrossRef]

J. Leach and M. J. Padgett, New J. Phys. 5, 154 (2003).
[CrossRef]

Opt. Commun. (2)

Q. Zhan and J. R. Leger, Opt. Commun. 213, 241 (2002).
[CrossRef]

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

Opt. Express (2)

Opt. Lett. (4)

Opt. Spectrosc. (1)

A. V. Volyar and T. A. Fadeeva, Opt. Spectrosc. 94, 235 (2003).
[CrossRef]

Phys. Rev. Lett. (1)

G. Gbur, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 88, 013901 (2002).
[CrossRef] [PubMed]

Other (1)

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

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Figures (3)

Fig. 1
Fig. 1

Polarization state transformation is represented as trajectories on the Poincare sphere. Rotation of the grating by θ results in a 2 θ phase modification. This phase equals half of the area enclosed by the geodesic lines. Inset, scanning electron microscope image of the PBOE surface for m = 1 .

Fig. 2
Fig. 2

(a) Measured intensity distributions for linearly polarized vectorial vortices embedded in polychromatic beams. (b) Same as (a) but imaged through a linear analyzer. (c) Schematic representation of the polarization state of the linearly polarized vectorial vortices.

Fig. 3
Fig. 3

Measured intensity distributions for unpolarized vortices with m = 2 , 4 in (a) and (b), respectively. (c) Measured diffraction pattern obtained from a refractive spiral phase plate for m = 1 .

Equations (4)

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T ( x , y ; λ ) = η 0 ( λ ) I + η 1 ( λ ) { R L exp [ i 2 θ ( x , y ) ] + L R exp [ i 2 θ ( x , y ) ] } ,
E out ( λ ) = T E in = S ( λ ) η 0 ( λ ) L + η 1 ( λ ) exp ( i m φ ) R .
E = S ( λ ) η 1 ( λ ) exp ( i m φ ) R .
E out ( λ ) = T E in = η 0 ( λ ) H + η 1 ( λ ) φ m ,

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