Abstract

Propagation-invariant vectorial Bessel beams with linearly polarized axial symmetry based on quantized Pancharatnam–Berry phase optical elements are described. The geometric phase is formed through the use of discrete computer-generated space-variant subwavelength dielectric gratings. We have verified the polarization properties of our elements for laser radiation at 10.6µm wavelength and also demonstrated propagation-invariant, controlled rotation of a propeller-shaped intensity pattern through the simple rotation of a polarizer.

© 2004 Optical Society of America

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  1. J. Durnin, J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
    [CrossRef] [PubMed]
  2. V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
    [CrossRef]
  3. J. Tervo and J. Turunen, Opt. Commun. 192, 13 (2001).
    [CrossRef]
  4. P. Pääkkönen, J. Tervo, P. Vehimaa, J. Turunen, and F. Gori, Opt. Express 10, 949 (2002), http://www.opticsexpress.org .
    [CrossRef]
  5. Z. Bomzon, A. Niv, G. Biener, V. Kleiner, and E. Hasman, Appl. Phys. Lett. 80, 3685 (2002).
    [CrossRef]
  6. A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 28, 510 (2003).
    [CrossRef] [PubMed]
  7. R. Oron, S. Bilt, N. Davidson, A. A. Freisem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
    [CrossRef]
  8. J. A. Davis, D. E. McNamara, D. M. Cottrel, and T. Sonehara, Appl. Opt. 39, 1594 (2000).
    [CrossRef]
  9. E. Hasman, V. Kleiner, G. Biener, and A. Niv, Appl. Phys. Lett. 82, 328 (2003).
    [CrossRef]
  10. M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
    [CrossRef] [PubMed]
  11. N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 88, 326 (1992).
    [CrossRef]

2003 (2)

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 28, 510 (2003).
[CrossRef] [PubMed]

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

2002 (4)

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

P. Pääkkönen, J. Tervo, P. Vehimaa, J. Turunen, and F. Gori, Opt. Express 10, 949 (2002), http://www.opticsexpress.org .
[CrossRef]

Z. Bomzon, A. Niv, G. Biener, V. Kleiner, and E. Hasman, Appl. Phys. Lett. 80, 3685 (2002).
[CrossRef]

2001 (1)

J. Tervo and J. Turunen, Opt. Commun. 192, 13 (2001).
[CrossRef]

2000 (2)

R. Oron, S. Bilt, N. Davidson, A. A. Freisem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

J. A. Davis, D. E. McNamara, D. M. Cottrel, and T. Sonehara, Appl. Opt. 39, 1594 (2000).
[CrossRef]

1992 (1)

N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 88, 326 (1992).
[CrossRef]

1987 (1)

J. Durnin, J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Arlt, J.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

Biener, G.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 28, 510 (2003).
[CrossRef] [PubMed]

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

Z. Bomzon, A. Niv, G. Biener, V. Kleiner, and E. Hasman, Appl. Phys. Lett. 80, 3685 (2002).
[CrossRef]

Bilt, S.

R. Oron, S. Bilt, N. Davidson, A. A. Freisem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Bomzon, Z.

Z. Bomzon, A. Niv, G. Biener, V. Kleiner, and E. Hasman, Appl. Phys. Lett. 80, 3685 (2002).
[CrossRef]

R. Oron, S. Bilt, N. Davidson, A. A. Freisem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Cottrel, D. M.

J. A. Davis, D. E. McNamara, D. M. Cottrel, and T. Sonehara, Appl. Opt. 39, 1594 (2000).
[CrossRef]

Davidson, N.

R. Oron, S. Bilt, N. Davidson, A. A. Freisem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 88, 326 (1992).
[CrossRef]

Davis, J. A.

J. A. Davis, D. E. McNamara, D. M. Cottrel, and T. Sonehara, Appl. Opt. 39, 1594 (2000).
[CrossRef]

Dholakia, K.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

Durnin, J.

J. Durnin, J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Freisem, A. A.

R. Oron, S. Bilt, N. Davidson, A. A. Freisem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Friesem, A. A.

N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 88, 326 (1992).
[CrossRef]

Garcés-Chávez, V.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

Gori, F.

Hasman, E.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 28, 510 (2003).
[CrossRef] [PubMed]

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

Z. Bomzon, A. Niv, G. Biener, V. Kleiner, and E. Hasman, Appl. Phys. Lett. 80, 3685 (2002).
[CrossRef]

R. Oron, S. Bilt, N. Davidson, A. A. Freisem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 88, 326 (1992).
[CrossRef]

Kleiner, V.

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

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 28, 510 (2003).
[CrossRef] [PubMed]

Z. Bomzon, A. Niv, G. Biener, V. Kleiner, and E. Hasman, Appl. Phys. Lett. 80, 3685 (2002).
[CrossRef]

MacDonald, M. P.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

McGloin, D.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

McNamara, D. E.

J. A. Davis, D. E. McNamara, D. M. Cottrel, and T. Sonehara, Appl. Opt. 39, 1594 (2000).
[CrossRef]

Melville, H.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

Miceli, J.

J. Durnin, J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Niv, A.

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

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 28, 510 (2003).
[CrossRef] [PubMed]

Z. Bomzon, A. Niv, G. Biener, V. Kleiner, and E. Hasman, Appl. Phys. Lett. 80, 3685 (2002).
[CrossRef]

Oron, R.

R. Oron, S. Bilt, N. Davidson, A. A. Freisem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Pääkkönen, P.

Paterson, L.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

Sibbett, W.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

Sonehara, T.

J. A. Davis, D. E. McNamara, D. M. Cottrel, and T. Sonehara, Appl. Opt. 39, 1594 (2000).
[CrossRef]

Tervo, J.

Turunen, J.

Vehimaa, P.

Volke-Sepulveda, K.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

Appl. Opt. (1)

J. A. Davis, D. E. McNamara, D. M. Cottrel, and T. Sonehara, Appl. Opt. 39, 1594 (2000).
[CrossRef]

Appl. Phys. Lett. (3)

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

R. Oron, S. Bilt, N. Davidson, A. A. Freisem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Z. Bomzon, A. Niv, G. Biener, V. Kleiner, and E. Hasman, Appl. Phys. Lett. 80, 3685 (2002).
[CrossRef]

Nature (1)

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

Opt. Commun. (2)

J. Tervo and J. Turunen, Opt. Commun. 192, 13 (2001).
[CrossRef]

N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 88, 326 (1992).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

J. Durnin, J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Science (1)

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

(a) Magnified geometries of the masks for various polarization orders. (b) Scanning-electron microscope images of the central parts of the corresponding elements.

Fig. 2
Fig. 2

(a) Experimental intensity distributions, directly after the elements, for beams emerging from a linear polarizer for four polarization orders. (b) Measured local azimuthal angles of the beams.

Fig. 3
Fig. 3

Intensity distributions at 8 cm beyond the axicon for (a) m=2 and (b) m=3. The strips arranged along the circumference of a beam illustrate the local azimuthal angles. (c), (d) Experimental (filled circles) and theoretical (solid curves) intensity cross sections for m=2 and m=3, respectively, at 8, 9, and 10 cm beyond the axicon.

Fig. 4
Fig. 4

(a) Propeller-shaped intensity patterns of the emerging beams from the QPBOEs followed by an axicon and a polarizer for four polarization orders, m=1,2,3,4, from left to right. (b) Controlled rotation of the propeller-shaped intensities by rotation of the polarizer by 90°; dashed lines and dotted curves, rotation angles of the patterns.

Equations (2)

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|Bm=Kz[fr|Pm]παz/λexpik1-α2/2z+r2/2z-λ/8×-imJmkαr|Pm,
|Eout=12expi2θr,ω|R+12exp-i2θr,ω|L.

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