Abstract

Spiral phase elements with topological charges based on space-variant Pancharatnam–Berry phase optical elements are presented. Such elements can be achieved by use of continuous computer-generated space-variant subwavelength dielectric gratings. We present a theoretical analysis and experimentally demonstrate spiral geometrical phases for infrared radiation at a wavelength of 10.6 µm.

© 2002 Optical Society of America

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References

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    [CrossRef]

2002

2001

Z. Bomzon, V. Kleiner, and E. Hasman, Opt. Lett. 26, 1424 (2001).
[CrossRef]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

1998

1994

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

1984

M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
[CrossRef]

1956

S. Pancharatnam, Proc. Ind. Acad. Sci. A 44, 247 (1956).

Allen, L.

L. Allen, M. J. Padgett, and M. Babiker, in Progress in Optics, E. Wolf, ed. (Pergamon, London, 1999), Vol. XXXIX, p. 291.
[CrossRef]

Arlt, J.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

Babiker, M.

L. Allen, M. J. Padgett, and M. Babiker, in Progress in Optics, E. Wolf, ed. (Pergamon, London, 1999), Vol. XXXIX, p. 291.
[CrossRef]

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Berry, M. V.

M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
[CrossRef]

Biener, G.

Bomzon, Z.

Bryant, P. E.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Davidson, N.

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, in Progress in Optics, E. Wolf, ed. (Pergamon, London, 2001), Vol. XDII, p. 325.
[CrossRef]

Dholakia, K.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

Friesem, A. A.

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, in Progress in Optics, E. Wolf, ed. (Pergamon, London, 2001), Vol. XDII, p. 325.
[CrossRef]

Hasman, E.

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 27, 285 (2002).
[CrossRef]

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

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 27, 1141 (2002).
[CrossRef]

Z. Bomzon, V. Kleiner, and E. Hasman, Opt. Lett. 26, 1424 (2001).
[CrossRef]

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, in Progress in Optics, E. Wolf, ed. (Pergamon, London, 2001), Vol. XDII, p. 325.
[CrossRef]

Kleiner, V.

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

MacDonald, M. P.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Niv, A.

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

Oron, R.

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, in Progress in Optics, E. Wolf, ed. (Pergamon, London, 2001), Vol. XDII, p. 325.
[CrossRef]

Padgett, M. J.

L. Allen, M. J. Padgett, and M. Babiker, in Progress in Optics, E. Wolf, ed. (Pergamon, London, 1999), Vol. XXXIX, p. 291.
[CrossRef]

Pancharatnam, S.

S. Pancharatnam, Proc. Ind. Acad. Sci. A 44, 247 (1956).

Paterson, L.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

Rozas, D.

Sacks, Z. S.

Sibbett, W.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

Swartzlander, G. A.

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Appl. Phys. Lett.

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

J. Opt. Soc. Am. B

Nature

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Opt. Commun.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Opt. Lett.

Proc. Ind. Acad. Sci. A

S. Pancharatnam, Proc. Ind. Acad. Sci. A 44, 247 (1956).

Proc. R. Soc. London Ser. A

M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
[CrossRef]

Science

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

Other

L. Allen, M. J. Padgett, and M. Babiker, in Progress in Optics, E. Wolf, ed. (Pergamon, London, 1999), Vol. XXXIX, p. 291.
[CrossRef]

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, in Progress in Optics, E. Wolf, ed. (Pergamon, London, 2001), Vol. XDII, p. 325.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) Illustration of the principle of PBOEs by use of the Poincaré sphere; insets, local orientations of the subwavelength grooves. (b) Geometrical definition of the grating vector.

Fig. 2
Fig. 2

Top, geometry of the subwavelength gratings for four topological charges. Bottom, image of a typical grating profile taken with a scanning-electron microscope.

Fig. 3
Fig. 3

(a) Interferogram measurements of the spiral PBOEs. (b) The corresponding spiral phases for different topological charges.

Fig. 4
Fig. 4

Experimental far-field images and their calculated and measured cross sections for the helical beams with l=14.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

Tr,ω=12tx+ty expiϕ1001+12tx-ty×expiϕ0expi2θr,ωexp-i2θr,ω0,
|Eout=ηE|Ein+ηRexpi2θr,ω|R+ηLexp-i2θr,ω|L,
|Eout=exp-i2θr,ω|L.

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