Abstract

We report the appearance of a geometrical phase in space-variant polarization-state manipulations. This phase is related to the classic Pancharatnam–Berry phase. We show a method with which to calculate it and experimentally demonstrate its effect, using subwavelength metal stripe space-variant gratings. The experiment is based on a unique grating for converting circularly polarized light at a wavelength of 10.6 μm into an azimuthally polarized beam. Our experimental evidence relies on analysis of far-field images of the resultant polarization.

© 2001 Optical Society of America

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References

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  1. S. Pancharatnam, Proc. Ind. Acad. Sci. 44, 247 (1956).
  2. M. V. Berry, J. Mod. Opt. 34, 1401 (1987).
    [CrossRef]
  3. R. Bhanderi and J. Samuel, Phys. Rev. Lett. 60, 1211 (1988).
    [CrossRef]
  4. T. H. Chyba, L. J. Wang, L. Mandel, and R. Simon, Opt. Lett. 13, 562 (1988).
    [CrossRef]
  5. Z. Bomzon, V. Kleiner, and E. Hasman, Opt. Lett. 26, 33 (2000).
    [CrossRef]
  6. E. Collet, Polarized Light (Dekker, New York, 1993).
  7. M. G. Moharam and T. K. Gaylord, J. Opt. Soc. Am. A 3, 1780 (1986).
    [CrossRef]
  8. P. K. Aravind, Opt. Commun. 94, 191 (1992).
    [CrossRef]
  9. Z. Bomzon, V. Kleiner, and E. Hasman, in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), pp. 188–189.
  10. W. H. Lee, Appl. Opt. 13, 1677 (1974).
    [CrossRef] [PubMed]
  11. R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, Opt. Lett. 25, 939 (2000).
    [CrossRef]
  12. S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
    [CrossRef]

2000 (3)

1992 (1)

P. K. Aravind, Opt. Commun. 94, 191 (1992).
[CrossRef]

1988 (2)

1987 (1)

M. V. Berry, J. Mod. Opt. 34, 1401 (1987).
[CrossRef]

1986 (1)

1974 (1)

1956 (1)

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

Aravind, P. K.

P. K. Aravind, Opt. Commun. 94, 191 (1992).
[CrossRef]

Berry, M. V.

M. V. Berry, J. Mod. Opt. 34, 1401 (1987).
[CrossRef]

Bhanderi, R.

R. Bhanderi and J. Samuel, Phys. Rev. Lett. 60, 1211 (1988).
[CrossRef]

Bomzon, Z.

Z. Bomzon, V. Kleiner, and E. Hasman, Opt. Lett. 26, 33 (2000).
[CrossRef]

Z. Bomzon, V. Kleiner, and E. Hasman, in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), pp. 188–189.

Chyba, T. H.

Collet, E.

E. Collet, Polarized Light (Dekker, New York, 1993).

Davidson, N.

Dorn, R.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Friesem, A. A.

Gaylord, T. K.

Glöckl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Hasman, E.

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, Opt. Lett. 25, 939 (2000).
[CrossRef]

Z. Bomzon, V. Kleiner, and E. Hasman, Opt. Lett. 26, 33 (2000).
[CrossRef]

Z. Bomzon, V. Kleiner, and E. Hasman, in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), pp. 188–189.

Kleiner, V.

Z. Bomzon, V. Kleiner, and E. Hasman, Opt. Lett. 26, 33 (2000).
[CrossRef]

Z. Bomzon, V. Kleiner, and E. Hasman, in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), pp. 188–189.

Lee, W. H.

Leuchs, G.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Mandel, L.

Moharam, M. G.

Oron, R.

Pancharatnam, S.

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

Quabis, S.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Samuel, J.

R. Bhanderi and J. Samuel, Phys. Rev. Lett. 60, 1211 (1988).
[CrossRef]

Simon, R.

Wang, L. J.

Appl. Opt. (1)

J. Mod. Opt. (1)

M. V. Berry, J. Mod. Opt. 34, 1401 (1987).
[CrossRef]

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

Opt. Commun. (2)

P. K. Aravind, Opt. Commun. 94, 191 (1992).
[CrossRef]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. Lett. (1)

R. Bhanderi and J. Samuel, Phys. Rev. Lett. 60, 1211 (1988).
[CrossRef]

Proc. Ind. Acad. Sci. (1)

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

Other (2)

E. Collet, Polarized Light (Dekker, New York, 1993).

Z. Bomzon, V. Kleiner, and E. Hasman, in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), pp. 188–189.

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Figures (4)

Fig. 1
Fig. 1

Demonstration of space-variant polarization-state manipulations on a Poincaré sphere. Inset, resultant local polarization ellipse.

Fig. 2
Fig. 2

Illustration of the instantaneous real part of the electric field vectors of in-phase and antiphase azimuthal polarization.

Fig. 3
Fig. 3

(a) Magnified geometry of the grating for converting circular polarization into azimuthal polarization and (b) experimental measurement of the local azimuthal angle ψ.

Fig. 4
Fig. 4

Measured and calculated cross sections of the far-field images for (a) the in-phase and (b) the antiphase azimuthal polarization. Inset, experimental intensity distributions.

Equations (8)

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Kgx,y=2π/Λx,ycosβx,yx^+sinβx,yy^,
Jx,y=Mβx,yJΛx,yM-1βx,y,
JΛ=pooqexpiγexpiφ,
EB1=piqexpiγexpiφ,EB2=pcosθ+iqexpiγsinθ-psinθ+iqexpiγcosθexpiφ
argEB1,EB2=θ-arctan2pqcosγsinθp2+q2cosθ=θ-arctansin2χtanθ,
Exx,yEyx,y=iexpiθ-sinθcosθ.
ϕ=Kgdr=2πr0Λ0cosΔψΛ0×(θ-rtanΔψΛrrdr),
K0=2π/Λr=2π/Λ0(r0cosΔψΛ0/rcosΔψΛr).

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