Abstract

Spin–orbit interaction resulting from spatial polarization state manipulation is demonstrated. Polarization-state manipulation is achieved by utilizing the effective birefringent nature of subwavelength structures acting as an anisotropic inhomogeneous medium. Experimental verification is obtained by measuring the effect of the unavoidable spin-dependent Pancharatnam–Berry phase modulation on the far-field diffraction pattern of the beam. Unlike the usual dynamic spin–orbit interaction that splits spin states in the temporal frequency (energy) domain, this topological spin–orbit interaction results in the splitting of spin states degenerated by their spatial frequencies (momentum).

© 2008 Optical Society of America

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References

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  1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. E 45, 8185 (1992).
  2. K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 030404 (2008).
    [CrossRef] [PubMed]
  3. M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
    [CrossRef] [PubMed]
  4. Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008).
    [CrossRef] [PubMed]
  5. L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
    [CrossRef] [PubMed]
  6. B. A. Garetz and S. Arnold, Opt. Commun. 31, 1 (1979).
    [CrossRef]
  7. M. V. Berry, Proc. R. Soc. London, Ser. A 392, 45 (1984).
    [CrossRef]
  8. A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Commun. 251, 306 (2005).
    [CrossRef]

2008 (2)

K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 030404 (2008).
[CrossRef] [PubMed]

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008).
[CrossRef] [PubMed]

2006 (1)

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef] [PubMed]

2005 (1)

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

2004 (1)

M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef] [PubMed]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. E 45, 8185 (1992).

1984 (1)

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

1979 (1)

B. A. Garetz and S. Arnold, Opt. Commun. 31, 1 (1979).
[CrossRef]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. E 45, 8185 (1992).

Arnold, S.

B. A. Garetz and S. Arnold, Opt. Commun. 31, 1 (1979).
[CrossRef]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. E 45, 8185 (1992).

Berry, M. V.

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

Biener, G.

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

Bliokh, K. Y.

K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 030404 (2008).
[CrossRef] [PubMed]

Garetz, B. A.

B. A. Garetz and S. Arnold, Opt. Commun. 31, 1 (1979).
[CrossRef]

Gorodetski, Y.

K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 030404 (2008).
[CrossRef] [PubMed]

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008).
[CrossRef] [PubMed]

Hasman, E.

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008).
[CrossRef] [PubMed]

K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 030404 (2008).
[CrossRef] [PubMed]

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

Kleiner, V.

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008).
[CrossRef] [PubMed]

K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 030404 (2008).
[CrossRef] [PubMed]

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

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef] [PubMed]

Marrucci, L.

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef] [PubMed]

Murakami, S.

M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef] [PubMed]

Nagaosa, N.

M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef] [PubMed]

Niv, A.

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008).
[CrossRef] [PubMed]

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

Onoda, M.

M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef] [PubMed]

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef] [PubMed]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. E 45, 8185 (1992).

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. E 45, 8185 (1992).

Opt. Commun. (2)

B. A. Garetz and S. Arnold, Opt. Commun. 31, 1 (1979).
[CrossRef]

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

Phys. Rev. E (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. E 45, 8185 (1992).

Phys. Rev. Lett. (4)

K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 030404 (2008).
[CrossRef] [PubMed]

M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef] [PubMed]

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008).
[CrossRef] [PubMed]

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef] [PubMed]

Proc. R. Soc. London, Ser. A (1)

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

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Figures (3)

Fig. 1
Fig. 1

Illustration of the rotational Doppler effect on a circularly polarized laser beam at frequency ω incident upon a π-retardation waveplate rotating at frequency Ω.

Fig. 2
Fig. 2

Schematic illustration of the experiment.

Fig. 3
Fig. 3

Upper row shows the captured intensity distributions for different illumination helicities (circular polarized light: left-handed, σ = 1 ; right-handed, σ = + 1 ). The lower row shows experimental (crosses) and predicted (solid curve) typical cross sections.

Equations (4)

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Δ ω = 2 σ Ω .
ϕ PB = 2 σ Ω d ξ ,
θ = m ϑ 2 ,
ϕ PB = σ m ϑ .

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