Abstract

The longitudinal and transverse beam shifts, namely, the Goos–Hänchen (GH) and the Spin-Hall (SH) shifts are usually observed at planar interfaces. It has recently been shown that the transverse SH shift may also arise due to scattering of plane waves. Here, we show that analogous in-plane (longitudinal) shifts also exist in the scattering of plane waves from micro/nano systems. We study both the GH and the SH shifts in plasmonic metal nanoparticles/nanostructures and dielectric micro-particles employing a unified framework that utilizes the transverse components of the Poynting vector of the scattered wave. The results demonstrate that the interference of neighboring resonance modes in plasmonic nanostructures (e.g., electric dipolar and quadrupolar modes in metal spheres) leads to great enhancement of the GH shift in scattering from such systems. We also unravel interesting correlations between these shifts with the polarimetry parameters, diattenuation and retardance.

© 2014 Optical Society of America

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References

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  1. F. Goos and H. Hänchen, Ann. Phys. 436, 333 (1947).
    [CrossRef]
  2. F. I. Fedorov, Dokl. Akad. Nauk SSSR 105, 465 (1955).
  3. C. Imbert, Phys. Rev. D 5, 787 (1972).
    [CrossRef]
  4. K. Y. Bliokh and A. Aiello, J. Opt. 15, 014001 (2013).
    [CrossRef]
  5. J. B. Gotte and M. R. Dennis, New J. Phys. 14, 073016 (2012).
    [CrossRef]
  6. M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photonics 3, 337 (2009).
    [CrossRef]
  7. D. Golla and S. D. Gupta, Pramana-J. Phys. 76, 603 (2011).
  8. O. Hosten and P. Kwiat, Science 319, 787 (2008).
    [CrossRef]
  9. K. Y. Bliokh, I. V. Shadrivov, and Y. S. Kivshar, Opt. Lett. 34, 389 (2009).
    [CrossRef]
  10. A. Aiello and J. P. Woerdman, Opt. Lett. 33, 1437 (2008).
    [CrossRef]
  11. K. Y. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
    [CrossRef]
  12. K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 030404 (2008).
    [CrossRef]
  13. A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 103, 100401 (2009).
    [CrossRef]
  14. D. Haefner, S. Sukhov, and A. Dogariu, Phys. Rev. Lett. 102, 123903 (2009).
    [CrossRef]
  15. J. Soni, S. Ghosh, S. Mansha, A. Kumar, S. Dutta Gupta, A. Banerjee, and N. Ghosh, Opt. Lett. 38, 1748 (2013).
    [CrossRef]
  16. J. Soni, H. Purwar, and N. Ghosh, Opt. Commun. 285, 1599 (2012).
    [CrossRef]
  17. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  18. H. F. Arnoldus, X. Li, and J. Shu, Opt. Lett. 33, 1446 (2008).
    [CrossRef]
  19. J. Shu, X. Li, and H. F. Arnoldus, J. Opt. Soc. Am. A 26, 395 (2009).
    [CrossRef]
  20. A. M. Stefan, Plasmonics: Fundamentals and Applications (Springer, 2007).
  21. M. Kumari and S. Dutta Gupta, Opt. Commun. 285, 617 (2012).
    [CrossRef]
  22. C. Schwartz and A. Dogariu, Opt. Express 14, 8425 (2006).
    [CrossRef]

2013

2012

J. B. Gotte and M. R. Dennis, New J. Phys. 14, 073016 (2012).
[CrossRef]

J. Soni, H. Purwar, and N. Ghosh, Opt. Commun. 285, 1599 (2012).
[CrossRef]

M. Kumari and S. Dutta Gupta, Opt. Commun. 285, 617 (2012).
[CrossRef]

2011

D. Golla and S. D. Gupta, Pramana-J. Phys. 76, 603 (2011).

2009

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photonics 3, 337 (2009).
[CrossRef]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 103, 100401 (2009).
[CrossRef]

D. Haefner, S. Sukhov, and A. Dogariu, Phys. Rev. Lett. 102, 123903 (2009).
[CrossRef]

J. Shu, X. Li, and H. F. Arnoldus, J. Opt. Soc. Am. A 26, 395 (2009).
[CrossRef]

K. Y. Bliokh, I. V. Shadrivov, and Y. S. Kivshar, Opt. Lett. 34, 389 (2009).
[CrossRef]

2008

A. Aiello and J. P. Woerdman, Opt. Lett. 33, 1437 (2008).
[CrossRef]

H. F. Arnoldus, X. Li, and J. Shu, Opt. Lett. 33, 1446 (2008).
[CrossRef]

O. Hosten and P. Kwiat, Science 319, 787 (2008).
[CrossRef]

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

2006

K. Y. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef]

C. Schwartz and A. Dogariu, Opt. Express 14, 8425 (2006).
[CrossRef]

1972

C. Imbert, Phys. Rev. D 5, 787 (1972).
[CrossRef]

1955

F. I. Fedorov, Dokl. Akad. Nauk SSSR 105, 465 (1955).

1947

F. Goos and H. Hänchen, Ann. Phys. 436, 333 (1947).
[CrossRef]

Aiello, A.

K. Y. Bliokh and A. Aiello, J. Opt. 15, 014001 (2013).
[CrossRef]

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photonics 3, 337 (2009).
[CrossRef]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 103, 100401 (2009).
[CrossRef]

A. Aiello and J. P. Woerdman, Opt. Lett. 33, 1437 (2008).
[CrossRef]

Arnoldus, H. F.

Banerjee, A.

Bliokh, K. Y.

K. Y. Bliokh and A. Aiello, J. Opt. 15, 014001 (2013).
[CrossRef]

K. Y. Bliokh, I. V. Shadrivov, and Y. S. Kivshar, Opt. Lett. 34, 389 (2009).
[CrossRef]

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

K. Y. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef]

Bliokh, Y. P.

K. Y. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Dennis, M. R.

J. B. Gotte and M. R. Dennis, New J. Phys. 14, 073016 (2012).
[CrossRef]

Dogariu, A.

D. Haefner, S. Sukhov, and A. Dogariu, Phys. Rev. Lett. 102, 123903 (2009).
[CrossRef]

C. Schwartz and A. Dogariu, Opt. Express 14, 8425 (2006).
[CrossRef]

Dutta Gupta, S.

Fedorov, F. I.

F. I. Fedorov, Dokl. Akad. Nauk SSSR 105, 465 (1955).

Ghosh, N.

Ghosh, S.

Golla, D.

D. Golla and S. D. Gupta, Pramana-J. Phys. 76, 603 (2011).

Goos, F.

F. Goos and H. Hänchen, Ann. Phys. 436, 333 (1947).
[CrossRef]

Gorodetski, Y.

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

Gotte, J. B.

J. B. Gotte and M. R. Dennis, New J. Phys. 14, 073016 (2012).
[CrossRef]

Gupta, S. D.

D. Golla and S. D. Gupta, Pramana-J. Phys. 76, 603 (2011).

Haefner, D.

D. Haefner, S. Sukhov, and A. Dogariu, Phys. Rev. Lett. 102, 123903 (2009).
[CrossRef]

Hänchen, H.

F. Goos and H. Hänchen, Ann. Phys. 436, 333 (1947).
[CrossRef]

Hasman, E.

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

Hosten, O.

O. Hosten and P. Kwiat, Science 319, 787 (2008).
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Imbert, C.

C. Imbert, Phys. Rev. D 5, 787 (1972).
[CrossRef]

Kivshar, Y. S.

Kleiner, V.

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

Kumar, A.

Kumari, M.

M. Kumari and S. Dutta Gupta, Opt. Commun. 285, 617 (2012).
[CrossRef]

Kwiat, P.

O. Hosten and P. Kwiat, Science 319, 787 (2008).
[CrossRef]

Leuchs, G.

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 103, 100401 (2009).
[CrossRef]

Li, X.

Lindlein, N.

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 103, 100401 (2009).
[CrossRef]

Mansha, S.

Marquardt, C.

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 103, 100401 (2009).
[CrossRef]

Merano, M.

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photonics 3, 337 (2009).
[CrossRef]

Purwar, H.

J. Soni, H. Purwar, and N. Ghosh, Opt. Commun. 285, 1599 (2012).
[CrossRef]

Schwartz, C.

Shadrivov, I. V.

Shu, J.

Soni, J.

Stefan, A. M.

A. M. Stefan, Plasmonics: Fundamentals and Applications (Springer, 2007).

Sukhov, S.

D. Haefner, S. Sukhov, and A. Dogariu, Phys. Rev. Lett. 102, 123903 (2009).
[CrossRef]

van Exter, M. P.

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photonics 3, 337 (2009).
[CrossRef]

Woerdman, J. P.

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photonics 3, 337 (2009).
[CrossRef]

A. Aiello and J. P. Woerdman, Opt. Lett. 33, 1437 (2008).
[CrossRef]

Ann. Phys.

F. Goos and H. Hänchen, Ann. Phys. 436, 333 (1947).
[CrossRef]

Dokl. Akad. Nauk SSSR

F. I. Fedorov, Dokl. Akad. Nauk SSSR 105, 465 (1955).

J. Opt.

K. Y. Bliokh and A. Aiello, J. Opt. 15, 014001 (2013).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Photonics

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photonics 3, 337 (2009).
[CrossRef]

New J. Phys.

J. B. Gotte and M. R. Dennis, New J. Phys. 14, 073016 (2012).
[CrossRef]

Opt. Commun.

J. Soni, H. Purwar, and N. Ghosh, Opt. Commun. 285, 1599 (2012).
[CrossRef]

M. Kumari and S. Dutta Gupta, Opt. Commun. 285, 617 (2012).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. D

C. Imbert, Phys. Rev. D 5, 787 (1972).
[CrossRef]

Phys. Rev. Lett.

K. Y. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef]

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

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 103, 100401 (2009).
[CrossRef]

D. Haefner, S. Sukhov, and A. Dogariu, Phys. Rev. Lett. 102, 123903 (2009).
[CrossRef]

Pramana-J. Phys.

D. Golla and S. D. Gupta, Pramana-J. Phys. 76, 603 (2011).

Science

O. Hosten and P. Kwiat, Science 319, 787 (2008).
[CrossRef]

Other

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

A. M. Stefan, Plasmonics: Fundamentals and Applications (Springer, 2007).

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Figures (3)

Fig. 1.
Fig. 1.

(a) Scattering angle θ dependence of the computed GH shift Δ GH for Ag nanosphere ( a = 50 nm ), at two wavelengths, λ = 380 nm (red solid line), 430 nm (black-dotted line). The shifts are shown for incident X -polarized light ( | H state) in the scattering plane ϕ = 0 . The inset shows the corresponding shifts for incident Y -polarized light ( | V state). (b) The wavelength dependence of the strength of the interference of the dipolar a 1 and the quadrupolar a 2 plasmon modes ( Re ( a 2 * a 1 ) ) (blue-dotted line, left axis) and the corresponding phase difference (in radian) between them (red solid line, right axis). The inset shows the variation of retardance parameter of scattering δ (in radian) as a function of θ at two wavelengths, λ = 380 and 430 nm for the same Ag nanosphere.

Fig. 2.
Fig. 2.

(a) Computed SH shift Δ SH as a function of θ for the same 50 nm Ag nanosphere of Fig. 1, for two wavelengths, λ = 380 nm (red solid line) and 430 nm (black-dotted line). (b) The angular variation of diattenuation d for the Ag nanosphere, at λ = 380 nm (red solid line) and 430 nm (black-dotted line).

Fig. 3.
Fig. 3.

(a) Computed GH shift Δ GH as a function of θ for a dielectric microsphere ( a = 1 μm , refractive refractive index = 1.6 , λ = 632.8 nm ). (b) The angular variation of retardance δ (in radians) for the same dielectric scatterer.

Equations (7)

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Δ⃗ GH = lim r r ( P θ θ ^ | P r | ) ,
Δ GH = 1 k ( | Im ( S 2 * [ n = 1 ( 2 n + 1 ) a n π n ] cos 2 φ S 1 [ n = 1 ( 2 n + 1 ) b n π n ] * sin 2 φ ) | | S 1 | 2 sin 2 φ + | S 2 | 2 cos 2 φ ) sin θ .
S 1 = n = 1 ( 2 n + 1 ) n ( n + 1 ) ( a n π n + b n τ n ) , S 2 = n = 1 ( 2 n + 1 ) n ( n + 1 ) ( a n τ n + b n π n ) .
Δ⃗ SH = lim r r ( P ϕ ϕ ^ ) | P r | ) ,
Δ SH = σ k ( | Re ( S 1 * [ n = 1 ( 2 n + 1 ) a n π n ] + S 2 [ n = 1 ( 2 n + 1 ) b n π n ] * ) | | S 1 | 2 + | S 2 | 2 ) sin θ ,
δ ( θ ) = tan 1 [ Im ( S 2 * ( θ ) S 1 ( θ ) ) Re ( S 2 * ( θ ) S 1 ( θ ) ) ] .
d ( θ ) = { | S 2 ( θ ) | 2 cos 2 θ | S 1 ( θ ) | 2 | S 2 ( θ ) | 2 cos 2 θ + | S 1 ( θ ) | 2 } .

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