Abstract

We study the spiral spectra scattered off transparent dielectric spheres when probed by different Laguerre–Gaussian light beams, carrying nested topological wavefront dislocations. We show that such scattering data may be employed to determine geometrical properties of the spheres, such as their position. The technique is a generalization of standard Mie scattering, and it can be extended to study and to characterize nanospheres.

© 2012 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. A 45, 8185 (1992).
    [CrossRef]
  2. L. Torner, J. P. Torres, and S. Carrasco, Opt. Express 13, 873 (2005).
    [CrossRef]
  3. G. Molina-Terriza, L. Rebane, J. P. Torres, L. Torner, and S. Carrasco, J. Eur. Opt. Soc. 2, 07014 (2007).
    [CrossRef]
  4. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  5. G. Gouesbet, J. Quant. Spectrosc. Radiat. Transfer 110, 1223 (2009).
    [CrossRef]
  6. A. S. van de Nes and P. Torok, Opt. Express 15, 13360 (2007).
    [CrossRef]
  7. V. Garbin, G. Volpe, E. Ferrari, M. Versluis, D. Cojoc, and D. Petrov, New J. Phys. 11, 013046 (2009).
    [CrossRef]
  8. Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, Phys. Rev. Lett. 99, 073901 (2007).
    [CrossRef]
  9. G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2002).
    [CrossRef]
  10. J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
    [CrossRef]
  11. M. V. Vasnetsov, J. P. Torres, D. V. Petrov, and L. Torner, Opt. Lett. 28, 2285 (2003).
    [CrossRef]
  12. R. Zambrini and S. M. Barnett, Phys. Rev. Lett. 96, 113901 (2006).
    [CrossRef]
  13. C.-S. Guo, S.-J. Yue, and G.-X. Wei, Appl. Phys. Lett. 94, 231104 (2009).
    [CrossRef]
  14. G. C. G. Berkhout and M. W. Beijersbergen, Phys. Rev. Lett. 101, 100801 (2008).
    [CrossRef]
  15. I. K. Ludlow and J. Everitt, J. Opt. Soc. Am. A 17, 2229 (2000).
    [CrossRef]
  16. J. S. Jaffe, Opt. Express 15, 12217 (2007).
    [CrossRef]
  17. G. Molina-Terriza, Phys. Rev. A 78, 053819 (2008).
    [CrossRef]

2009 (3)

G. Gouesbet, J. Quant. Spectrosc. Radiat. Transfer 110, 1223 (2009).
[CrossRef]

V. Garbin, G. Volpe, E. Ferrari, M. Versluis, D. Cojoc, and D. Petrov, New J. Phys. 11, 013046 (2009).
[CrossRef]

C.-S. Guo, S.-J. Yue, and G.-X. Wei, Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

2008 (2)

G. C. G. Berkhout and M. W. Beijersbergen, Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef]

G. Molina-Terriza, Phys. Rev. A 78, 053819 (2008).
[CrossRef]

2007 (4)

J. S. Jaffe, Opt. Express 15, 12217 (2007).
[CrossRef]

G. Molina-Terriza, L. Rebane, J. P. Torres, L. Torner, and S. Carrasco, J. Eur. Opt. Soc. 2, 07014 (2007).
[CrossRef]

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, Phys. Rev. Lett. 99, 073901 (2007).
[CrossRef]

A. S. van de Nes and P. Torok, Opt. Express 15, 13360 (2007).
[CrossRef]

2006 (1)

R. Zambrini and S. M. Barnett, Phys. Rev. Lett. 96, 113901 (2006).
[CrossRef]

2005 (1)

2003 (1)

2002 (2)

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2002).
[CrossRef]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

2000 (1)

1992 (1)

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

Allen, L.

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

Barnett, S. M.

R. Zambrini and S. M. Barnett, Phys. Rev. Lett. 96, 113901 (2006).
[CrossRef]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

Beijersbergen, M. W.

G. C. G. Berkhout and M. W. Beijersbergen, Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef]

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

Berkhout, G. C. G.

G. C. G. Berkhout and M. W. Beijersbergen, Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef]

Bohren, C. F.

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

Carrasco, S.

G. Molina-Terriza, L. Rebane, J. P. Torres, L. Torner, and S. Carrasco, J. Eur. Opt. Soc. 2, 07014 (2007).
[CrossRef]

L. Torner, J. P. Torres, and S. Carrasco, Opt. Express 13, 873 (2005).
[CrossRef]

Chiu, D. T.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, Phys. Rev. Lett. 99, 073901 (2007).
[CrossRef]

Cojoc, D.

V. Garbin, G. Volpe, E. Ferrari, M. Versluis, D. Cojoc, and D. Petrov, New J. Phys. 11, 013046 (2009).
[CrossRef]

Courtial, J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

Edgar, J. S.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, Phys. Rev. Lett. 99, 073901 (2007).
[CrossRef]

Everitt, J.

Ferrari, E.

V. Garbin, G. Volpe, E. Ferrari, M. Versluis, D. Cojoc, and D. Petrov, New J. Phys. 11, 013046 (2009).
[CrossRef]

Franke-Arnold, S.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

Garbin, V.

V. Garbin, G. Volpe, E. Ferrari, M. Versluis, D. Cojoc, and D. Petrov, New J. Phys. 11, 013046 (2009).
[CrossRef]

Gouesbet, G.

G. Gouesbet, J. Quant. Spectrosc. Radiat. Transfer 110, 1223 (2009).
[CrossRef]

Guo, C.-S.

C.-S. Guo, S.-J. Yue, and G.-X. Wei, Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

Huffman, D. R.

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

Jaffe, J. S.

Jeffries, G. D. M.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, Phys. Rev. Lett. 99, 073901 (2007).
[CrossRef]

Leach, J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

Ludlow, I. K.

McGloin, D.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, Phys. Rev. Lett. 99, 073901 (2007).
[CrossRef]

Molina-Terriza, G.

G. Molina-Terriza, Phys. Rev. A 78, 053819 (2008).
[CrossRef]

G. Molina-Terriza, L. Rebane, J. P. Torres, L. Torner, and S. Carrasco, J. Eur. Opt. Soc. 2, 07014 (2007).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2002).
[CrossRef]

Padgett, M. J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

Petrov, D.

V. Garbin, G. Volpe, E. Ferrari, M. Versluis, D. Cojoc, and D. Petrov, New J. Phys. 11, 013046 (2009).
[CrossRef]

Petrov, D. V.

Rebane, L.

G. Molina-Terriza, L. Rebane, J. P. Torres, L. Torner, and S. Carrasco, J. Eur. Opt. Soc. 2, 07014 (2007).
[CrossRef]

Spreeuw, R. J. C.

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

Torner, L.

G. Molina-Terriza, L. Rebane, J. P. Torres, L. Torner, and S. Carrasco, J. Eur. Opt. Soc. 2, 07014 (2007).
[CrossRef]

L. Torner, J. P. Torres, and S. Carrasco, Opt. Express 13, 873 (2005).
[CrossRef]

M. V. Vasnetsov, J. P. Torres, D. V. Petrov, and L. Torner, Opt. Lett. 28, 2285 (2003).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2002).
[CrossRef]

Torok, P.

Torres, J. P.

G. Molina-Terriza, L. Rebane, J. P. Torres, L. Torner, and S. Carrasco, J. Eur. Opt. Soc. 2, 07014 (2007).
[CrossRef]

L. Torner, J. P. Torres, and S. Carrasco, Opt. Express 13, 873 (2005).
[CrossRef]

M. V. Vasnetsov, J. P. Torres, D. V. Petrov, and L. Torner, Opt. Lett. 28, 2285 (2003).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2002).
[CrossRef]

van de Nes, A. S.

Vasnetsov, M. V.

Versluis, M.

V. Garbin, G. Volpe, E. Ferrari, M. Versluis, D. Cojoc, and D. Petrov, New J. Phys. 11, 013046 (2009).
[CrossRef]

Volpe, G.

V. Garbin, G. Volpe, E. Ferrari, M. Versluis, D. Cojoc, and D. Petrov, New J. Phys. 11, 013046 (2009).
[CrossRef]

Wei, G.-X.

C.-S. Guo, S.-J. Yue, and G.-X. Wei, Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

Woerdman, J. P.

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

Yue, S.-J.

C.-S. Guo, S.-J. Yue, and G.-X. Wei, Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

Zambrini, R.

R. Zambrini and S. M. Barnett, Phys. Rev. Lett. 96, 113901 (2006).
[CrossRef]

Zhao, Y.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, Phys. Rev. Lett. 99, 073901 (2007).
[CrossRef]

Appl. Phys. Lett. (1)

C.-S. Guo, S.-J. Yue, and G.-X. Wei, Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

J. Eur. Opt. Soc. (1)

G. Molina-Terriza, L. Rebane, J. P. Torres, L. Torner, and S. Carrasco, J. Eur. Opt. Soc. 2, 07014 (2007).
[CrossRef]

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

J. Quant. Spectrosc. Radiat. Transfer (1)

G. Gouesbet, J. Quant. Spectrosc. Radiat. Transfer 110, 1223 (2009).
[CrossRef]

New J. Phys. (1)

V. Garbin, G. Volpe, E. Ferrari, M. Versluis, D. Cojoc, and D. Petrov, New J. Phys. 11, 013046 (2009).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. A (2)

G. Molina-Terriza, Phys. Rev. A 78, 053819 (2008).
[CrossRef]

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

Phys. Rev. Lett. (5)

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, Phys. Rev. Lett. 99, 073901 (2007).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2002).
[CrossRef]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

G. C. G. Berkhout and M. W. Beijersbergen, Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef]

R. Zambrini and S. M. Barnett, Phys. Rev. Lett. 96, 113901 (2006).
[CrossRef]

Other (1)

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

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Figures (3)

Fig. 1.
Fig. 1.

Experimental setup. See text for details.

Fig. 2.
Fig. 2.

Dependence of the spiral spectra in the total scattering field versus the sphere position for three spiral modes m=+1, m=0, and m=1. The sphere diameter is 2 μm in columns (a) and (b) and 1 μm in (c). Solid lines represent linearly polarized Gaussian (a) or LG0,1 (b), (c) input beams. In column (b), the results with linear, left- and right-polarized input beams showed practically the same dependence. All modes normalized to the maximum value of the output mode m=mi.

Fig. 3.
Fig. 3.

Results of numerical simulations of the mode transformation efficiency when the incident wave is the Gaussian beam [(a)] and the LG beam [(b), (c)]. The size of the sphere is 2 μm [(a), (b)] and 1 μm [(c)]. The spiral spectra of the modes transformed due to the Mie scattering are normalized on the maximal value of the spiral spectrum of the incident mode.

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