Abstract

Laguerre–Gaussian beams of integer azimuthal index satisfy the fundamental principle of quantization of orbital angular momentum. Here, we consider light-induced orbiting of a trapped microparticle as a probe of the local orbital angular momentum density in both integer- and fractional-index perfect vortex beams. Simulations suggest that the distribution and the corresponding light-induced motion of the particle may be uniform in beams with integer azimuthal index, but fundamentally this cannot be achieved in beams with fractional index. We experimentally verify these predictions by light-induced trapping and rotation of individual microparticles in fractional index beams where we distribute the phase dislocations around the annular profile.

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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. M. Padgett and R. Bowman, Nat. Photonics 5, 343 (2011).
    [Crossref]
  3. A. S. Ostrovsky, C. Rickenstorff-Parrao, and V. Arrizón, Opt. Lett. 38, 534 (2013).
    [Crossref]
  4. M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, Opt. Lett. 38, 4919 (2013).
    [Crossref]
  5. J. García-García, C. Rickenstorff-Parrao, R. Ramos-García, V. Arrizón, and A. S. Ostrovsky, Opt. Lett. 39, 5305 (2014).
    [Crossref]
  6. R. Paez-Lopez, U. Ruiz, V. Arrizón, and R. Ramos-García, Opt. Lett. 41, 4138 (2016).
    [Crossref]
  7. W. M. Lee, X.-C. Yuan, and K. Dholakia, Opt. Commun. 239, 129 (2004).
    [Crossref]
  8. J. B. Götte, S. Franke-Arnold, R. Zambrini, and S. M. Barnett, J. Mod. Opt. 54, 1723 (2007).
    [Crossref]
  9. M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, Opt. Rev. 22, 162 (2015).
    [Crossref]
  10. N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Lett. 22, 52 (1997).
    [Crossref]
  11. M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Nature 394, 348 (1998).
    [Crossref]
  12. A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601 (2002).
    [Crossref]
  13. V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, Phys. Rev. A 66, 063402 (2002).
    [Crossref]
  14. V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, Phys. Rev. Lett. 91, 093602 (2003).
    [Crossref]
  15. V. Garcés-Chávez, D. McGloin, M. D. Summers, A. Fernandez-Nieves, G. C. Spalding, G. Cristobal, and K. Dholakia, J. Opt. A 6, S235 (2004).
    [Crossref]
  16. K. T. Gahagan and G. A. Swartzlander, Opt. Lett. 21, 827 (1996).
    [Crossref]
  17. J. E. Curtis and D. G. Grier, Phys. Rev. Lett. 90, 133901 (2003).
    [Crossref]
  18. T. Čižmár, M. Mazilu, and K. Dholakia, Nat. Photonics 4, 338 (2010).
    [Crossref]
  19. G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
    [Crossref]
  20. A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, Adv. Opt. Photon. 7, 66 (2015).
    [Crossref]
  21. G. Tkachenko, M. Chen, K. Dholakia, and M. Mazilu, University of St. Andrews (2017), http://dx.doi.org/10.17630/49bd9620-2d38-4a50-a950-591b5a3fb578 .

2016 (1)

2015 (2)

2014 (1)

2013 (2)

2011 (1)

M. Padgett and R. Bowman, Nat. Photonics 5, 343 (2011).
[Crossref]

2010 (1)

T. Čižmár, M. Mazilu, and K. Dholakia, Nat. Photonics 4, 338 (2010).
[Crossref]

2007 (2)

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[Crossref]

J. B. Götte, S. Franke-Arnold, R. Zambrini, and S. M. Barnett, J. Mod. Opt. 54, 1723 (2007).
[Crossref]

2004 (2)

W. M. Lee, X.-C. Yuan, and K. Dholakia, Opt. Commun. 239, 129 (2004).
[Crossref]

V. Garcés-Chávez, D. McGloin, M. D. Summers, A. Fernandez-Nieves, G. C. Spalding, G. Cristobal, and K. Dholakia, J. Opt. A 6, S235 (2004).
[Crossref]

2003 (2)

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, Phys. Rev. Lett. 91, 093602 (2003).
[Crossref]

J. E. Curtis and D. G. Grier, Phys. Rev. Lett. 90, 133901 (2003).
[Crossref]

2002 (2)

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601 (2002).
[Crossref]

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, Phys. Rev. A 66, 063402 (2002).
[Crossref]

1998 (1)

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Nature 394, 348 (1998).
[Crossref]

1997 (1)

1996 (1)

1992 (1)

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

Ahmed, N.

Allen, L.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601 (2002).
[Crossref]

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Lett. 22, 52 (1997).
[Crossref]

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

Arita, Y.

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, Opt. Rev. 22, 162 (2015).
[Crossref]

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, Opt. Lett. 38, 4919 (2013).
[Crossref]

Arrizón, V.

Ashrafi, N.

Ashrafi, S.

Bao, C.

Barnett, S. M.

J. B. Götte, S. Franke-Arnold, R. Zambrini, and S. M. Barnett, J. Mod. Opt. 54, 1723 (2007).
[Crossref]

Beijersbergen, M. W.

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

Bowman, R.

M. Padgett and R. Bowman, Nat. Photonics 5, 343 (2011).
[Crossref]

Cao, Y.

Chávez-Cerda, S.

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, Phys. Rev. A 66, 063402 (2002).
[Crossref]

Chen, M.

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, Opt. Rev. 22, 162 (2015).
[Crossref]

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, Opt. Lett. 38, 4919 (2013).
[Crossref]

Cižmár, T.

T. Čižmár, M. Mazilu, and K. Dholakia, Nat. Photonics 4, 338 (2010).
[Crossref]

Cristobal, G.

V. Garcés-Chávez, D. McGloin, M. D. Summers, A. Fernandez-Nieves, G. C. Spalding, G. Cristobal, and K. Dholakia, J. Opt. A 6, S235 (2004).
[Crossref]

Curtis, J. E.

J. E. Curtis and D. G. Grier, Phys. Rev. Lett. 90, 133901 (2003).
[Crossref]

Dholakia, K.

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, Opt. Rev. 22, 162 (2015).
[Crossref]

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, Opt. Lett. 38, 4919 (2013).
[Crossref]

T. Čižmár, M. Mazilu, and K. Dholakia, Nat. Photonics 4, 338 (2010).
[Crossref]

V. Garcés-Chávez, D. McGloin, M. D. Summers, A. Fernandez-Nieves, G. C. Spalding, G. Cristobal, and K. Dholakia, J. Opt. A 6, S235 (2004).
[Crossref]

W. M. Lee, X.-C. Yuan, and K. Dholakia, Opt. Commun. 239, 129 (2004).
[Crossref]

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, Phys. Rev. Lett. 91, 093602 (2003).
[Crossref]

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, Phys. Rev. A 66, 063402 (2002).
[Crossref]

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Lett. 22, 52 (1997).
[Crossref]

Dultz, W.

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, Phys. Rev. Lett. 91, 093602 (2003).
[Crossref]

Fernandez-Nieves, A.

V. Garcés-Chávez, D. McGloin, M. D. Summers, A. Fernandez-Nieves, G. C. Spalding, G. Cristobal, and K. Dholakia, J. Opt. A 6, S235 (2004).
[Crossref]

Franke-Arnold, S.

J. B. Götte, S. Franke-Arnold, R. Zambrini, and S. M. Barnett, J. Mod. Opt. 54, 1723 (2007).
[Crossref]

Friese, M. E. J.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Nature 394, 348 (1998).
[Crossref]

Gahagan, K. T.

Garcés-Chávez, V.

V. Garcés-Chávez, D. McGloin, M. D. Summers, A. Fernandez-Nieves, G. C. Spalding, G. Cristobal, and K. Dholakia, J. Opt. A 6, S235 (2004).
[Crossref]

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, Phys. Rev. Lett. 91, 093602 (2003).
[Crossref]

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, Phys. Rev. A 66, 063402 (2002).
[Crossref]

García-García, J.

Götte, J. B.

J. B. Götte, S. Franke-Arnold, R. Zambrini, and S. M. Barnett, J. Mod. Opt. 54, 1723 (2007).
[Crossref]

Grier, D. G.

J. E. Curtis and D. G. Grier, Phys. Rev. Lett. 90, 133901 (2003).
[Crossref]

Heckenberg, N. R.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Nature 394, 348 (1998).
[Crossref]

Huang, H.

Lavery, M. P. J.

Lee, W. M.

W. M. Lee, X.-C. Yuan, and K. Dholakia, Opt. Commun. 239, 129 (2004).
[Crossref]

Li, L.

MacVicar, I.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601 (2002).
[Crossref]

Mazilu, M.

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, Opt. Rev. 22, 162 (2015).
[Crossref]

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, Opt. Lett. 38, 4919 (2013).
[Crossref]

T. Čižmár, M. Mazilu, and K. Dholakia, Nat. Photonics 4, 338 (2010).
[Crossref]

McGloin, D.

V. Garcés-Chávez, D. McGloin, M. D. Summers, A. Fernandez-Nieves, G. C. Spalding, G. Cristobal, and K. Dholakia, J. Opt. A 6, S235 (2004).
[Crossref]

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, Phys. Rev. Lett. 91, 093602 (2003).
[Crossref]

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[Crossref]

Molisch, A. F.

Nieminen, T. A.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Nature 394, 348 (1998).
[Crossref]

O’Neil, A. T.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601 (2002).
[Crossref]

Ostrovsky, A. S.

Padgett, M.

M. Padgett and R. Bowman, Nat. Photonics 5, 343 (2011).
[Crossref]

Padgett, M. J.

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, Phys. Rev. Lett. 91, 093602 (2003).
[Crossref]

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601 (2002).
[Crossref]

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Lett. 22, 52 (1997).
[Crossref]

Paez-Lopez, R.

Ramachandran, S.

Ramos-García, R.

Ren, Y.

Rickenstorff-Parrao, C.

Rubinsztein-Dunlop, H.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Nature 394, 348 (1998).
[Crossref]

Ruiz, U.

Schmitzer, H.

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, Phys. Rev. Lett. 91, 093602 (2003).
[Crossref]

Sibbett, W.

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, Phys. Rev. A 66, 063402 (2002).
[Crossref]

Simpson, N. B.

Spalding, G. C.

V. Garcés-Chávez, D. McGloin, M. D. Summers, A. Fernandez-Nieves, G. C. Spalding, G. Cristobal, and K. Dholakia, J. Opt. A 6, S235 (2004).
[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]

Summers, M. D.

V. Garcés-Chávez, D. McGloin, M. D. Summers, A. Fernandez-Nieves, G. C. Spalding, G. Cristobal, and K. Dholakia, J. Opt. A 6, S235 (2004).
[Crossref]

Swartzlander, G. A.

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[Crossref]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[Crossref]

Tur, M.

Volke-Sepulveda, K.

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, Phys. Rev. A 66, 063402 (2002).
[Crossref]

Wang, J.

Willner, A. E.

Woerdman, J. P.

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

Wright, E. M.

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, Opt. Rev. 22, 162 (2015).
[Crossref]

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, Opt. Lett. 38, 4919 (2013).
[Crossref]

Xie, G.

Yan, Y.

Yuan, X.-C.

W. M. Lee, X.-C. Yuan, and K. Dholakia, Opt. Commun. 239, 129 (2004).
[Crossref]

Zambrini, R.

J. B. Götte, S. Franke-Arnold, R. Zambrini, and S. M. Barnett, J. Mod. Opt. 54, 1723 (2007).
[Crossref]

Zhao, Z.

Adv. Opt. Photon. (1)

J. Mod. Opt. (1)

J. B. Götte, S. Franke-Arnold, R. Zambrini, and S. M. Barnett, J. Mod. Opt. 54, 1723 (2007).
[Crossref]

J. Opt. A (1)

V. Garcés-Chávez, D. McGloin, M. D. Summers, A. Fernandez-Nieves, G. C. Spalding, G. Cristobal, and K. Dholakia, J. Opt. A 6, S235 (2004).
[Crossref]

Nat. Photonics (2)

T. Čižmár, M. Mazilu, and K. Dholakia, Nat. Photonics 4, 338 (2010).
[Crossref]

M. Padgett and R. Bowman, Nat. Photonics 5, 343 (2011).
[Crossref]

Nat. Phys. (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[Crossref]

Nature (1)

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Nature 394, 348 (1998).
[Crossref]

Opt. Commun. (1)

W. M. Lee, X.-C. Yuan, and K. Dholakia, Opt. Commun. 239, 129 (2004).
[Crossref]

Opt. Lett. (6)

Opt. Rev. (1)

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, Opt. Rev. 22, 162 (2015).
[Crossref]

Phys. Rev. A (2)

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

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, Phys. Rev. A 66, 063402 (2002).
[Crossref]

Phys. Rev. Lett. (3)

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, Phys. Rev. Lett. 91, 093602 (2003).
[Crossref]

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601 (2002).
[Crossref]

J. E. Curtis and D. G. Grier, Phys. Rev. Lett. 90, 133901 (2003).
[Crossref]

Other (1)

G. Tkachenko, M. Chen, K. Dholakia, and M. Mazilu, University of St. Andrews (2017), http://dx.doi.org/10.17630/49bd9620-2d38-4a50-a950-591b5a3fb578 .

Supplementary Material (1)

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Figures (5)

Fig. 1.
Fig. 1.

Sketch of the experimental setup. (a) Measured intensity profile of the incident annular beam. (b) Phase mask on the SLM, corresponding to =17.5 with N=2 distributed phase dislocations. (c)–(d) Simulated intensity profiles of the light sent to the zeroth and first diffraction orders. (e) Simulated intensity profile in the focal plane of lens L3, where the dark spots, D1 and D2, correspond to the above dislocations on the SLM. (f) Typical image of a bead and the PV ring. Scale bar is 10 μm.

Fig. 2.
Fig. 2.

(a)–(d) Experimental PV rings without intensity correction. (e)–(h) Intensity distribution along the azimuthal coordinate, θ: measured without correction (red markers); measured after intensity correction (blue markers); simulated (solid line). (i)–(l) Simulated decomposition of a fractional vortex beam into LG eigenmodes.

Fig. 3.
Fig. 3.

Numerically simulated nonuniformity of the local OAM, L, in a PV beam. ΔL is the normalized standard deviation of L as a function of (a) the azimuthal index, , in the case of three distributed phase dislocations, N=3, (b) the number of phase dislocations, N, for a fixed azimuthal index =17.5, and (c)  for a different number of phase dislocations, N.

Fig. 4.
Fig. 4.

Measured local OAM, L(θ), of a trapped microparticle driven by an intensity-corrected PV beam (a) with =17 and (b) with =17.5 and N=3 phase dislocations. Markers, experimental data; gray areas, standard deviation ranges (2ΔL).

Fig. 5.
Fig. 5.

Experimental probing of the local OAM density in integer and fractional PV beams. Standard deviation of the OAM of an optically rotated particle is plotted as a function of (a) the azimuthal index, , (b) the number of phase dislocations, N. (c) Full data set for one particle.

Equations (1)

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ϕ(,θ)=intθ+(int)[θmod(2π/N)],

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