Abstract

We analyze microparticle dynamics within a “perfect” vortex beam. In contrast to other vortex fields, for any given integer value of the topological charge, a “perfect” vortex beam has the same annular intensity profile with fixed radius of peak intensity. For a given topological charge, the field possesses a well-defined orbital angular momentum density at each point in space, invariant with respect to azimuthal position. We experimentally create a perfect vortex and correct the field in situ, to trap and set in motion trapped microscopic particles. For a given topological charge, a single trapped particle exhibits the same local angular velocity moving in such a field independent of its azimuthal position. We also investigate particle dynamics in “perfect” vortex beams of fractional topological charge. This light field may be applied for novel studies in optical trapping of particles, atoms, and quantum gases.

© 2013 Optical Society of America

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References

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

2013

2011

P. Öhberg, J. Opt. 13, 064024 (2011).
[CrossRef]

J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, Rev. Mod. Phys. 83, 1523 (2011).
[CrossRef]

2010

2008

2007

C. Ryu, M. F. Andersen, P. Cladé, V. Natarajan, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 99, 260401 (2007).
[CrossRef]

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

2006

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

S. H. Tao, X.-C. Yuan, J. Lin, and Y. Y. Sun, J. Appl. Phys. 100, 043105 (2006).
[CrossRef]

2005

2004

J. Leach, E. Yao, and M. J. Padgett, New J. Phys. 6, 71 (2004).
[CrossRef]

2003

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

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, S82 (2002).
[CrossRef]

2001

J. Arlt, R. Kuhn, and K. Dholakia, J. Mod. Opt. 48, 783 (2001).

1998

I. Manek, Y. B. Ovchinnikov, and R. Grimm, Opt. Commun. 147, 67 (1998).
[CrossRef]

P. Thévenaz, U. Ruttimann, and M. Unser, IEEE Trans. Image Process. 7, 27 (1998).
[CrossRef]

1996

N. B. Simpson, L. Allen, and M. J. Padgett, J. Mod. Opt. 43, 2485 (1996).
[CrossRef]

1992

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

1983

Allen, L.

N. B. Simpson, L. Allen, and M. J. Padgett, J. Mod. Opt. 43, 2485 (1996).
[CrossRef]

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

Alpmann, C.

Andersen, M. F.

C. Ryu, M. F. Andersen, P. Cladé, V. Natarajan, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 99, 260401 (2007).
[CrossRef]

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

Andrews, L. C.

Arlt, J.

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, S82 (2002).
[CrossRef]

J. Arlt, R. Kuhn, and K. Dholakia, J. Mod. Opt. 48, 783 (2001).

Arrizón, V.

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. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Bouchal, Z.

Bowman, R.

Carruthers, A. E.

Chávez-Cerda, S.

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, S82 (2002).
[CrossRef]

Cižmár, T.

Cladé, P.

C. Ryu, M. F. Andersen, P. Cladé, V. Natarajan, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 99, 260401 (2007).
[CrossRef]

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

Curtis, J. E.

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

Dalibard, J.

J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, Rev. Mod. Phys. 83, 1523 (2011).
[CrossRef]

Denz, C.

Dholakia, K.

T. Čižmár, M. Mazilu, and K. Dholakia, Nat. Photonics 4, 388 (2010).
[CrossRef]

T. Čižmár, V. Kollárová, X. Tsampoula, F. Gunn-Moore, W. Sibbett, Z. Bouchal, and K. Dholakia, Opt. Express 16, 14024 (2008).
[CrossRef]

J. E. Morris, A. E. Carruthers, M. Mazilu, P. J. Reece, T. Čižmár, P. Fischer, and K. Dholakia, Opt. Express 16, 10117 (2008).
[CrossRef]

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

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, S82 (2002).
[CrossRef]

J. Arlt, R. Kuhn, and K. Dholakia, J. Mod. Opt. 48, 783 (2001).

Dultz, W.

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

Fischer, P.

Foreman, B. A.

J.-J. Song, B. A. Foreman, X.-J. Liu, and C. H. Oh, Europhys. Lett. 84, 20012 (2008).
[CrossRef]

Franke-Arnold, S.

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

Garcés-Chávez, V.

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

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, S82 (2002).
[CrossRef]

Gerbier, F.

J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, Rev. Mod. Phys. 83, 1523 (2011).
[CrossRef]

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]

Grimm, R.

I. Manek, Y. B. Ovchinnikov, and R. Grimm, Opt. Commun. 147, 67 (1998).
[CrossRef]

Gunn-Moore, F.

Hanna, S.

Helmerson, K.

C. Ryu, M. F. Andersen, P. Cladé, V. Natarajan, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 99, 260401 (2007).
[CrossRef]

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

Juzeliunas, G.

J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, Rev. Mod. Phys. 83, 1523 (2011).
[CrossRef]

Kollárová, V.

Kuhn, R.

J. Arlt, R. Kuhn, and K. Dholakia, J. Mod. Opt. 48, 783 (2001).

Leach, J.

J. Leach, E. Yao, and M. J. Padgett, New J. Phys. 6, 71 (2004).
[CrossRef]

Lin, J.

S. H. Tao, X.-C. Yuan, J. Lin, and Y. Y. Sun, J. Appl. Phys. 100, 043105 (2006).
[CrossRef]

S. H. Tao, X.-C. Yuan, and J. Lin, Opt. Express 13, 7726 (2005).
[CrossRef]

Liu, X.-J.

J.-J. Song, B. A. Foreman, X.-J. Liu, and C. H. Oh, Europhys. Lett. 84, 20012 (2008).
[CrossRef]

Manek, I.

I. Manek, Y. B. Ovchinnikov, and R. Grimm, Opt. Commun. 147, 67 (1998).
[CrossRef]

Mazilu, M.

McGloin, D.

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

Morris, J. E.

Natarajan, V.

C. Ryu, M. F. Andersen, P. Cladé, V. Natarajan, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 99, 260401 (2007).
[CrossRef]

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

Oh, C. H.

J.-J. Song, B. A. Foreman, X.-J. Liu, and C. H. Oh, Europhys. Lett. 84, 20012 (2008).
[CrossRef]

Öhberg, P.

P. Öhberg, J. Opt. 13, 064024 (2011).
[CrossRef]

J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, Rev. Mod. Phys. 83, 1523 (2011).
[CrossRef]

Ostrovsky, A. S.

Ovchinnikov, Y. B.

I. Manek, Y. B. Ovchinnikov, and R. Grimm, Opt. Commun. 147, 67 (1998).
[CrossRef]

Padgett, M.

Padgett, M. J.

J. Leach, E. Yao, and M. J. Padgett, New J. Phys. 6, 71 (2004).
[CrossRef]

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

N. B. Simpson, L. Allen, and M. J. Padgett, J. Mod. Opt. 43, 2485 (1996).
[CrossRef]

Phillips, R. L.

Phillips, W. D.

C. Ryu, M. F. Andersen, P. Cladé, V. Natarajan, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 99, 260401 (2007).
[CrossRef]

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

Reece, P. J.

Rickenstorff-Parrao, C.

Ruttimann, U.

P. Thévenaz, U. Ruttimann, and M. Unser, IEEE Trans. Image Process. 7, 27 (1998).
[CrossRef]

Ryu, C.

C. Ryu, M. F. Andersen, P. Cladé, V. Natarajan, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 99, 260401 (2007).
[CrossRef]

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

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.

Simpson, N. B.

N. B. Simpson, L. Allen, and M. J. Padgett, J. Mod. Opt. 43, 2485 (1996).
[CrossRef]

Simpson, S. H.

Song, J.-J.

J.-J. Song, B. A. Foreman, X.-J. Liu, and C. H. Oh, Europhys. Lett. 84, 20012 (2008).
[CrossRef]

Spreeuw, R. C.

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

Sun, Y. Y.

S. H. Tao, X.-C. Yuan, J. Lin, and Y. Y. Sun, J. Appl. Phys. 100, 043105 (2006).
[CrossRef]

Tao, S. H.

S. H. Tao, X.-C. Yuan, J. Lin, and Y. Y. Sun, J. Appl. Phys. 100, 043105 (2006).
[CrossRef]

S. H. Tao, X.-C. Yuan, and J. Lin, Opt. Express 13, 7726 (2005).
[CrossRef]

Thévenaz, P.

P. Thévenaz, U. Ruttimann, and M. Unser, IEEE Trans. Image Process. 7, 27 (1998).
[CrossRef]

Tsampoula, X.

Unser, M.

P. Thévenaz, U. Ruttimann, and M. Unser, IEEE Trans. Image Process. 7, 27 (1998).
[CrossRef]

Vaziri, A.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

Volke-Sepulveda, K.

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, S82 (2002).
[CrossRef]

Woerdeman, M.

Woerdman, J. P.

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

Yao, E.

J. Leach, E. Yao, and M. J. Padgett, New J. Phys. 6, 71 (2004).
[CrossRef]

Yuan, X.-C.

S. H. Tao, X.-C. Yuan, J. Lin, and Y. Y. Sun, J. Appl. Phys. 100, 043105 (2006).
[CrossRef]

S. H. Tao, X.-C. Yuan, and J. Lin, Opt. Express 13, 7726 (2005).
[CrossRef]

Zambrini, R.

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

Appl. Opt.

Europhys. Lett.

J.-J. Song, B. A. Foreman, X.-J. Liu, and C. H. Oh, Europhys. Lett. 84, 20012 (2008).
[CrossRef]

IEEE Trans. Image Process.

P. Thévenaz, U. Ruttimann, and M. Unser, IEEE Trans. Image Process. 7, 27 (1998).
[CrossRef]

J. Appl. Phys.

S. H. Tao, X.-C. Yuan, J. Lin, and Y. Y. Sun, J. Appl. Phys. 100, 043105 (2006).
[CrossRef]

J. Mod. Opt.

J. Arlt, R. Kuhn, and K. Dholakia, J. Mod. Opt. 48, 783 (2001).

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

N. B. Simpson, L. Allen, and M. J. Padgett, J. Mod. Opt. 43, 2485 (1996).
[CrossRef]

J. Opt.

P. Öhberg, J. Opt. 13, 064024 (2011).
[CrossRef]

J. Opt. B

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, S82 (2002).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Photonics

T. Čižmár, M. Mazilu, and K. Dholakia, Nat. Photonics 4, 388 (2010).
[CrossRef]

New J. Phys.

J. Leach, E. Yao, and M. J. Padgett, New J. Phys. 6, 71 (2004).
[CrossRef]

Opt. Commun.

I. Manek, Y. B. Ovchinnikov, and R. Grimm, Opt. Commun. 147, 67 (1998).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

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

Phys. Rev. Lett.

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]

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef]

C. Ryu, M. F. Andersen, P. Cladé, V. Natarajan, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 99, 260401 (2007).
[CrossRef]

Rev. Mod. Phys.

J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, Rev. Mod. Phys. 83, 1523 (2011).
[CrossRef]

Supplementary Material (7)

» Media 1: MOV (1530 KB)     
» Media 2: MOV (284 KB)     
» Media 3: MOV (683 KB)     
» Media 4: MOV (1349 KB)     
» Media 5: MOV (1353 KB)     
» Media 6: MOV (1417 KB)     
» Media 7: MOV (1499 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

Schematic of the experimental setup used for trapping with a perfect vortex beam. A1 is an axicon, and L1L5 are lenses. MO1 is a microscope objective. Inset figures show the created perfect vortex beams with (a) =15, (b) =25, (c) =35, and (d) =25 with the scattered light of 13 trapped microparticles (Media 1), and (e) a vortex mask with =20.

Fig. 2.
Fig. 2.

Paraxial simulation of the generation of perfect vortex beams with both integer and noninteger charges. (a), (d) show the beams in the xz plane for the cases =3 and =3.3, respectively. Both beams propagate from left to right. (b), (c) and (e), (f) show the transverse intensity and phase profiles on the final plane, respectively, for these two topological charges.

Fig. 3.
Fig. 3.

Relationship between the particle rotation rate and the integer topological charge for a perfect vortex beam. Positive rotation rate is defined as counterclockwise rotation. The solid lines represent a least-square linear regression of the original data.

Fig. 4.
Fig. 4.

Relationship between the particle rotation rate and the fractional topological charge for a perfect vortex beam. The solid line, including our specific prefactor and offset, shows the trend equivalent to the theoretical prediction of OAM per photon of a fractional vortex as sin(2π)/(2π) [16].

Fig. 5.
Fig. 5.

(a) shows a perfect vortex beam with =25 before the amplitude correction. (b) shows the beam with the scattered light from a single trapped particle. The red arrow indicates the position where the particle stops (Media 2). (c) shows the beam after the amplitude correction. The trapped particle can sustain the rotation along the annulus as shown by (d) and in (Media 3).

Fig. 6.
Fig. 6.

Flow chart of local OAM density correction.

Fig. 7.
Fig. 7.

Bright field images of trapped particles. (a) and (b) show a single particle trapped by a perfect vortex beam before (Media 4) and after (Media 5) local OAM density correction. (c) and (d) show two (Media 6) and three (Media 7) well-separated particles trapped by a perfect vortex beam after local OAM density correction.

Equations (1)

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V(ρ,θ)=exp((ρρ0)2Δρ2)eiθ,

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