Abstract

We achieve controllable noninterferometric rotation of a bored helical beam by introducing a phase shift exclusively to the annular helical region of the phase. We present a derivation based on the decomposition of the beams, which shows that a constant phase shift of ΔΦ between the bore and the surrounding helical phase with topological charge ℓ will rotate the intensity profile by ΔΦ/ about its center. The effect of the phase shifting is verified with experiments. This technique is simple, while it preserves the transverse intensity profiles of the beams. Our report may find applications in optical manipulation and trapping.

© 2010 Optical Society of America

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References

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  1. A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. USA 94, 4853-4860 (1997).
    [CrossRef] [PubMed]
  2. D. McGloin, “Optical tweezers: 20 years on,” Phil. Trans. R. Soc. A 364, 3521-3537 (2006).
    [CrossRef] [PubMed]
  3. K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787-2809 (2004).
    [CrossRef]
  4. J. E. Molloy, K. Dholakia, and M. J. Padgett, “Optical tweezers in a new light,” J. Mod. Opt. 50, 1501-1507 (2003).
  5. J. E. Molloy and M. J. Padgett, “Lights, action: optical tweezers,” Contemp. Phys. 43, 241-258 (2002).
    [CrossRef]
  6. K. Dholakia, P. Reece, and M. Gu, “Optical micromanipulation,” Chem. Soc. Rev. 37, 42-55 (2008).
    [CrossRef] [PubMed]
  7. D. W. Zhang and X.-C. Yuan, “Optical doughnut for optical tweezers,” Opt. Lett. 28, 740-742 (2003).
    [CrossRef] [PubMed]
  8. A. Forrester, J. Courtial, and M. J. Padgett, “Performance of a rotating aperture for spinning and orienting objects in optical tweezers,” J. Mod. Opt. 50, 1533-1538 (2003).
  9. A. T. O'Neil and M. J. Padgett, “Rotational control within optical tweezers by use of a rotating aperture,” Opt. Lett. 27, 743-745 (2002).
    [CrossRef]
  10. M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, “Revolving interference patterns for the rotation of optically trapped particles,” Opt. Commun. 201, 21-28 (2002).
    [CrossRef]
  11. M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical torque controlled by elliptical polarization,” Opt. Lett. 23, 1-3 (1998).
    [CrossRef]
  12. L. Paterson, M. P. MacDonald, J. Arlt, W. Dultz, H. Schmitzer, W. Sibbett, and K. Dholakia, “Controlled simultaneous rotation of multiple optically trapped particles,” J. Mod. Opt. 50, 1591-1599 (2003).
  13. N. B. Simpson, L. Allen, and M. J. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. 43, 2485-2491 (1996).
    [CrossRef]
  14. S. H. Tao, X-C. Yuan, J. Lin, X. Peng, and H. B. Niu, “Fractional optical vortex beam induced rotation of particles,” Opt. Express 13, 7726-7731 (2005).
    [CrossRef] [PubMed]
  15. D. McGloin, V. Garcés-Chávez, and K. Dholakia, “Interfering Bessel beams for optical micromanipulation,” Opt. Lett. 28, 657-659 (2003).
    [CrossRef] [PubMed]
  16. S. Franke-Arnold, J. Leach, M. J. Padgett, V. E. Lembessis, D. Ellinas, A. J. Wright, J. M. Girkin, P. Ohberg, and A. S. Arnold, “Optical ferris wheel for ultracold atoms,” Opt. Express 15, 8619-8625 (2007).
    [CrossRef] [PubMed]
  17. S. A. Baluyot and N. Hermosa, “Intensity profiles and propagation of optical beams with bored helical phase,” Opt. Express 17, 16244-16254 (2009).
    [CrossRef] [PubMed]
  18. H. L. Royden, Real Analysis, 3rd ed. (Macmillan, 1988).
  19. A. E. Siegman, Lasers, 1st ed. (University Science, 1986).
  20. J. Goodman, Introduction to Fourier Optics, 1st ed. (McGraw-Hill, 1968).
  21. V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985-990(1992).
    [CrossRef]

2009 (1)

2008 (1)

K. Dholakia, P. Reece, and M. Gu, “Optical micromanipulation,” Chem. Soc. Rev. 37, 42-55 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (1)

D. McGloin, “Optical tweezers: 20 years on,” Phil. Trans. R. Soc. A 364, 3521-3537 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (1)

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

2003 (5)

J. E. Molloy, K. Dholakia, and M. J. Padgett, “Optical tweezers in a new light,” J. Mod. Opt. 50, 1501-1507 (2003).

D. W. Zhang and X.-C. Yuan, “Optical doughnut for optical tweezers,” Opt. Lett. 28, 740-742 (2003).
[CrossRef] [PubMed]

A. Forrester, J. Courtial, and M. J. Padgett, “Performance of a rotating aperture for spinning and orienting objects in optical tweezers,” J. Mod. Opt. 50, 1533-1538 (2003).

D. McGloin, V. Garcés-Chávez, and K. Dholakia, “Interfering Bessel beams for optical micromanipulation,” Opt. Lett. 28, 657-659 (2003).
[CrossRef] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Dultz, H. Schmitzer, W. Sibbett, and K. Dholakia, “Controlled simultaneous rotation of multiple optically trapped particles,” J. Mod. Opt. 50, 1591-1599 (2003).

2002 (3)

A. T. O'Neil and M. J. Padgett, “Rotational control within optical tweezers by use of a rotating aperture,” Opt. Lett. 27, 743-745 (2002).
[CrossRef]

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, “Revolving interference patterns for the rotation of optically trapped particles,” Opt. Commun. 201, 21-28 (2002).
[CrossRef]

J. E. Molloy and M. J. Padgett, “Lights, action: optical tweezers,” Contemp. Phys. 43, 241-258 (2002).
[CrossRef]

1998 (1)

1997 (1)

A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. USA 94, 4853-4860 (1997).
[CrossRef] [PubMed]

1996 (1)

N. B. Simpson, L. Allen, and M. J. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. 43, 2485-2491 (1996).
[CrossRef]

1992 (1)

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985-990(1992).
[CrossRef]

Allen, L.

N. B. Simpson, L. Allen, and M. J. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. 43, 2485-2491 (1996).
[CrossRef]

Arlt, J.

L. Paterson, M. P. MacDonald, J. Arlt, W. Dultz, H. Schmitzer, W. Sibbett, and K. Dholakia, “Controlled simultaneous rotation of multiple optically trapped particles,” J. Mod. Opt. 50, 1591-1599 (2003).

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, “Revolving interference patterns for the rotation of optically trapped particles,” Opt. Commun. 201, 21-28 (2002).
[CrossRef]

Arnold, A. S.

Ashkin, A.

A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. USA 94, 4853-4860 (1997).
[CrossRef] [PubMed]

Baluyot, S. A.

Bazhenov, V. Yu.

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985-990(1992).
[CrossRef]

Block, S. M.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

Courtial, J.

A. Forrester, J. Courtial, and M. J. Padgett, “Performance of a rotating aperture for spinning and orienting objects in optical tweezers,” J. Mod. Opt. 50, 1533-1538 (2003).

Dholakia, K.

K. Dholakia, P. Reece, and M. Gu, “Optical micromanipulation,” Chem. Soc. Rev. 37, 42-55 (2008).
[CrossRef] [PubMed]

J. E. Molloy, K. Dholakia, and M. J. Padgett, “Optical tweezers in a new light,” J. Mod. Opt. 50, 1501-1507 (2003).

D. McGloin, V. Garcés-Chávez, and K. Dholakia, “Interfering Bessel beams for optical micromanipulation,” Opt. Lett. 28, 657-659 (2003).
[CrossRef] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Dultz, H. Schmitzer, W. Sibbett, and K. Dholakia, “Controlled simultaneous rotation of multiple optically trapped particles,” J. Mod. Opt. 50, 1591-1599 (2003).

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, “Revolving interference patterns for the rotation of optically trapped particles,” Opt. Commun. 201, 21-28 (2002).
[CrossRef]

Dultz, W.

L. Paterson, M. P. MacDonald, J. Arlt, W. Dultz, H. Schmitzer, W. Sibbett, and K. Dholakia, “Controlled simultaneous rotation of multiple optically trapped particles,” J. Mod. Opt. 50, 1591-1599 (2003).

Ellinas, D.

Forrester, A.

A. Forrester, J. Courtial, and M. J. Padgett, “Performance of a rotating aperture for spinning and orienting objects in optical tweezers,” J. Mod. Opt. 50, 1533-1538 (2003).

Franke-Arnold, S.

Friese, M. E. J.

Garcés-Chávez, V.

Girkin, J. M.

Goodman, J.

J. Goodman, Introduction to Fourier Optics, 1st ed. (McGraw-Hill, 1968).

Gu, M.

K. Dholakia, P. Reece, and M. Gu, “Optical micromanipulation,” Chem. Soc. Rev. 37, 42-55 (2008).
[CrossRef] [PubMed]

Heckenberg, N. R.

Hermosa, N.

Leach, J.

Lembessis, V. E.

Lin, J.

MacDonald, M. P.

L. Paterson, M. P. MacDonald, J. Arlt, W. Dultz, H. Schmitzer, W. Sibbett, and K. Dholakia, “Controlled simultaneous rotation of multiple optically trapped particles,” J. Mod. Opt. 50, 1591-1599 (2003).

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, “Revolving interference patterns for the rotation of optically trapped particles,” Opt. Commun. 201, 21-28 (2002).
[CrossRef]

McGloin, D.

Molloy, J. E.

J. E. Molloy, K. Dholakia, and M. J. Padgett, “Optical tweezers in a new light,” J. Mod. Opt. 50, 1501-1507 (2003).

J. E. Molloy and M. J. Padgett, “Lights, action: optical tweezers,” Contemp. Phys. 43, 241-258 (2002).
[CrossRef]

Neuman, K. C.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

Nieminen, T. A.

Niu, H. B.

Ohberg, P.

O'Neil, A. T.

Padgett, M. J.

S. Franke-Arnold, J. Leach, M. J. Padgett, V. E. Lembessis, D. Ellinas, A. J. Wright, J. M. Girkin, P. Ohberg, and A. S. Arnold, “Optical ferris wheel for ultracold atoms,” Opt. Express 15, 8619-8625 (2007).
[CrossRef] [PubMed]

J. E. Molloy, K. Dholakia, and M. J. Padgett, “Optical tweezers in a new light,” J. Mod. Opt. 50, 1501-1507 (2003).

A. Forrester, J. Courtial, and M. J. Padgett, “Performance of a rotating aperture for spinning and orienting objects in optical tweezers,” J. Mod. Opt. 50, 1533-1538 (2003).

A. T. O'Neil and M. J. Padgett, “Rotational control within optical tweezers by use of a rotating aperture,” Opt. Lett. 27, 743-745 (2002).
[CrossRef]

J. E. Molloy and M. J. Padgett, “Lights, action: optical tweezers,” Contemp. Phys. 43, 241-258 (2002).
[CrossRef]

N. B. Simpson, L. Allen, and M. J. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. 43, 2485-2491 (1996).
[CrossRef]

Paterson, L.

L. Paterson, M. P. MacDonald, J. Arlt, W. Dultz, H. Schmitzer, W. Sibbett, and K. Dholakia, “Controlled simultaneous rotation of multiple optically trapped particles,” J. Mod. Opt. 50, 1591-1599 (2003).

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, “Revolving interference patterns for the rotation of optically trapped particles,” Opt. Commun. 201, 21-28 (2002).
[CrossRef]

Peng, X.

Reece, P.

K. Dholakia, P. Reece, and M. Gu, “Optical micromanipulation,” Chem. Soc. Rev. 37, 42-55 (2008).
[CrossRef] [PubMed]

Royden, H. L.

H. L. Royden, Real Analysis, 3rd ed. (Macmillan, 1988).

Rubinsztein-Dunlop, H.

Schmitzer, H.

L. Paterson, M. P. MacDonald, J. Arlt, W. Dultz, H. Schmitzer, W. Sibbett, and K. Dholakia, “Controlled simultaneous rotation of multiple optically trapped particles,” J. Mod. Opt. 50, 1591-1599 (2003).

Sibbett, W.

L. Paterson, M. P. MacDonald, J. Arlt, W. Dultz, H. Schmitzer, W. Sibbett, and K. Dholakia, “Controlled simultaneous rotation of multiple optically trapped particles,” J. Mod. Opt. 50, 1591-1599 (2003).

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, “Revolving interference patterns for the rotation of optically trapped particles,” Opt. Commun. 201, 21-28 (2002).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers, 1st ed. (University Science, 1986).

Simpson, N. B.

N. B. Simpson, L. Allen, and M. J. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. 43, 2485-2491 (1996).
[CrossRef]

Soskin, M. S.

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985-990(1992).
[CrossRef]

Tao, S. H.

Vasnetsov, M. V.

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985-990(1992).
[CrossRef]

Volke-Sepulveda, K.

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, “Revolving interference patterns for the rotation of optically trapped particles,” Opt. Commun. 201, 21-28 (2002).
[CrossRef]

Wright, A. J.

Yuan, X.-C.

Yuan, X-C.

Zhang, D. W.

Chem. Soc. Rev. (1)

K. Dholakia, P. Reece, and M. Gu, “Optical micromanipulation,” Chem. Soc. Rev. 37, 42-55 (2008).
[CrossRef] [PubMed]

Contemp. Phys. (1)

J. E. Molloy and M. J. Padgett, “Lights, action: optical tweezers,” Contemp. Phys. 43, 241-258 (2002).
[CrossRef]

J. Mod. Opt. (5)

A. Forrester, J. Courtial, and M. J. Padgett, “Performance of a rotating aperture for spinning and orienting objects in optical tweezers,” J. Mod. Opt. 50, 1533-1538 (2003).

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985-990(1992).
[CrossRef]

J. E. Molloy, K. Dholakia, and M. J. Padgett, “Optical tweezers in a new light,” J. Mod. Opt. 50, 1501-1507 (2003).

L. Paterson, M. P. MacDonald, J. Arlt, W. Dultz, H. Schmitzer, W. Sibbett, and K. Dholakia, “Controlled simultaneous rotation of multiple optically trapped particles,” J. Mod. Opt. 50, 1591-1599 (2003).

N. B. Simpson, L. Allen, and M. J. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. 43, 2485-2491 (1996).
[CrossRef]

Opt. Commun. (1)

M. P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, and K. Dholakia, “Revolving interference patterns for the rotation of optically trapped particles,” Opt. Commun. 201, 21-28 (2002).
[CrossRef]

Opt. Express (3)

Opt. Lett. (4)

Phil. Trans. R. Soc. A (1)

D. McGloin, “Optical tweezers: 20 years on,” Phil. Trans. R. Soc. A 364, 3521-3537 (2006).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. USA (1)

A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. USA 94, 4853-4860 (1997).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

Other (3)

H. L. Royden, Real Analysis, 3rd ed. (Macmillan, 1988).

A. E. Siegman, Lasers, 1st ed. (University Science, 1986).

J. Goodman, Introduction to Fourier Optics, 1st ed. (McGraw-Hill, 1968).

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Figures (5)

Fig. 1
Fig. 1

Intensity profiles of BH beams (theoretical) vary with the bore radius ρ i and topological charge ℓ of the phase. Larger values of ρ i give intense “arms” while smaller values have encapsulated “blades.” The number of “arms” and “blades” is equal to ℓ.

Fig. 2
Fig. 2

(a) Rotation of the profiles of BH beams (theoretical) with identical bore radii by varying Δ Φ . The rotation is dependent on Δ Φ and the topological charge ℓ. (b) Rotation is independent of the bore radius. For the purpose of comparison, the initial profiles have been oriented identically.

Fig. 3
Fig. 3

Comparison of = 5 , ρ i = 0.4 ρ o BH beams (theoretical) with differing phase shift schemes: (a) no phase shift, (b) phase shift of 13 π / 4 in both plane and helical phase regions (i.e., no relative shift between the two regions), and (c) a relative phase shift is maintained by introducing the phase shift of 13 π / 4 exclusive to the helical region. (a), (b), and (c) are viewed at identical z planes, while (d) is beam (a) propagated to a distance z + Δ z . Intensity profiles in (a) and (b) are identical.

Fig. 4
Fig. 4

Experimental setup used is similar to [17]. Once an image of the beam is captured, another shifted BH CGH is placed in the holder. (a) The expanded and collimated He–Ne ( λ = 632.8 nm ) laser beam is imprinted with the bored helical phase via a CGH. The BH beam is then diffracted using a lens of f = f 1 . The first-order diffraction is isolated by blocking other orders. The transverse intensity profile of the first-order beam is then imaged into a CCD camera using a lens of f = f 2 . (b) Enlarged samples of shifted BH CGH for = 2 , ρ i = 0.4.5 ρ o .

Fig. 5
Fig. 5

Comparison between the theoretical and experimental results for = 2 and Δ Φ = 2 π / 3 . Both profiles are rotated by π / 3 r a d s for every relative phase increment of 2 π / 3 .

Equations (9)

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Φ BH ( ρ , φ , z = 0 ) { φ ; ρ i ρ < ρ o 0 ; otherwise = χ O / I ( ρ ) φ ,
I { ρ + U { 0 } : ρ < ρ i } ; ρ i + U ( 0 ) , O { ρ + U { 0 } : ρ < ρ o } ; ρ o + ; ρ i < ρ o ,
χ A ( x ) { 1 ; x A 0 ; x A .
u BH ( ρ , φ , z = 0 ) C χ O ( ρ ) exp ( ρ 2 σ 2 ) exp [ i Φ BH ( ρ , φ , z = 0 ) ] ,
u BH ( ρ , φ , z ) = C k exp ( i k z ) i z exp ( i k 2 z ρ 2 ) { 0 + χ I ( ρ ) exp [ ( 1 σ 2 + i k 2 z ) ρ 2 ] J 0 ( k ρ z ρ ) ρ d ρ + i | | exp ( i φ ) 0 + χ O / I ( ρ ) exp [ ( - 1 σ 2 + i k 2 z ) ρ ' 2 ] J | | ( k ρ z ρ ) ρ d ρ }
= u I ( ρ , z ) + u O ( ρ , φ , z ) .
Φ ( ρ , φ , z = 0 ) = { 0 ; 0 ρ < ρ i φ + Δ Φ ; ρ i ρ < ρ o = χ O / I ( ρ ) [ φ + Δ Φ ] ,
u BH ( ρ , φ , z ) = C k exp ( i k z ) i z exp ( i k 2 z ρ 2 ) { 0 + χ I ( ρ ) exp [ ( 1 σ 2 + i k 2 z ) ρ 2 ] J 0 ( k ρ z ρ ) ρ d ρ + i | | exp ( i φ + Δ Φ ) 0 + χ O / I ( ρ ) exp [ ( - 1 σ 2 + i k 2 z ) ρ ' 2 ] J | | ( k ρ z ρ ) ρ d ρ } = u I ( ρ , z ) + u O ( ρ , φ + Δ Φ , z ) = u BH ( ρ , φ + Δ Φ , z ) .
φ R = Δ Φ .

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