Abstract

An idea of an optimal annulus structure phase mask with helical wavefront is suggested; the resulting helical mode can be focused into a very clear optical vortex ring with the best contrast. Dependences of the optimal annulus width and the radius of the optical vortex ring on topological charge are found. The desired multi-optical vortices as the promising dynamic multi-optical tweezers are realized by extending our idea to the multi-annulus structure. Such multi-optical vortex rings allow carrying the same or different angular momentum flux in magnitude and direction. The idea offers flexibility and more dimensions for designing and producing the complicated optical vortices. For the Gaussian beam illumination, the optimal spot size, which ensures the high energy/power efficiency for generating the best contrast principal ring, is also found.

© 2004 Optical Society of America

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References

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Appl. Phys. Lett.

M. E. J. Friese, H. Rubinsztein-Dunlop, J. Gold, P. Hagberg, and D. Hanstorp, �??Optically driven micromachine elements,�?? Appl. Phys. Lett. 78, 547�??549 (2001)
[CrossRef]

Terray, A., Oakey, J. & Marr, D. W. M, �??Fabrication of linear colloidal structures for microfluidic applications,�?? Appl. Phys. Lett. 81, 1555�??1557 (2002)
[CrossRef]

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

J. Opt. Soc. Am. B

Nature

D. G. Grier, �??A revolution in optical manipulation,�?? Nature, 424, 810-816 (2003)
[CrossRef] [PubMed]

Opt. Commun.

M. J. Padgett and L. Allen, �??The Poynting vector in Laguerre-Gaussian laser modes,�?? Opt. Commun. 121, 36�??40 (1995)
[CrossRef]

J. E. Curtis, B. A. Koss, and D. G. Grier, �??Dynamic holographic optical tweezers,�?? Opt. Commun. 207, 169�??175 (2002)
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, �??Astigmatic laser mode converters and transfer of orbital angular momentum,�?? Opt. Commun. 96, 123-132 (1993)
[CrossRef]

Opt. Eng.

A. Marquez, C. Lemmi, I. Moreno, J. Davis, J. Campos and M. Yzuel, �??Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model,�?? Opt. Eng. 40, 2558-2564 (2001)
[CrossRef]

Opt. Lett.

Phys. Rev. A

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, �??Optical angular-momentum transfer to trapped absorbing particles,�?? Phys. Rev. A 54, 1593�??1596 (1996)
[CrossRef] [PubMed]

Phys. Rev. Lett.

A. T. O�??Neil, I. MacVicar, L. Allen, and M. J. Padgett, �??Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,�?? Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef]

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, �??Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,�?? Phys. Rev. Lett. 75, 826�??829 (1995).
[CrossRef] [PubMed]

G. A. Swartzlander, Jr. and C. T. Law, �??Optical vortex solitons observed in Kerr nonlinear media,�?? Phys. Rev. Lett. 69, 2503-2506 (1992)
[CrossRef] [PubMed]

J. E. Curtis and D. G. Grier, �??Structure of optical vortices�?? Phys. Rev. Lett. 90, 133901 (2003)
[CrossRef] [PubMed]

Prog. Opt.

L. Allen, M. J. Padgett, and M. Babiker, �??The orbital angular momentum of light,�?? Prog. Opt. 39, 291�??372 (1999)
[CrossRef]

Science

Terray, A., Oakey, J. & Marr, D. W. M. �??Microfluidic control using colloidal devices,�?? Science 296, 1841�?? 1844 (2002)
[CrossRef] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, �??Controlled rotation of optically trapped microscopic particles,�?? Science 292, 912�??914 (2001)
[CrossRef] [PubMed]

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Figures (8)

Fig. 1.
Fig. 1.

(a) Spoke-like structure phase mask with ℓ - 40 and (b) corresponding image of optical vortex produced.

Fig. 2.
Fig. 2.

Intensity distribution of ℓ = 40 optical vortices created by the annulus structure phase mask of R 0 = 256 pixels, along the radial direction when R 1 is (a) 0, (b) 125, (c) 200 and (d) 230 pixels, respectively.

Fig. 3.
Fig. 3.

Dependence of the peak intensity of the principal ring (a) and the first subsidiary ring (b) on the annulus width at different topological charges. The solid, dash, short dash, dash-dot, and dash-dot-dot lines are ℓ = 10, 20, 30, 40, and 50, respectively.

Fig. 4.
Fig. 4.

Variation of the peak intensity of the principal ring with the spot size of Gaussian beam when R 0 =256 pixels, ℓ = 40 and ΔRRopt = 50 pixels. The solid line is the theoretical values, while the circles are the experimental results.

Fig. 5.
Fig. 5.

(a) An example of the helical mode annulus phase mask, (b) simulated intensity pattern of optical vortex, (c) simulated phase pattern of optical vortex, and (d) experimentally observed intensity pattern of optical vortex.

Fig. 6.
Fig. 6.

(a) and (c) are two examples of bi-annulus phase masks, and (b) and (d) are the respective optical vortices produced. Bi-optical vortices have the opposite angular momentum directions in Fig. 6(b) and have the same radii and directions in Fig. 6(d).

Fig. 7.
Fig. 7.

Observed patterns of optical vortices in experiments for the non-perfect phase masks with the phase variation ranging from zero to 1.5π. (a), (b), (c) and (d) correspond to Fig. 1, Fig. 5, Fig. 6(b) and Fig. 6(d), respectively.

Fig. 8.
Fig. 8.

Dependence of the depth of the azimuthal modulation on the phase deviation for the optimal annulus phase mask with R 0 = 256 pixels, ℓ = 40 and ΔRopt ((40) = 50 pixels.

Equations (7)

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u f ρ ϕ = 2 π ( i ) exp ( i ϕ ) 0 R 0 rdr J ( 2 π λf ρr )
= 2 π R 0 2 p ( i ) exp ( i ϕ ) ( 2 + ) Γ ( 1 + ) 1 F 2 [ 1 + 2 , ( 2 + 2,1 + ) ; p 2 ]
Δ R opt ( ) = 1.4043 R 0 0.5363
ρ P ( ) = 2.1140 ( 1 + 0.2458 ) λf π R 0
u f ρ ϕ = 2 π ( i ) exp ( i ϕ ) ( Δ r ) 2 m = 1 N m u 0 ( m Δ r , ω ) J ( 2 πm Δ r λf ρ )
u 0 r ω = A 0 ω exp ( r 2 ω 2 )
ω opt = 1.43 R m

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