Abstract

We describe a kind of true 3D array of focused vortices with tunable topological charge, called the 3D Dammann vortex array. This 3D Dammann vortex array is arranged into the structure of a true 3D lattice in the focal region of a focusing objective, and these focused vortices are located at each node of the 3D lattice. A scheme based on a Dammann vortex grating (DVG) and a mirror is proposed to provide a choice for changing the topological charge of the 3D Dammann vortex array. For experimental demonstration, a 5×5×5 Dammann vortex array is implemented by combining a 1×7 DVG, a 1×5 Dammann zone plate, and another 5×5 Dammann grating. The topological charge of this Dammann vortex array can be tuned (from 2 to +2 with an interval of +1) by moving and rotating the mirror to select different diffraction orders of the 1×7 DVG as the incident beam. Because of these attractive properties, this 3D Dammann vortex array should be of high interest for its potential applications in various areas, such as 3D simultaneous optical manipulation, 3D parallel vortex scanning microscope, and also parallel vortex information transmission.

© 2012 Optical Society of America

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2012 (1)

2011 (2)

2010 (2)

V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, Y. V. Izdebskaya, W. Z. Krolikowski, and Y. S. Kivshar, “Optical vortex beams for trapping and transport of particles in air,” Appl. Phys. A 100, 327–331 (2010).
[CrossRef]

N. Zhang, X. C. Yuan, and R. E. Burge, “Extending the detection range of optical vortices by Dammann vortex gratings,” Opt. Lett. 35, 3495–3497 (2010).
[CrossRef]

2009 (2)

2008 (1)

2007 (1)

2006 (2)

2004 (2)

2003 (2)

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90, 4 (2003).
[CrossRef]

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[CrossRef]

2002 (3)

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]

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

A. Dreischuh, S. Chervenkov, D. Neshev, G. G. Paulus, and H. Walther, “Generation of lattice structures of optical vortices,” J. Opt. Soc. Am. B 19, 550–556 (2002).
[CrossRef]

2001 (1)

1995 (2)

C. Zhou and L. Liu, “Numerical study of Dammann array illuminators,” Appl. Opt. 34, 5961–5969 (1995).
[CrossRef]

M. Vaupel and C. O. Weiss, “Circling optical vortices,” Phys. Rev. A 51, 4078 (1995).
[CrossRef]

1992 (1)

Allen, L.

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]

Barnett, S.

Burge, R. E.

Cao, H.

Cao, W.

Chervenkov, S.

Cottrell, D.

Cottrell, D. M.

Courtial, J.

Curtis, J. E.

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90, 4 (2003).
[CrossRef]

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

Daria, V. R.

V. R. Daria, P. J. Rodrigo, and J. Gluckstad, “Dynamic array of dark optical traps,” Appl. Phys. Lett. 84, 323–325 (2004).
[CrossRef]

Davis, J.

Davis, J. A.

Desyatnikov, A. S.

V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, Y. V. Izdebskaya, W. Z. Krolikowski, and Y. S. Kivshar, “Optical vortex beams for trapping and transport of particles in air,” Appl. Phys. A 100, 327–331 (2010).
[CrossRef]

Dreischuh, A.

Franke-Arnold, S.

Gibson, G.

Gluckstad, J.

V. R. Daria, P. J. Rodrigo, and J. Gluckstad, “Dynamic array of dark optical traps,” Appl. Phys. Lett. 84, 323–325 (2004).
[CrossRef]

Grier, D. G.

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90, 4 (2003).
[CrossRef]

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[CrossRef]

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

Heckenberg, N. R.

Hell, S. W.

Hernandez, T.

Izdebskaya, Y. V.

V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, Y. V. Izdebskaya, W. Z. Krolikowski, and Y. S. Kivshar, “Optical vortex beams for trapping and transport of particles in air,” Appl. Phys. A 100, 327–331 (2010).
[CrossRef]

Janicijevic, L.

Jia, W.

Kivshar, Y. S.

V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, Y. V. Izdebskaya, W. Z. Krolikowski, and Y. S. Kivshar, “Optical vortex beams for trapping and transport of particles in air,” Appl. Phys. A 100, 327–331 (2010).
[CrossRef]

Koss, B. A.

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

Krolikowski, W. Z.

V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, Y. V. Izdebskaya, W. Z. Krolikowski, and Y. S. Kivshar, “Optical vortex beams for trapping and transport of particles in air,” Appl. Phys. A 100, 327–331 (2010).
[CrossRef]

Lasser, T.

Leitgeb, R. A.

Leutenegger, M.

Liu, L.

Ma, J.

MacVicar, I.

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]

Martínez, J.

Martínez-Corral, M.

Masajada, J.

J. Masajada, “Phase singularities in microscopic imaging,” Proc. SPIE 8338, 833806 (2011).
[CrossRef]

McDuff, R.

Mitry, M. J.

Moneron, G.

Moreno, I.

Muñoz-Escrivá, L.

Neshev, D.

O’Neil, A. T.

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]

Padgett, M.

Padgett, M. J.

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]

Pas’ko, V.

Pascoguin, B. M. L.

Paulus, G. G.

Pons, A.

Rao, R.

Rode, A. V.

V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, Y. V. Izdebskaya, W. Z. Krolikowski, and Y. S. Kivshar, “Optical vortex beams for trapping and transport of particles in air,” Appl. Phys. A 100, 327–331 (2010).
[CrossRef]

Rodrigo, P. J.

V. R. Daria, P. J. Rodrigo, and J. Gluckstad, “Dynamic array of dark optical traps,” Appl. Phys. Lett. 84, 323–325 (2004).
[CrossRef]

Senthilkumaran, P.

Shvedov, V. G.

V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, Y. V. Izdebskaya, W. Z. Krolikowski, and Y. S. Kivshar, “Optical vortex beams for trapping and transport of particles in air,” Appl. Phys. A 100, 327–331 (2010).
[CrossRef]

Smith, C. P.

Swartzlander, G. A.

G. A. Swartzlander, “The optical vortex lens,” Opt. Photon. News 17(11), 39–43 (2006).
[CrossRef]

Topuzoski, S.

Vasnetsov, M.

Vaupel, M.

M. Vaupel and C. O. Weiss, “Circling optical vortices,” Phys. Rev. A 51, 4078 (1995).
[CrossRef]

Vyas, S.

Walther, H.

Wang, S.

Weiss, C. O.

M. Vaupel and C. O. Weiss, “Circling optical vortices,” Phys. Rev. A 51, 4078 (1995).
[CrossRef]

White, A. G.

Yu, J.

Yuan, X. C.

Zhang, N.

Zhou, C.

Appl. Opt. (5)

Appl. Phys. A (1)

V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, Y. V. Izdebskaya, W. Z. Krolikowski, and Y. S. Kivshar, “Optical vortex beams for trapping and transport of particles in air,” Appl. Phys. A 100, 327–331 (2010).
[CrossRef]

Appl. Phys. Lett. (1)

V. R. Daria, P. J. Rodrigo, and J. Gluckstad, “Dynamic array of dark optical traps,” Appl. Phys. Lett. 84, 323–325 (2004).
[CrossRef]

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

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

Nature (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[CrossRef]

Opt. Commun. (1)

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

Opt. Express (3)

Opt. Lett. (3)

Opt. Photon. News (1)

G. A. Swartzlander, “The optical vortex lens,” Opt. Photon. News 17(11), 39–43 (2006).
[CrossRef]

Phys. Rev. A (1)

M. Vaupel and C. O. Weiss, “Circling optical vortices,” Phys. Rev. A 51, 4078 (1995).
[CrossRef]

Phys. Rev. Lett. (2)

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]

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90, 4 (2003).
[CrossRef]

Proc. SPIE (1)

J. Masajada, “Phase singularities in microscopic imaging,” Proc. SPIE 8338, 833806 (2011).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Binary pure-phase 1×7 DVG with base charge of l=1. (a) Theoretical phase distribution of the transmission function. The black denotes π phase shift and white denotes 0 phase shift; (b) microscopic image of the fabricated sample (scale bar is 50 μm); (c) experimental intensity distribution of the diffractive field.

Fig. 2.
Fig. 2.

Layout of experimental setup. Moving distance Δx along positive x-axis is defined as positive and that along negative x-axis is negative, and the rotating angle Δγ in anticlockwise direction is defined as positive and that in clockwise direction is negative. L1 and L2 is a lens pair for beam expanding; L3 and L4 is another lens pair for adjusting the diffractive angle of the beam from the DG; MO1 is microscopy objective for focusing; MO2 is microscopy objective for magnifying.

Fig. 3.
Fig. 3.

Experimental results of the 5×5×5 Dammann array of focused vortex with different topological charges on five axial planes. Charges: (a) 2; (b) 1; (c) 0; (d) 1; (e) 2. The position of the geometrical plane along z-axis is always defined as z=0mm (scale bar is 50 μm).

Equations (9)

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TDG(ρ,φ)=m=Cmexp(i2mπΛρcosϕ),
Cm={iΛ2mπ[1+2n=1N1(1)nexp(i2πmxn)+(1)Nexp(i2πmxN)]m0Λ[2n=1N1(1)nxn+(1)NxN]m=0,
TDVG(ρ,φ)=m=Cmexp[im(2πΛρcosφ+lφ)].
Eo(x,y,z)=00{TDZP(kx,ky)TDG(kx,ky)Et(kx,ky)/cosθ}ei(kxx+kyy)dkxdky=I{TDZP(ξ)}I{TDG(kx,ky)}Ev(x,y,z),
Ev(x,y,z)=0α02πA(θ)eilφEt(θ,φ)×exp[ik(xsinθcosφ+ysinθsinφzcosθ)]sinθdφdθ,
Io(x,y,z)=m=n=q=CmCnCqIv(xmΔx,ynΔy,zqΔz),
Δx=Nx2sinαλ,
Δy=Ny2sinαλ,
Δz=Nξ1cosαλ,

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