Abstract

Different spatial distributions of optical vortices have been generated and characterized by implementing arrays of devil’s vortex lenses in a reconfigurable spatial light modulator. A simple design procedure assigns the preferred position and topological charge value to each vortex in the structure, tuning the desired angular momentum. Distributions with charges and momenta of the opposite sign have been experimentally demonstrated. The angular velocity exhibited by the phase distribution around the focal plane has been visualized, showing an excellent agreement with the simulations. The practical limits of the method, with interest for applications involving particle transfer and manipulation, have been evaluated.

© 2013 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2013 (3)

S. H. Tao, B. C. Yang, H. Xia, and W. X. Yu, “Tailorable three-dimensional distribution of laser foci based on customized fractal zone plates,” Laser Phys. Lett. 10, 035003 (2013).
[CrossRef]

B. Ma, B. Yao, Z. Li, M. Lei, S. Yan, P. Gao, D. Dan, and T. Ye, “Generation of three-dimensional optical structures by dynamic holograms displayed on a twisted nematic liquid crystal display,” Appl. Phys. B 110, 531–537 (2013).
[CrossRef]

L. Wei, Y. Gao, X. Wen, Z. Zhao, L. Cao, and Y. Gu, “Fractional spiral zone plates,” J. Opt. Soc. Am. A 30, 233–237 (2013).
[CrossRef]

2012 (5)

2010 (2)

W. D. Furlan, F. Giménez, A. Calatayud, L. Remón, and J. A. Monsoriu, “Volumetric multiple optical traps produced by devil’s lenses,” J. Eur. Opt. Soc. 5, 100375 (2010).
[CrossRef]

I. Moreno, J. A. Davis, D. M. Cottrell, N. Zhang, and X.-C. Yuan, “Encoding generalized phase functions on Dammann gratings,” Opt. Lett. 35, 1536–1538 (2010).
[CrossRef]

2009 (1)

2007 (2)

2006 (3)

J. Courtial, R. Zambrini, M. R. Dennis, and M. Vasnetsov, “Angular momentum of optical vortex arrays,” Opt. Express 14, 938–949 (2006).
[CrossRef]

G. Gbur and T. D. Visser, “Phase singularities and coherence vortices in linear optical systems,” Opt. Commun. 259, 428–435 (2006).
[CrossRef]

S. H. Tao, X.-C. Yuan, J. Lin, and R. Burge, “Sequence of focused optical vortices generated by a spiral fractal zone plates,” Appl. Phys. Lett. 89, 031105 (2006).
[CrossRef]

2004 (3)

2003 (2)

G. Saavedra, W. D. Furlan, and J. A. Monsoriu, “Fractal zone plates,” Opt. Lett. 28, 971–973 (2003).
[CrossRef]

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

2001 (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photon,” Nature 412, 313–316 (2001).
[CrossRef]

1999 (1)

1996 (1)

1995 (1)

H. Me, 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]

1991 (1)

D. R. Chalice, “A characterization of the cantor function,” Amer. Math. Monthly 98, 255–258 (1991).
[CrossRef]

Anderson, M. E.

Burge, R.

S. H. Tao, X.-C. Yuan, J. Lin, and R. Burge, “Sequence of focused optical vortices generated by a spiral fractal zone plates,” Appl. Phys. Lett. 89, 031105 (2006).
[CrossRef]

Calatayud, A.

A. Calatayud, J. A. Rodrigo, L. Remón, W. D. Furlan, G. Cristóbal, and J. A. Monsoriu, “Experimental generation and characterization of Devil’s vortex-lenses,” Appl. Phys. B. 106, 915–919 (2012).
[CrossRef]

W. D. Furlan, F. Giménez, A. Calatayud, L. Remón, and J. A. Monsoriu, “Volumetric multiple optical traps produced by devil’s lenses,” J. Eur. Opt. Soc. 5, 100375 (2010).
[CrossRef]

W. D. Furlan, F. Giménez, A. Calatayud, and J. A. Monsoriu, “Devil’s vortex-lenses,” Opt. Express 17, 21891–21896 (2009).
[CrossRef]

Cao, L.

Cao, W.

Chalice, D. R.

D. R. Chalice, “A characterization of the cantor function,” Amer. Math. Monthly 98, 255–258 (1991).
[CrossRef]

Chaloupka, J. L.

Cheong, W. C.

Cho, S.-W.

Cottrell, D. M.

Courtial, J.

Cristóbal, G.

A. Calatayud, J. A. Rodrigo, L. Remón, W. D. Furlan, G. Cristóbal, and J. A. Monsoriu, “Experimental generation and characterization of Devil’s vortex-lenses,” Appl. Phys. B. 106, 915–919 (2012).
[CrossRef]

Dan, D.

B. Ma, B. Yao, Z. Li, M. Lei, S. Yan, P. Gao, D. Dan, and T. Ye, “Generation of three-dimensional optical structures by dynamic holograms displayed on a twisted nematic liquid crystal display,” Appl. Phys. B 110, 531–537 (2013).
[CrossRef]

Davis, J. A.

Dennis, M. R.

Doughty, D. C.

Friese, M. E. J.

H. Me, 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]

Furlan, W. D.

A. Calatayud, J. A. Rodrigo, L. Remón, W. D. Furlan, G. Cristóbal, and J. A. Monsoriu, “Experimental generation and characterization of Devil’s vortex-lenses,” Appl. Phys. B. 106, 915–919 (2012).
[CrossRef]

W. D. Furlan, F. Giménez, A. Calatayud, L. Remón, and J. A. Monsoriu, “Volumetric multiple optical traps produced by devil’s lenses,” J. Eur. Opt. Soc. 5, 100375 (2010).
[CrossRef]

W. D. Furlan, F. Giménez, A. Calatayud, and J. A. Monsoriu, “Devil’s vortex-lenses,” Opt. Express 17, 21891–21896 (2009).
[CrossRef]

J. A. Monsoriu, W. D. Furlan, G. Saavedra, and F. Giménez, “Devil’s lenses,” Opt. Express 15, 13858–13864 (2007).
[CrossRef]

G. Saavedra, W. D. Furlan, and J. A. Monsoriu, “Fractal zone plates,” Opt. Lett. 28, 971–973 (2003).
[CrossRef]

Gahagan, K. T.

Gao, P.

B. Ma, B. Yao, Z. Li, M. Lei, S. Yan, P. Gao, D. Dan, and T. Ye, “Generation of three-dimensional optical structures by dynamic holograms displayed on a twisted nematic liquid crystal display,” Appl. Phys. B 110, 531–537 (2013).
[CrossRef]

Gao, Y.

García-Martínez, P.

Gbur, G.

G. Gbur and T. D. Visser, “Phase singularities and coherence vortices in linear optical systems,” Opt. Commun. 259, 428–435 (2006).
[CrossRef]

Giménez, F.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, (McGraw-Hill, 1996).

Grier, D. G.

Gu, Y.

Hahn, J.

Haist, T.

Heckenberg, N. R.

H. Me, 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]

Jia, W.

Kim, H.

Ladavac, K.

Lee, B.

Lee, W. M.

Lei, M.

B. Ma, B. Yao, Z. Li, M. Lei, S. Yan, P. Gao, D. Dan, and T. Ye, “Generation of three-dimensional optical structures by dynamic holograms displayed on a twisted nematic liquid crystal display,” Appl. Phys. B 110, 531–537 (2013).
[CrossRef]

Li, Z.

B. Ma, B. Yao, Z. Li, M. Lei, S. Yan, P. Gao, D. Dan, and T. Ye, “Generation of three-dimensional optical structures by dynamic holograms displayed on a twisted nematic liquid crystal display,” Appl. Phys. B 110, 531–537 (2013).
[CrossRef]

Lin, J.

S. H. Tao, X.-C. Yuan, J. Lin, and R. Burge, “Sequence of focused optical vortices generated by a spiral fractal zone plates,” Appl. Phys. Lett. 89, 031105 (2006).
[CrossRef]

Ma, B.

B. Ma, B. Yao, Z. Li, M. Lei, S. Yan, P. Gao, D. Dan, and T. Ye, “Generation of three-dimensional optical structures by dynamic holograms displayed on a twisted nematic liquid crystal display,” Appl. Phys. B 110, 531–537 (2013).
[CrossRef]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photon,” Nature 412, 313–316 (2001).
[CrossRef]

Me, H.

H. Me, 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]

Mitry, M.

Monsoriu, J. A.

A. Calatayud, J. A. Rodrigo, L. Remón, W. D. Furlan, G. Cristóbal, and J. A. Monsoriu, “Experimental generation and characterization of Devil’s vortex-lenses,” Appl. Phys. B. 106, 915–919 (2012).
[CrossRef]

W. D. Furlan, F. Giménez, A. Calatayud, L. Remón, and J. A. Monsoriu, “Volumetric multiple optical traps produced by devil’s lenses,” J. Eur. Opt. Soc. 5, 100375 (2010).
[CrossRef]

W. D. Furlan, F. Giménez, A. Calatayud, and J. A. Monsoriu, “Devil’s vortex-lenses,” Opt. Express 17, 21891–21896 (2009).
[CrossRef]

J. A. Monsoriu, W. D. Furlan, G. Saavedra, and F. Giménez, “Devil’s lenses,” Opt. Express 15, 13858–13864 (2007).
[CrossRef]

G. Saavedra, W. D. Furlan, and J. A. Monsoriu, “Fractal zone plates,” Opt. Lett. 28, 971–973 (2003).
[CrossRef]

Moreno, I.

Reicherter, M.

Remón, L.

A. Calatayud, J. A. Rodrigo, L. Remón, W. D. Furlan, G. Cristóbal, and J. A. Monsoriu, “Experimental generation and characterization of Devil’s vortex-lenses,” Appl. Phys. B. 106, 915–919 (2012).
[CrossRef]

W. D. Furlan, F. Giménez, A. Calatayud, L. Remón, and J. A. Monsoriu, “Volumetric multiple optical traps produced by devil’s lenses,” J. Eur. Opt. Soc. 5, 100375 (2010).
[CrossRef]

Rodrigo, J. A.

A. Calatayud, J. A. Rodrigo, L. Remón, W. D. Furlan, G. Cristóbal, and J. A. Monsoriu, “Experimental generation and characterization of Devil’s vortex-lenses,” Appl. Phys. B. 106, 915–919 (2012).
[CrossRef]

Roux, F. S.

F. S. Roux, “Distribution of angular momentum and vortex morphology in optical beams,” Opt. Commun. 242, 45–55 (2004).
[CrossRef]

Rubinsztein-Dunlop, H.

H. Me, 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]

Saavedra, G.

Sánchez-López, M. M.

Sand, D.

Senthikumaran, P.

Swartzlander, G. A.

Tao, S. H.

S. H. Tao, B. C. Yang, H. Xia, and W. X. Yu, “Tailorable three-dimensional distribution of laser foci based on customized fractal zone plates,” Laser Phys. Lett. 10, 035003 (2013).
[CrossRef]

S. H. Tao, X.-C. Yuan, J. Lin, and R. Burge, “Sequence of focused optical vortices generated by a spiral fractal zone plates,” Appl. Phys. Lett. 89, 031105 (2006).
[CrossRef]

Tiziani, H. J.

Vasnetsov, M.

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photon,” Nature 412, 313–316 (2001).
[CrossRef]

Visser, T. D.

G. Gbur and T. D. Visser, “Phase singularities and coherence vortices in linear optical systems,” Opt. Commun. 259, 428–435 (2006).
[CrossRef]

Vyas, S.

Wagemann, E. U.

Wang, S.

Wei, L.

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photon,” Nature 412, 313–316 (2001).
[CrossRef]

Wen, X.

Wu, J.

Xia, H.

S. H. Tao, B. C. Yang, H. Xia, and W. X. Yu, “Tailorable three-dimensional distribution of laser foci based on customized fractal zone plates,” Laser Phys. Lett. 10, 035003 (2013).
[CrossRef]

Yan, S.

B. Ma, B. Yao, Z. Li, M. Lei, S. Yan, P. Gao, D. Dan, and T. Ye, “Generation of three-dimensional optical structures by dynamic holograms displayed on a twisted nematic liquid crystal display,” Appl. Phys. B 110, 531–537 (2013).
[CrossRef]

Yang, B. C.

S. H. Tao, B. C. Yang, H. Xia, and W. X. Yu, “Tailorable three-dimensional distribution of laser foci based on customized fractal zone plates,” Laser Phys. Lett. 10, 035003 (2013).
[CrossRef]

Yao, B.

B. Ma, B. Yao, Z. Li, M. Lei, S. Yan, P. Gao, D. Dan, and T. Ye, “Generation of three-dimensional optical structures by dynamic holograms displayed on a twisted nematic liquid crystal display,” Appl. Phys. B 110, 531–537 (2013).
[CrossRef]

Ye, T.

B. Ma, B. Yao, Z. Li, M. Lei, S. Yan, P. Gao, D. Dan, and T. Ye, “Generation of three-dimensional optical structures by dynamic holograms displayed on a twisted nematic liquid crystal display,” Appl. Phys. B 110, 531–537 (2013).
[CrossRef]

Yu, J.

Yu, W. X.

S. H. Tao, B. C. Yang, H. Xia, and W. X. Yu, “Tailorable three-dimensional distribution of laser foci based on customized fractal zone plates,” Laser Phys. Lett. 10, 035003 (2013).
[CrossRef]

Yuan, X. C.

Yuan, X.-C.

I. Moreno, J. A. Davis, D. M. Cottrell, N. Zhang, and X.-C. Yuan, “Encoding generalized phase functions on Dammann gratings,” Opt. Lett. 35, 1536–1538 (2010).
[CrossRef]

S. H. Tao, X.-C. Yuan, J. Lin, and R. Burge, “Sequence of focused optical vortices generated by a spiral fractal zone plates,” Appl. Phys. Lett. 89, 031105 (2006).
[CrossRef]

Zambrini, R.

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photon,” Nature 412, 313–316 (2001).
[CrossRef]

Zhang, N.

Zhao, Z.

Zhou, C.

Amer. Math. Monthly (1)

D. R. Chalice, “A characterization of the cantor function,” Amer. Math. Monthly 98, 255–258 (1991).
[CrossRef]

Appl. Opt. (5)

Appl. Phys. B (1)

B. Ma, B. Yao, Z. Li, M. Lei, S. Yan, P. Gao, D. Dan, and T. Ye, “Generation of three-dimensional optical structures by dynamic holograms displayed on a twisted nematic liquid crystal display,” Appl. Phys. B 110, 531–537 (2013).
[CrossRef]

Appl. Phys. B. (1)

A. Calatayud, J. A. Rodrigo, L. Remón, W. D. Furlan, G. Cristóbal, and J. A. Monsoriu, “Experimental generation and characterization of Devil’s vortex-lenses,” Appl. Phys. B. 106, 915–919 (2012).
[CrossRef]

Appl. Phys. Lett. (1)

S. H. Tao, X.-C. Yuan, J. Lin, and R. Burge, “Sequence of focused optical vortices generated by a spiral fractal zone plates,” Appl. Phys. Lett. 89, 031105 (2006).
[CrossRef]

J. Eur. Opt. Soc. (1)

W. D. Furlan, F. Giménez, A. Calatayud, L. Remón, and J. A. Monsoriu, “Volumetric multiple optical traps produced by devil’s lenses,” J. Eur. Opt. Soc. 5, 100375 (2010).
[CrossRef]

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

Laser Phys. Lett. (1)

S. H. Tao, B. C. Yang, H. Xia, and W. X. Yu, “Tailorable three-dimensional distribution of laser foci based on customized fractal zone plates,” Laser Phys. Lett. 10, 035003 (2013).
[CrossRef]

Nature (2)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photon,” Nature 412, 313–316 (2001).
[CrossRef]

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

Opt. Commun. (2)

F. S. Roux, “Distribution of angular momentum and vortex morphology in optical beams,” Opt. Commun. 242, 45–55 (2004).
[CrossRef]

G. Gbur and T. D. Visser, “Phase singularities and coherence vortices in linear optical systems,” Opt. Commun. 259, 428–435 (2006).
[CrossRef]

Opt. Express (4)

Opt. Lett. (5)

Phys. Rev. Lett. (1)

H. Me, 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]

Other (1)

J. W. Goodman, Introduction to Fourier Optics, (McGraw-Hill, 1996).

Supplementary Material (3)

» Media 1: MOV (3050 KB)     
» Media 2: MOV (3082 KB)     
» Media 3: MOV (3028 KB)     

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Figures (9)

Fig. 1.
Fig. 1.

Triadic Cantor set for s=1 and s=2. The Cantor function of devil’s staircase for s=2 is plotted under the Cantor set.

Fig. 2.
Fig. 2.

Phase profiles for a DVL with s=2 and topological charge: (a) m=1, (b) m=2, and (c) m=3.

Fig. 3.
Fig. 3.

Experimental setup.

Fig. 4.
Fig. 4.

Phase images of (a) the 1×3 matrix and (b) the 2×2 matrix codified in the SLM, with a DVL diameter of 499 pixels.

Fig. 5.
Fig. 5.

Results for the 1×3 DVL matrix. Simulated (a) and experimental (b) axial profiles, and magnification for the central lens, simulation (c) and experiment (d).

Fig. 6.
Fig. 6.

Results for the 2×2 DVL matrix. Simulated (a) and experimental (b) axial profiles for the upper lenses, and magnification for the upper right lens, simulation (c) and experiment (d).

Fig. 7.
Fig. 7.

Single-frame excerpts from videos showing the transversal images around the main focus. (a) 1×3 matrix: experiment (above) and simulation (below) (see Media 1). (b) 2×2 matrix: experiment (right) and simulation (left) (see Media 2). (c) Phase variation for the 1×3 matrix: experiment (above) and simulation (below) (see Media 3).

Fig. 8.
Fig. 8.

Limits of spatial resolution for DVL design. (a) Last segment width as a function of the fractal order s and minimum last segment width Lmin (in red). (b) Minimum lens radius for a given fractal order s.

Fig. 9.
Fig. 9.

Simulation of the irradiance at the main focus of a DVL with s=2, m=2 and diameter of (a) 269 pixels; (b) 259 pixels; (c) 249 pixels; and (d) 239 pixels, when the diaphragm used in the experiment has been considered.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

Fs(x)={l2sifps,lxqs,l12sxqs,lps,l+1qs,l+l2sifqs,lxps,l+1,
Q(ζ)=exp[i2s+1πFs(ζ)],
Q(ζ,θ)=exp[i2s+1πFs(ζ)]×exp[imθ].
I(z,r)=(2πλz)2|01Q(ζ)exp[iπλza2ζ]Jm(2πλzarζ)dζ|,
Φ(z,r,θ)=m(θ+π2)2πλzπr2λzπ2.
L(s,a)=a[1(13s)1/2].
a=Lmin/[1(13s)1/2].
νx=x/λfνy=y/λf.

Metrics