Abstract

We present a unique method for experimentally generating multiple vortices by way of a devil’s vortex lens combined with a Fresnel lens using a spatial light modulator. These lenses have the multifocal properties of fractal zone plates combined with the orbital angular momentum of a spiral phase plate and can be tailored to fit within a small space on an optical bench. Results are presented alongside numerical simulations, demonstrating the robust nature of both the experimental method and the predictive power of the Huygens–Fresnel wavelet theory.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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  21. 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]

2012

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]

I. Augustyniak, A. Popiolek-Masajada, J. Masajada, and S. Drobczyński, “New scanning technique for the optical vortex microscope,” Appl. Opt. 51, C117–C124 (2012).
[CrossRef]

2010

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle—orbital angular momentum variables,” Science 329, 662–665 (2010).
[CrossRef]

2009

2008

2007

2006

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

2005

2004

2003

1999

1996

1992

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
[CrossRef]

L. Allen, M. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef]

1991

D. R. Chalice, “A characterization of the Cantor function,” Am. Math. Mon. 98, 255–258 (1991).
[CrossRef]

1974

J. F. Nye and M. V. Berry, “Dislocations in wavetrains,” Proc. R. Soc. A 336, 165–190 (1974).
[CrossRef]

1931

P. A. M. Dirac, “Quantised singularities in the electromagnetic field,” Proc. R. Soc. A 133, 60–72 (1931).
[CrossRef]

Alieva, T.

Allen, L.

L. Allen, M. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef]

Augustyniak, I.

Bak, P.

P. Bak, “The devil’s staircase,” Phys. Today39(12), 38–45 (1986).
[CrossRef]

Barnett, S. M.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle—orbital angular momentum variables,” Science 329, 662–665 (2010).
[CrossRef]

Beijersbergen, M.

L. Allen, M. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef]

Bernet, S.

Berry, M. V.

J. F. Nye and M. V. Berry, “Dislocations in wavetrains,” Proc. R. Soc. A 336, 165–190 (1974).
[CrossRef]

Boyd, R. W.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle—orbital angular momentum variables,” Science 329, 662–665 (2010).
[CrossRef]

Burge, R.

S. H. Tao, x. C. Yuan, J. Lin, and R. Burge, “Sequence of focused optical vortices generated by a spiral fractal zone plate,” 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. Gimnez, A. Calatayud, and J. A. Monsoriu, “Devil’s vortex-lenses,” Opt. Express 17, 21891–21896 (2009).
[CrossRef]

Calvo, M. L.

Chalice, D. R.

D. R. Chalice, “A characterization of the Cantor function,” Am. Math. Mon. 98, 255–258 (1991).
[CrossRef]

Chen, Q. D.

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]

Davis, J. A.

Dennis, M. R.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” in Vol. 53 of Progress in Optics (Elsevier, 2009), Chap. 5, pp. 293–363.
[CrossRef]

Dirac, P. A. M.

P. A. M. Dirac, “Quantised singularities in the electromagnetic field,” Proc. R. Soc. A 133, 60–72 (1931).
[CrossRef]

Drobczynski, S.

Franke-Arnold, S.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle—orbital angular momentum variables,” Science 329, 662–665 (2010).
[CrossRef]

Fu¨rhapter, S.

Furlan, W. D.

Gahagan, K. T.

Gimnez, F.

Grier, D. G.

Haist, T.

Heckenberg, N. R.

Ireland, D. G.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle—orbital angular momentum variables,” Science 329, 662–665 (2010).
[CrossRef]

Jack, B.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle—orbital angular momentum variables,” Science 329, 662–665 (2010).
[CrossRef]

Jesacher, A.

Jha, A. K.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle—orbital angular momentum variables,” Science 329, 662–665 (2010).
[CrossRef]

Ladavac, K.

Leach, J.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle—orbital angular momentum variables,” Science 329, 662–665 (2010).
[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 plate,” Appl. Phys. Lett. 89, 031105 (2006).
[CrossRef]

Martn-Romo, J. A.

Masajada, J.

McDuff, R.

Monsoriu, J. A.

Niu, L. G.

Nye, J. F.

J. F. Nye and M. V. Berry, “Dislocations in wavetrains,” Proc. R. Soc. A 336, 165–190 (1974).
[CrossRef]

O’Holleran, K.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” in Vol. 53 of Progress in Optics (Elsevier, 2009), Chap. 5, pp. 293–363.
[CrossRef]

Padgett, M. J.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle—orbital angular momentum variables,” Science 329, 662–665 (2010).
[CrossRef]

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” in Vol. 53 of Progress in Optics (Elsevier, 2009), Chap. 5, pp. 293–363.
[CrossRef]

Popiolek-Masajada, A.

Ramirez, L.

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]

Ritsch-Marte, M.

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]

Romero, J.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle—orbital angular momentum variables,” Science 329, 662–665 (2010).
[CrossRef]

Saavedra, G.

Smith, C. P.

Spreeuw, R. J. C.

L. Allen, M. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef]

Sun, H. B.

Swartzlander, G. A.

Tao, S. H.

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

Tiziani, H. J.

Wagemann, E. U.

Wang, R.

White, A. G.

Woerdman, J. P.

L. Allen, M. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef]

Wu, D.

Yao, A. M.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle—orbital angular momentum variables,” Science 329, 662–665 (2010).
[CrossRef]

Yuan, x. C.

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

Am. Math. Mon.

D. R. Chalice, “A characterization of the Cantor function,” Am. Math. Mon. 98, 255–258 (1991).
[CrossRef]

Appl. Opt.

Appl. Phys. B

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.

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

Opt. Express

Opt. Lett.

Phys. Rev. A

L. Allen, M. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef]

Proc. R. Soc. A

P. A. M. Dirac, “Quantised singularities in the electromagnetic field,” Proc. R. Soc. A 133, 60–72 (1931).
[CrossRef]

J. F. Nye and M. V. Berry, “Dislocations in wavetrains,” Proc. R. Soc. A 336, 165–190 (1974).
[CrossRef]

Science

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle—orbital angular momentum variables,” Science 329, 662–665 (2010).
[CrossRef]

Other

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” in Vol. 53 of Progress in Optics (Elsevier, 2009), Chap. 5, pp. 293–363.
[CrossRef]

P. Bak, “The devil’s staircase,” Phys. Today39(12), 38–45 (1986).
[CrossRef]

D. Cottrell, “Coherent Optics freeware,” http://www-rohan.sdsu.edu/~dcottrel/ .

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Figures (6)

Fig. 1.
Fig. 1.

(a) Plot of F3(ζ). (b) Phase variation of Φ3,0(ζ,θ), which is a devil’s lens or a DVL with a charge of 0. (c) Phase variation of Φ3,1(ζ,θ), which is a DVL with a vortex charge of 1.

Fig. 2.
Fig. 2.

Phase plots of each component that makes up a DVFL. The sum of all three phases, where s=3, m=3, and f0=4.62m, produces the final DVFL seen here.

Fig. 3.
Fig. 3.

(a) Irradiance from a DVL with s=3 and m=2, where the z axis goes from 06.85m. (b) Irradiance from the same DVL, but with the addition of a Fresnel lens with a focal length of 1.3 m. The y axis ranges from 665.5μm665.5μm for both plots. The z axis goes from 01.95m. By incorporating a Fresnel lens, the diffracted light is contained in a much closer region.

Fig. 4.
Fig. 4.

Schematic drawing of the optical setup used. The SLM is tilted to reflect the beam along the path away from the incident beam path.

Fig. 5.
Fig. 5.

Side-by-side comparisons of the calculated cross-section irradiance (bottom row) versus experimental data (top row). (a) s=1, m=8; (b) s=2, m=8; (c) s=3, m=8; (d) s=4, m=8. For each plot, both the x and y axes range from [1331μm, 1331 μm].

Fig. 6.
Fig. 6.

Side-by-side comparisons of calculated irradiance versus experimental data. Again, (a) s=1, m=8; (b) s=2, m=8; (c) s=3, m=8; (d) s=4, m=8. For each plot, z ranges from [623 mm, 1463 mm], and y [1331μm, 1331 μm].

Tables (1)

Tables Icon

Table 1. Values of qs,l and ps,l+1 for s=0, 1, 2

Equations (7)

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

Fs(x)={l2s,if,ps,lxqs,l12sxqs,lps,l+1qs,l+l2s,if,qs,lxps,l+1,
Qs(ζ)=exp[i2s+1πFs(ζ)],ζ=(r/a)2,
Φs,m(ζ,θ)=Qs(ζ)radial×Vm(θ)azimuthal,Φs,m(ζ,θ)=exp[i2s+1πFs(ζ)]exp[imθ],
fs=a2/2λ3s.
f1=20.77m,f2=6.92m,f3=2.31m,f4=0.77m.
Lf0(ζ)=exp[iπζa2/λf0],
Ωs,m,f0,(ζ,θ)=Qs(ζ)×Vm(θ)×Lf0(ζ),Ωs,m,f0,(ζ,θ)=exp[i2s+1πFs(ζ)]exp[imθ]exp[iπζa2/λf0].

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