Abstract

Optical vortex beams, generated by Diffractive Optical Elements (DOEs), are capable of creating optical traps and other multi-functional micromanipulators for very specific tasks in the microscopic scale. Using the Fibonacci sequence, we have discovered a new family of DOEs that inherently behave as bifocal vortex lenses, and where the ratio of the two focal distances approaches the golden mean. The disctintive optical properties of these Fibonacci vortex lenses are experimentally demonstrated. We believe that the versatility and potential scalability of these lenses may allow for new applications in micro and nanophotonics.

© 2013 OSA

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References

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  1. A. Sakdinawat and Y. Liu, “Soft-x-ray microscopy using spiral zone plates,” Opt. Lett.32, 2635–2637 (2007).
    [CrossRef] [PubMed]
  2. A. Siemion, A. Siemion, M. Makowski, J. Suszek, J. Bomba, A. Czerwinski, F. Garet, J.-L. Coutaz, and M. Sypek, “Diffractive paper lens for terahertz optics,” Opt. Lett.37, 4320–4322 (2012).
    [CrossRef] [PubMed]
  3. G. Saavedra, W. D. Furlan, and J. A. Monsoriu, “Fractal zone plates,” Opt. Lett.28, 971–973 (2003).
    [CrossRef] [PubMed]
  4. J. A. Davis, S. P. Sigarlaki, J. M. Craven, and M. L. Calvo, “Fourier series analysis of fractal lenses: theory and experiments with a liquid-crystal display,” Appl. Opt.45, 1187–1192 (2006).
    [CrossRef] [PubMed]
  5. W. D. Furlan, G. Saavedra, and J. A. Monsoriu, “White-light imaging with fractal zone plates,” Opt. Lett.32, 2109–2111 (2007).
    [CrossRef] [PubMed]
  6. F. S. Roux, “Distribution of angular momentum and vortex morphology in optical beams,” Opt. Commun.242, 45–55 (2004).
    [CrossRef]
  7. G. Gbur and T. D. Visser, “Phase singularities and coherence vortices in linear optical systems,” Opt. Commun.259, 428–435 (2006).
    [CrossRef]
  8. A. Bishop, T. Nieminen, N. Heckenberg, and H. Rubinsztein-Dunlop, “Optical application and measurement of torque on microparticles of isotropic nonabsorbing material,” Phys. Rev. A68, 033802 (2003).
    [CrossRef]
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    [CrossRef] [PubMed]
  11. S. H. Tao, X.-C. Yuan, J. Lin, and R. E. Burge, “Sequence of focused optical vortices generated by a spiral fractal zone plate,” Appl. Phys. Lett.89, 031105 (2006).
    [CrossRef]
  12. W. D. Furlan, F. Giménez, A. Calatayud, and J. A. Monsoriu, “Devils vortex-lenses,” Opt. Express17, 21891–21896 (2009).
    [CrossRef] [PubMed]
  13. J. A. Monsoriu, A. Calatayud, L. Remón, W. D. Furlan, G. Saavedra, and P. Andrés, “Zone plates generated with the Fibonacci sequence,” in Proceedings of EOS Topical Meeting on Diffractive Optics, pp. 151–152 (2010).
  14. J. A. Monsoriu, A. Calatayud, L. Remón, W. D. Furlan, G. Saavedra, and P. Andrés, “Bifocal Fibonacci diffractive lenses,” IEEE Photon. J. (to be published), DOI: .
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  20. J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett.90, 133901 (2003).
    [CrossRef] [PubMed]
  21. A. Calatayud, W. D. Furlan, and J. A. Monsoriu, “Experimental generation and characterization of devils vortex-lenses,” Appl. Phys. B106, 915–919 (2012).
    [CrossRef]

2012

E. Maciá, “Exploiting aperiodic designs in nanophotonic devices,” Rep. Prog. Phys.75, 1–42 (2012).
[CrossRef]

A. Calatayud, W. D. Furlan, and J. A. Monsoriu, “Experimental generation and characterization of devils vortex-lenses,” Appl. Phys. B106, 915–919 (2012).
[CrossRef]

A. Siemion, A. Siemion, M. Makowski, J. Suszek, J. Bomba, A. Czerwinski, F. Garet, J.-L. Coutaz, and M. Sypek, “Diffractive paper lens for terahertz optics,” Opt. Lett.37, 4320–4322 (2012).
[CrossRef] [PubMed]

2011

2010

J. A. Monsoriu, A. Calatayud, L. Remón, W. D. Furlan, G. Saavedra, and P. Andrés, “Zone plates generated with the Fibonacci sequence,” in Proceedings of EOS Topical Meeting on Diffractive Optics, pp. 151–152 (2010).

2009

2007

2006

J. A. Davis, S. P. Sigarlaki, J. M. Craven, and M. L. Calvo, “Fourier series analysis of fractal lenses: theory and experiments with a liquid-crystal display,” Appl. Opt.45, 1187–1192 (2006).
[CrossRef] [PubMed]

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. E. Burge, “Sequence of focused optical vortices generated by a spiral fractal zone plate,” Appl. Phys. Lett.89, 031105 (2006).
[CrossRef]

2004

2003

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

A. Bishop, T. Nieminen, N. Heckenberg, and H. Rubinsztein-Dunlop, “Optical application and measurement of torque on microparticles of isotropic nonabsorbing material,” Phys. Rev. A68, 033802 (2003).
[CrossRef]

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

2001

1995

Y. Sah and G. Ranganath, “Optical diffraction in some Fibonacci structures,” Opt. Commun.114, 18–24 (1995).
[CrossRef]

Andrés, P.

J. A. Monsoriu, A. Calatayud, L. Remón, W. D. Furlan, G. Saavedra, and P. Andrés, “Zone plates generated with the Fibonacci sequence,” in Proceedings of EOS Topical Meeting on Diffractive Optics, pp. 151–152 (2010).

J. A. Monsoriu, A. Calatayud, L. Remón, W. D. Furlan, G. Saavedra, and P. Andrés, “Bifocal Fibonacci diffractive lenses,” IEEE Photon. J. (to be published), DOI: .
[CrossRef]

Bishop, A.

A. Bishop, T. Nieminen, N. Heckenberg, and H. Rubinsztein-Dunlop, “Optical application and measurement of torque on microparticles of isotropic nonabsorbing material,” Phys. Rev. A68, 033802 (2003).
[CrossRef]

Bomba, J.

Burge, R. E.

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

Calatayud, A.

A. Calatayud, W. D. Furlan, and J. A. Monsoriu, “Experimental generation and characterization of devils vortex-lenses,” Appl. Phys. B106, 915–919 (2012).
[CrossRef]

J. A. Monsoriu, A. Calatayud, L. Remón, W. D. Furlan, G. Saavedra, and P. Andrés, “Zone plates generated with the Fibonacci sequence,” in Proceedings of EOS Topical Meeting on Diffractive Optics, pp. 151–152 (2010).

W. D. Furlan, F. Giménez, A. Calatayud, and J. A. Monsoriu, “Devils vortex-lenses,” Opt. Express17, 21891–21896 (2009).
[CrossRef] [PubMed]

J. A. Monsoriu, A. Calatayud, L. Remón, W. D. Furlan, G. Saavedra, and P. Andrés, “Bifocal Fibonacci diffractive lenses,” IEEE Photon. J. (to be published), DOI: .
[CrossRef]

Calvo, M. L.

Cheong, W. C.

Coutaz, J.-L.

Craven, J. M.

Curtis, J. E.

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

Czerwinski, A.

Dai, H. T.

H. T. Dai, Y. J. Liu, and X. W. Sun, “The focusing property of the spiral Fibonacci zone plate,” in Optical Components and Materials IX, S. Jiang, M. J. F. Digonnet, and J. C. Dries, eds., Proc. SPIE8257, 82570T1 (2012).
[CrossRef]

Davis, J. A.

Furlan, W. D.

A. Calatayud, W. D. Furlan, and J. A. Monsoriu, “Experimental generation and characterization of devils vortex-lenses,” Appl. Phys. B106, 915–919 (2012).
[CrossRef]

J. A. Monsoriu, A. Calatayud, L. Remón, W. D. Furlan, G. Saavedra, and P. Andrés, “Zone plates generated with the Fibonacci sequence,” in Proceedings of EOS Topical Meeting on Diffractive Optics, pp. 151–152 (2010).

W. D. Furlan, F. Giménez, A. Calatayud, and J. A. Monsoriu, “Devils vortex-lenses,” Opt. Express17, 21891–21896 (2009).
[CrossRef] [PubMed]

W. D. Furlan, G. Saavedra, and J. A. Monsoriu, “White-light imaging with fractal zone plates,” Opt. Lett.32, 2109–2111 (2007).
[CrossRef] [PubMed]

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

J. A. Monsoriu, A. Calatayud, L. Remón, W. D. Furlan, G. Saavedra, and P. Andrés, “Bifocal Fibonacci diffractive lenses,” IEEE Photon. J. (to be published), DOI: .
[CrossRef]

Gao, N.

Garet, F.

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.

Grier, D. G.

Heckenberg, N.

A. Bishop, T. Nieminen, N. Heckenberg, and H. Rubinsztein-Dunlop, “Optical application and measurement of torque on microparticles of isotropic nonabsorbing material,” Phys. Rev. A68, 033802 (2003).
[CrossRef]

Ladavac, K.

Lee, W. M.

Lin, J.

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

Liu, Y.

Liu, Y. J.

H. T. Dai, Y. J. Liu, and X. W. Sun, “The focusing property of the spiral Fibonacci zone plate,” in Optical Components and Materials IX, S. Jiang, M. J. F. Digonnet, and J. C. Dries, eds., Proc. SPIE8257, 82570T1 (2012).
[CrossRef]

Maciá, E.

E. Maciá, “Exploiting aperiodic designs in nanophotonic devices,” Rep. Prog. Phys.75, 1–42 (2012).
[CrossRef]

Makowski, M.

Monsoriu, J. A.

A. Calatayud, W. D. Furlan, and J. A. Monsoriu, “Experimental generation and characterization of devils vortex-lenses,” Appl. Phys. B106, 915–919 (2012).
[CrossRef]

J. A. Monsoriu, A. Calatayud, L. Remón, W. D. Furlan, G. Saavedra, and P. Andrés, “Zone plates generated with the Fibonacci sequence,” in Proceedings of EOS Topical Meeting on Diffractive Optics, pp. 151–152 (2010).

W. D. Furlan, F. Giménez, A. Calatayud, and J. A. Monsoriu, “Devils vortex-lenses,” Opt. Express17, 21891–21896 (2009).
[CrossRef] [PubMed]

W. D. Furlan, G. Saavedra, and J. A. Monsoriu, “White-light imaging with fractal zone plates,” Opt. Lett.32, 2109–2111 (2007).
[CrossRef] [PubMed]

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

J. A. Monsoriu, A. Calatayud, L. Remón, W. D. Furlan, G. Saavedra, and P. Andrés, “Bifocal Fibonacci diffractive lenses,” IEEE Photon. J. (to be published), DOI: .
[CrossRef]

Nieminen, T.

A. Bishop, T. Nieminen, N. Heckenberg, and H. Rubinsztein-Dunlop, “Optical application and measurement of torque on microparticles of isotropic nonabsorbing material,” Phys. Rev. A68, 033802 (2003).
[CrossRef]

Ranganath, G.

Y. Sah and G. Ranganath, “Optical diffraction in some Fibonacci structures,” Opt. Commun.114, 18–24 (1995).
[CrossRef]

Remón, L.

J. A. Monsoriu, A. Calatayud, L. Remón, W. D. Furlan, G. Saavedra, and P. Andrés, “Zone plates generated with the Fibonacci sequence,” in Proceedings of EOS Topical Meeting on Diffractive Optics, pp. 151–152 (2010).

J. A. Monsoriu, A. Calatayud, L. Remón, W. D. Furlan, G. Saavedra, and P. Andrés, “Bifocal Fibonacci diffractive lenses,” IEEE Photon. J. (to be published), DOI: .
[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.

A. Bishop, T. Nieminen, N. Heckenberg, and H. Rubinsztein-Dunlop, “Optical application and measurement of torque on microparticles of isotropic nonabsorbing material,” Phys. Rev. A68, 033802 (2003).
[CrossRef]

Saavedra, G.

J. A. Monsoriu, A. Calatayud, L. Remón, W. D. Furlan, G. Saavedra, and P. Andrés, “Zone plates generated with the Fibonacci sequence,” in Proceedings of EOS Topical Meeting on Diffractive Optics, pp. 151–152 (2010).

W. D. Furlan, G. Saavedra, and J. A. Monsoriu, “White-light imaging with fractal zone plates,” Opt. Lett.32, 2109–2111 (2007).
[CrossRef] [PubMed]

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

J. A. Monsoriu, A. Calatayud, L. Remón, W. D. Furlan, G. Saavedra, and P. Andrés, “Bifocal Fibonacci diffractive lenses,” IEEE Photon. J. (to be published), DOI: .
[CrossRef]

Sah, Y.

Y. Sah and G. Ranganath, “Optical diffraction in some Fibonacci structures,” Opt. Commun.114, 18–24 (1995).
[CrossRef]

Sakdinawat, A.

Siemion, A.

Sigarlaki, S. P.

Sun, X. W.

H. T. Dai, Y. J. Liu, and X. W. Sun, “The focusing property of the spiral Fibonacci zone plate,” in Optical Components and Materials IX, S. Jiang, M. J. F. Digonnet, and J. C. Dries, eds., Proc. SPIE8257, 82570T1 (2012).
[CrossRef]

Suszek, J.

Swartzlander, J.

Sypek, M.

Tao, S. H.

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

Xie, C.

Yuan, X.-C.

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

W. M. Lee, X.-C. Yuan, and W. C. Cheong, “Optical vortex beam shaping by use of highly efficient irregular spiral phase plates for optical micromanipulation,” Opt. Lett.29, 1796–1798 (2004).
[CrossRef] [PubMed]

Zhang, Y.

Appl. Opt.

Appl. Phys. B

A. Calatayud, W. D. Furlan, and J. A. Monsoriu, “Experimental generation and characterization of devils vortex-lenses,” Appl. Phys. B106, 915–919 (2012).
[CrossRef]

Appl. Phys. Lett.

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

Opt. Commun.

Y. Sah and G. Ranganath, “Optical diffraction in some Fibonacci structures,” Opt. Commun.114, 18–24 (1995).
[CrossRef]

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

Opt. Lett.

Phys. Rev. A

A. Bishop, T. Nieminen, N. Heckenberg, and H. Rubinsztein-Dunlop, “Optical application and measurement of torque on microparticles of isotropic nonabsorbing material,” Phys. Rev. A68, 033802 (2003).
[CrossRef]

Phys. Rev. Lett.

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

Proceedings of EOS Topical Meeting on Diffractive Optics

J. A. Monsoriu, A. Calatayud, L. Remón, W. D. Furlan, G. Saavedra, and P. Andrés, “Zone plates generated with the Fibonacci sequence,” in Proceedings of EOS Topical Meeting on Diffractive Optics, pp. 151–152 (2010).

Rep. Prog. Phys.

E. Maciá, “Exploiting aperiodic designs in nanophotonic devices,” Rep. Prog. Phys.75, 1–42 (2012).
[CrossRef]

Other

H. T. Dai, Y. J. Liu, and X. W. Sun, “The focusing property of the spiral Fibonacci zone plate,” in Optical Components and Materials IX, S. Jiang, M. J. F. Digonnet, and J. C. Dries, eds., Proc. SPIE8257, 82570T1 (2012).
[CrossRef]

J. A. Monsoriu, A. Calatayud, L. Remón, W. D. Furlan, G. Saavedra, and P. Andrés, “Bifocal Fibonacci diffractive lenses,” IEEE Photon. J. (to be published), DOI: .
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Bottom: Phase distributions of FVLs based on the Fibonacci sequence S8, with different topological charges. Top: The equivalent periodic lenses with the same number of zones.

Fig. 2
Fig. 2

Evolution of the transverse irradiance for S8 based FVLs with different topological charges and their periodic equivalent lenses.

Fig. 3
Fig. 3

Experimental setup used for studying the focusing properties of FVLs.

Fig. 4
Fig. 4

Experimental and computed transverse irradiance evolution along the optical axis provided by the S8 FVL with m = 6 and a = 1.1mm.

Fig. 5
Fig. 5

Experimental and numerical transverse irradiance at the focal planes provided by the S8 based on FVL with m = 6 and a = 1.1mm. The intensity profiles along the white, dotted lines are plotted (bottom) together with the numerical results for comparison.

Equations (4)

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

φ = lim j F j / F j 1 = ( 1 + 5 ) / 2 .
I ( u , v , θ ) = u 2 | 0 1 0 2 π t ( ζ , θ 0 ) exp ( i 2 π u ζ ) exp [ i 4 π u v ζ 1 / 2 cos ( θ θ 0 ) ] d ζ d θ 0 | 2 ,
0 2 π exp ( i m θ 0 ) exp [ i 4 π u v ζ 1 / 2 cos ( θ θ 0 ) ] d θ 0 = 2 π exp [ i m ( θ + π 2 ) ] J m ( 4 π u v ζ 1 / 2 ) ,
I ( u , v ) = 4 π 2 u 2 | 0 1 q ( ζ ) exp ( i 2 π u ζ ) J m ( 4 π u v ζ 1 / 2 ) d ζ | 2 ,

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