Abstract

Fibonacci zone plates are proving to be promising candidates in image forming devices. In this letter we show that the set of Fibonacci zone plates are a particular member of a new family of diffractive lenses which can be designed on the basis of a given m-bonacci sequence. These lenses produce twin axial foci whose separation depends on the m-golden mean. Therefore, with this generalization, bifocal systems can be freely designed under the requirement at particular focal planes. Experimental results support our proposal.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]
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  3. Q. Zhang, J. Wang, M. Wang, J. Bu, S. Zhu, B. Z. Gao, and X. Yuan, “Depth of focus enhancement of a modified imaging quasi-fractal zone plate,” Opt. Laser Technol. 44(7), 2140–2144 (2012).
    [Crossref] [PubMed]
  4. W. D. Furlan, G. Saavedra, and J. A. Monsoriu, “White-light imaging with fractal zone plates,” Opt. Lett. 32(15), 2109–2111 (2007).
    [Crossref] [PubMed]
  5. V. Ferrando, F. Giménez, W. D. Furlan, and J. A. Monsoriu, “Bifractal focusing and imaging properties of Thue-Morse Zone Plates,” Opt. Express 23(15), 19846–19853 (2015).
    [Crossref] [PubMed]
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  7. J. Monsoriu, G. Saavedra, and W. Furlan, “Fractal zone plates with variable lacunarity,” Opt. Express 12(18), 4227–4234 (2004).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  20. A. K. Yadav, S. Vashisth, H. Singh, and K. Singh, “A phase-image watermarking scheme in gyrator domain using devil’s vortex Fresnel lens as a phase mask,” Opt. Commun. 344, 172–180 (2015).
    [Crossref]
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    [Crossref]
  26. A. Calatayud, V. Ferrando, L. Remón, W. D. Furlan, and J. A. Monsoriu, “Twin axial vortices generated by Fibonacci lenses,” Opt. Express 21(8), 10234–10239 (2013).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]

2016 (3)

S. Cheng, X. Zhang, W. Ma, and S. Tao, “Fractal zone plate beam based optical tweezers,” Sci. Rep. 6(1), 34492 (2016).
[Crossref] [PubMed]

W. D. Furlan, V. Ferrando, J. A. Monsoriu, P. Zagrajek, E. Czerwińska, and M. Szustakowski, “3D printed diffractive terahertz lenses,” Opt. Lett. 41(8), 1748–1751 (2016).
[Crossref] [PubMed]

K. Wu and G. P. Wang, “Two-dimensional Fibonacci grating for far-field super-resolution imaging,” Sci. Rep. 6(1), 38651 (2016).
[Crossref] [PubMed]

2015 (5)

A. K. Yadav, S. Vashisth, H. Singh, and K. Singh, “A phase-image watermarking scheme in gyrator domain using devil’s vortex Fresnel lens as a phase mask,” Opt. Commun. 344, 172–180 (2015).
[Crossref]

J. Ke and J. Zhang, “Generalized Fibonacci photon sieves,” Appl. Opt. 54(24), 7278–7283 (2015).
[Crossref] [PubMed]

J. A. Monsoriu, M. H. Giménez, W. D. Furlan, J. C. Barreiro, and G. Saavedra, “Diffraction by m-bonacci gratings,” Eur. J. Phys. 36(6), 65005 (2015).
[Crossref]

J. Pu and P. H. Jones, “Devil’s lens optical tweezers,” Opt. Express 23(7), 8190–8199 (2015).
[Crossref] [PubMed]

V. Ferrando, F. Giménez, W. D. Furlan, and J. A. Monsoriu, “Bifractal focusing and imaging properties of Thue-Morse Zone Plates,” Opt. Express 23(15), 19846–19853 (2015).
[Crossref] [PubMed]

2014 (3)

2013 (5)

2012 (3)

J. F. Barrera, M. Tebaldi, D. Amaya, W. D. Furlan, J. A. Monsoriu, N. Bolognini, and R. Torroba, “Multiplexing of encrypted data using fractal masks,” Opt. Lett. 37(14), 2895–2897 (2012).
[Crossref] [PubMed]

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Wu, J. Chen, Z. Pan, K. Zhang, Y. Hong, P. Zhu, and Z. Wu, “Use of fractal zone plates for transmission X-ray microscopy,” Anal. Bioanal. Chem. 404(5), 1303–1309 (2012).
[Crossref] [PubMed]

Q. Zhang, J. Wang, M. Wang, J. Bu, S. Zhu, B. Z. Gao, and X. Yuan, “Depth of focus enhancement of a modified imaging quasi-fractal zone plate,” Opt. Laser Technol. 44(7), 2140–2144 (2012).
[Crossref] [PubMed]

2011 (1)

2010 (1)

2009 (1)

2008 (1)

H. Dai, J. Liu, S. Xuecheng, and Y. Dejin, “Programmable fractal zone plates (FraZPs) with foci finely tuned,” Opt. Commun. 281(22), 5515–5519 (2008).
[Crossref]

2007 (1)

2006 (2)

J. A. Monsoriu, C. J. Zapata-Rodriguez, and W. D. Furlan, “Fractal axicons,” Opt. Commun. 263(1), 1–5 (2006).
[Crossref]

F. Giménez, J. A. Monsoriu, W. D. Furlan, and A. Pons, “Fractal photon sieve,” Opt. Express 14(25), 11958–11963 (2006).
[Crossref] [PubMed]

2004 (1)

2003 (1)

Amaya, D.

Andrés, P.

V. Ferrando, A. Calatayud, P. Andrés, R. Torroba, W. D. Furlan, and J. A. Monsoriu, “Imaging properties of Kinoform Fibonacci lenses,” IEEE Photonics J. 6(1), 6500106 (2014).
[Crossref]

J. A. Monsoriu, A. Calatayud, L. Remón, W. D. Furlan, G. Saavedra, and P. Andrés, “Bifocal Fibonacci diffraction lenses,” IEEE Photonics J. 5(3), 3400106 (2013).
[Crossref]

Banerjee, V.

Barreiro, J. C.

J. A. Monsoriu, M. H. Giménez, W. D. Furlan, J. C. Barreiro, and G. Saavedra, “Diffraction by m-bonacci gratings,” Eur. J. Phys. 36(6), 65005 (2015).
[Crossref]

Barrera, J. F.

Bolognini, N.

Bu, J.

Q. Zhang, J. Wang, M. Wang, J. Bu, S. Zhu, B. Z. Gao, and X. Yuan, “Depth of focus enhancement of a modified imaging quasi-fractal zone plate,” Opt. Laser Technol. 44(7), 2140–2144 (2012).
[Crossref] [PubMed]

Calabuig, A.

Calatayud, A.

Chen, J.

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Wu, J. Chen, Z. Pan, K. Zhang, Y. Hong, P. Zhu, and Z. Wu, “Use of fractal zone plates for transmission X-ray microscopy,” Anal. Bioanal. Chem. 404(5), 1303–1309 (2012).
[Crossref] [PubMed]

Cheng, S.

S. Cheng, X. Zhang, W. Ma, and S. Tao, “Fractal zone plate beam based optical tweezers,” Sci. Rep. 6(1), 34492 (2016).
[Crossref] [PubMed]

Czerwinska, E.

Dai, H.

H. Dai, J. Liu, S. Xuecheng, and Y. Dejin, “Programmable fractal zone plates (FraZPs) with foci finely tuned,” Opt. Commun. 281(22), 5515–5519 (2008).
[Crossref]

Dejin, Y.

H. Dai, J. Liu, S. Xuecheng, and Y. Dejin, “Programmable fractal zone plates (FraZPs) with foci finely tuned,” Opt. Commun. 281(22), 5515–5519 (2008).
[Crossref]

Fernández-Alonso, M.

Ferrando, V.

Furlan, W.

Furlan, W. D.

W. D. Furlan, V. Ferrando, J. A. Monsoriu, P. Zagrajek, E. Czerwińska, and M. Szustakowski, “3D printed diffractive terahertz lenses,” Opt. Lett. 41(8), 1748–1751 (2016).
[Crossref] [PubMed]

J. A. Monsoriu, M. H. Giménez, W. D. Furlan, J. C. Barreiro, and G. Saavedra, “Diffraction by m-bonacci gratings,” Eur. J. Phys. 36(6), 65005 (2015).
[Crossref]

V. Ferrando, F. Giménez, W. D. Furlan, and J. A. Monsoriu, “Bifractal focusing and imaging properties of Thue-Morse Zone Plates,” Opt. Express 23(15), 19846–19853 (2015).
[Crossref] [PubMed]

V. Ferrando, A. Calatayud, P. Andrés, R. Torroba, W. D. Furlan, and J. A. Monsoriu, “Imaging properties of Kinoform Fibonacci lenses,” IEEE Photonics J. 6(1), 6500106 (2014).
[Crossref]

A. Calatayud, V. Ferrando, L. Remón, W. D. Furlan, and J. A. Monsoriu, “Twin axial vortices generated by Fibonacci lenses,” Opt. Express 21(8), 10234–10239 (2013).
[Crossref] [PubMed]

J. A. Monsoriu, A. Calatayud, L. Remón, W. D. Furlan, G. Saavedra, and P. Andrés, “Bifocal Fibonacci diffraction lenses,” IEEE Photonics J. 5(3), 3400106 (2013).
[Crossref]

V. Ferrando, A. Calatayud, F. Giménez, W. D. Furlan, and J. A. Monsoriu, “Cantor dust zone plates,” Opt. Express 21(3), 2701–2706 (2013).
[Crossref] [PubMed]

A. Calabuig, S. Sánchez-Ruiz, L. Martínez-León, E. Tajahuerce, M. Fernández-Alonso, W. D. Furlan, J. A. Monsoriu, and A. Pons-Martí, “Generation of programmable 3D optical vortex structures through devil’s vortex-lens arrays,” Appl. Opt. 52(23), 5822–5829 (2013).
[Crossref] [PubMed]

J. F. Barrera, M. Tebaldi, D. Amaya, W. D. Furlan, J. A. Monsoriu, N. Bolognini, and R. Torroba, “Multiplexing of encrypted data using fractal masks,” Opt. Lett. 37(14), 2895–2897 (2012).
[Crossref] [PubMed]

F. Giménez, W. D. Furlan, A. Calatayud, and J. A. Monsoriu, “Multifractal zone plates,” J. Opt. Soc. Am. A 27(8), 1851–1855 (2010).
[Crossref] [PubMed]

M. Tebaldi, W. D. Furlan, R. Torroba, and N. Bolognini, “Optical-data storage-readout technique based on fractal encrypting masks,” Opt. Lett. 34(3), 316–318 (2009).
[Crossref] [PubMed]

W. D. Furlan, G. Saavedra, and J. A. Monsoriu, “White-light imaging with fractal zone plates,” Opt. Lett. 32(15), 2109–2111 (2007).
[Crossref] [PubMed]

J. A. Monsoriu, C. J. Zapata-Rodriguez, and W. D. Furlan, “Fractal axicons,” Opt. Commun. 263(1), 1–5 (2006).
[Crossref]

F. Giménez, J. A. Monsoriu, W. D. Furlan, and A. Pons, “Fractal photon sieve,” Opt. Express 14(25), 11958–11963 (2006).
[Crossref] [PubMed]

G. Saavedra, W. D. Furlan, and J. A. Monsoriu, “Fractal zone plates,” Opt. Lett. 28(12), 971–973 (2003).
[Crossref] [PubMed]

Gao, B. Z.

Q. Zhang, J. Wang, M. Wang, J. Bu, S. Zhu, B. Z. Gao, and X. Yuan, “Depth of focus enhancement of a modified imaging quasi-fractal zone plate,” Opt. Laser Technol. 44(7), 2140–2144 (2012).
[Crossref] [PubMed]

Gao, K.

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Wu, J. Chen, Z. Pan, K. Zhang, Y. Hong, P. Zhu, and Z. Wu, “Use of fractal zone plates for transmission X-ray microscopy,” Anal. Bioanal. Chem. 404(5), 1303–1309 (2012).
[Crossref] [PubMed]

Gao, N.

Ge, X.

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Wu, J. Chen, Z. Pan, K. Zhang, Y. Hong, P. Zhu, and Z. Wu, “Use of fractal zone plates for transmission X-ray microscopy,” Anal. Bioanal. Chem. 404(5), 1303–1309 (2012).
[Crossref] [PubMed]

Giménez, F.

Giménez, M. H.

J. A. Monsoriu, M. H. Giménez, W. D. Furlan, J. C. Barreiro, and G. Saavedra, “Diffraction by m-bonacci gratings,” Eur. J. Phys. 36(6), 65005 (2015).
[Crossref]

Hong, Y.

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Wu, J. Chen, Z. Pan, K. Zhang, Y. Hong, P. Zhu, and Z. Wu, “Use of fractal zone plates for transmission X-ray microscopy,” Anal. Bioanal. Chem. 404(5), 1303–1309 (2012).
[Crossref] [PubMed]

Jones, P. H.

Ke, J.

Liu, J.

H. Dai, J. Liu, S. Xuecheng, and Y. Dejin, “Programmable fractal zone plates (FraZPs) with foci finely tuned,” Opt. Commun. 281(22), 5515–5519 (2008).
[Crossref]

Ma, W.

S. Cheng, X. Zhang, W. Ma, and S. Tao, “Fractal zone plate beam based optical tweezers,” Sci. Rep. 6(1), 34492 (2016).
[Crossref] [PubMed]

Martínez-León, L.

Monsoriu, J.

Monsoriu, J. A.

W. D. Furlan, V. Ferrando, J. A. Monsoriu, P. Zagrajek, E. Czerwińska, and M. Szustakowski, “3D printed diffractive terahertz lenses,” Opt. Lett. 41(8), 1748–1751 (2016).
[Crossref] [PubMed]

J. A. Monsoriu, M. H. Giménez, W. D. Furlan, J. C. Barreiro, and G. Saavedra, “Diffraction by m-bonacci gratings,” Eur. J. Phys. 36(6), 65005 (2015).
[Crossref]

V. Ferrando, F. Giménez, W. D. Furlan, and J. A. Monsoriu, “Bifractal focusing and imaging properties of Thue-Morse Zone Plates,” Opt. Express 23(15), 19846–19853 (2015).
[Crossref] [PubMed]

V. Ferrando, A. Calatayud, P. Andrés, R. Torroba, W. D. Furlan, and J. A. Monsoriu, “Imaging properties of Kinoform Fibonacci lenses,” IEEE Photonics J. 6(1), 6500106 (2014).
[Crossref]

A. Calatayud, V. Ferrando, L. Remón, W. D. Furlan, and J. A. Monsoriu, “Twin axial vortices generated by Fibonacci lenses,” Opt. Express 21(8), 10234–10239 (2013).
[Crossref] [PubMed]

J. A. Monsoriu, A. Calatayud, L. Remón, W. D. Furlan, G. Saavedra, and P. Andrés, “Bifocal Fibonacci diffraction lenses,” IEEE Photonics J. 5(3), 3400106 (2013).
[Crossref]

A. Calabuig, S. Sánchez-Ruiz, L. Martínez-León, E. Tajahuerce, M. Fernández-Alonso, W. D. Furlan, J. A. Monsoriu, and A. Pons-Martí, “Generation of programmable 3D optical vortex structures through devil’s vortex-lens arrays,” Appl. Opt. 52(23), 5822–5829 (2013).
[Crossref] [PubMed]

V. Ferrando, A. Calatayud, F. Giménez, W. D. Furlan, and J. A. Monsoriu, “Cantor dust zone plates,” Opt. Express 21(3), 2701–2706 (2013).
[Crossref] [PubMed]

J. F. Barrera, M. Tebaldi, D. Amaya, W. D. Furlan, J. A. Monsoriu, N. Bolognini, and R. Torroba, “Multiplexing of encrypted data using fractal masks,” Opt. Lett. 37(14), 2895–2897 (2012).
[Crossref] [PubMed]

F. Giménez, W. D. Furlan, A. Calatayud, and J. A. Monsoriu, “Multifractal zone plates,” J. Opt. Soc. Am. A 27(8), 1851–1855 (2010).
[Crossref] [PubMed]

W. D. Furlan, G. Saavedra, and J. A. Monsoriu, “White-light imaging with fractal zone plates,” Opt. Lett. 32(15), 2109–2111 (2007).
[Crossref] [PubMed]

J. A. Monsoriu, C. J. Zapata-Rodriguez, and W. D. Furlan, “Fractal axicons,” Opt. Commun. 263(1), 1–5 (2006).
[Crossref]

F. Giménez, J. A. Monsoriu, W. D. Furlan, and A. Pons, “Fractal photon sieve,” Opt. Express 14(25), 11958–11963 (2006).
[Crossref] [PubMed]

G. Saavedra, W. D. Furlan, and J. A. Monsoriu, “Fractal zone plates,” Opt. Lett. 28(12), 971–973 (2003).
[Crossref] [PubMed]

Pan, Z.

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Wu, J. Chen, Z. Pan, K. Zhang, Y. Hong, P. Zhu, and Z. Wu, “Use of fractal zone plates for transmission X-ray microscopy,” Anal. Bioanal. Chem. 404(5), 1303–1309 (2012).
[Crossref] [PubMed]

Pons, A.

Pons-Martí, A.

Pu, J.

Remón, L.

J. A. Monsoriu, A. Calatayud, L. Remón, W. D. Furlan, G. Saavedra, and P. Andrés, “Bifocal Fibonacci diffraction lenses,” IEEE Photonics J. 5(3), 3400106 (2013).
[Crossref]

A. Calatayud, V. Ferrando, L. Remón, W. D. Furlan, and J. A. Monsoriu, “Twin axial vortices generated by Fibonacci lenses,” Opt. Express 21(8), 10234–10239 (2013).
[Crossref] [PubMed]

Saavedra, G.

J. A. Monsoriu, M. H. Giménez, W. D. Furlan, J. C. Barreiro, and G. Saavedra, “Diffraction by m-bonacci gratings,” Eur. J. Phys. 36(6), 65005 (2015).
[Crossref]

J. A. Monsoriu, A. Calatayud, L. Remón, W. D. Furlan, G. Saavedra, and P. Andrés, “Bifocal Fibonacci diffraction lenses,” IEEE Photonics J. 5(3), 3400106 (2013).
[Crossref]

W. D. Furlan, G. Saavedra, and J. A. Monsoriu, “White-light imaging with fractal zone plates,” Opt. Lett. 32(15), 2109–2111 (2007).
[Crossref] [PubMed]

J. Monsoriu, G. Saavedra, and W. Furlan, “Fractal zone plates with variable lacunarity,” Opt. Express 12(18), 4227–4234 (2004).
[Crossref] [PubMed]

G. Saavedra, W. D. Furlan, and J. A. Monsoriu, “Fractal zone plates,” Opt. Lett. 28(12), 971–973 (2003).
[Crossref] [PubMed]

Sánchez-Ruiz, S.

Senthilkumaran, P.

Sharma, M. K.

Singh, H.

A. K. Yadav, S. Vashisth, H. Singh, and K. Singh, “A phase-image watermarking scheme in gyrator domain using devil’s vortex Fresnel lens as a phase mask,” Opt. Commun. 344, 172–180 (2015).
[Crossref]

Singh, K.

A. K. Yadav, S. Vashisth, H. Singh, and K. Singh, “A phase-image watermarking scheme in gyrator domain using devil’s vortex Fresnel lens as a phase mask,” Opt. Commun. 344, 172–180 (2015).
[Crossref]

Szustakowski, M.

Tajahuerce, E.

Tao, S.

S. Cheng, X. Zhang, W. Ma, and S. Tao, “Fractal zone plate beam based optical tweezers,” Sci. Rep. 6(1), 34492 (2016).
[Crossref] [PubMed]

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(3), 035003 (2013).
[Crossref]

Tebaldi, M.

Torroba, R.

Vashisth, S.

A. K. Yadav, S. Vashisth, H. Singh, and K. Singh, “A phase-image watermarking scheme in gyrator domain using devil’s vortex Fresnel lens as a phase mask,” Opt. Commun. 344, 172–180 (2015).
[Crossref]

Verma, R.

Wang, D.

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Wu, J. Chen, Z. Pan, K. Zhang, Y. Hong, P. Zhu, and Z. Wu, “Use of fractal zone plates for transmission X-ray microscopy,” Anal. Bioanal. Chem. 404(5), 1303–1309 (2012).
[Crossref] [PubMed]

Wang, G. P.

K. Wu and G. P. Wang, “Two-dimensional Fibonacci grating for far-field super-resolution imaging,” Sci. Rep. 6(1), 38651 (2016).
[Crossref] [PubMed]

Wang, J.

Q. Zhang, J. Wang, M. Wang, J. Bu, S. Zhu, B. Z. Gao, and X. Yuan, “Depth of focus enhancement of a modified imaging quasi-fractal zone plate,” Opt. Laser Technol. 44(7), 2140–2144 (2012).
[Crossref] [PubMed]

Wang, M.

Q. Zhang, J. Wang, M. Wang, J. Bu, S. Zhu, B. Z. Gao, and X. Yuan, “Depth of focus enhancement of a modified imaging quasi-fractal zone plate,” Opt. Laser Technol. 44(7), 2140–2144 (2012).
[Crossref] [PubMed]

Wang, Z.

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Wu, J. Chen, Z. Pan, K. Zhang, Y. Hong, P. Zhu, and Z. Wu, “Use of fractal zone plates for transmission X-ray microscopy,” Anal. Bioanal. Chem. 404(5), 1303–1309 (2012).
[Crossref] [PubMed]

Wu, K.

K. Wu and G. P. Wang, “Two-dimensional Fibonacci grating for far-field super-resolution imaging,” Sci. Rep. 6(1), 38651 (2016).
[Crossref] [PubMed]

Wu, Z.

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Wu, J. Chen, Z. Pan, K. Zhang, Y. Hong, P. Zhu, and Z. Wu, “Use of fractal zone plates for transmission X-ray microscopy,” Anal. Bioanal. Chem. 404(5), 1303–1309 (2012).
[Crossref] [PubMed]

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Wu, J. Chen, Z. Pan, K. Zhang, Y. Hong, P. Zhu, and Z. Wu, “Use of fractal zone plates for transmission X-ray microscopy,” Anal. Bioanal. Chem. 404(5), 1303–1309 (2012).
[Crossref] [PubMed]

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(3), 035003 (2013).
[Crossref]

Xie, C.

Xuecheng, S.

H. Dai, J. Liu, S. Xuecheng, and Y. Dejin, “Programmable fractal zone plates (FraZPs) with foci finely tuned,” Opt. Commun. 281(22), 5515–5519 (2008).
[Crossref]

Yadav, A. K.

A. K. Yadav, S. Vashisth, H. Singh, and K. Singh, “A phase-image watermarking scheme in gyrator domain using devil’s vortex Fresnel lens as a phase mask,” Opt. Commun. 344, 172–180 (2015).
[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(3), 035003 (2013).
[Crossref]

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(3), 035003 (2013).
[Crossref]

Yuan, X.

Q. Zhang, J. Wang, M. Wang, J. Bu, S. Zhu, B. Z. Gao, and X. Yuan, “Depth of focus enhancement of a modified imaging quasi-fractal zone plate,” Opt. Laser Technol. 44(7), 2140–2144 (2012).
[Crossref] [PubMed]

Zagrajek, P.

Zapata-Rodriguez, C. J.

J. A. Monsoriu, C. J. Zapata-Rodriguez, and W. D. Furlan, “Fractal axicons,” Opt. Commun. 263(1), 1–5 (2006).
[Crossref]

Zhang, J.

Zhang, K.

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Wu, J. Chen, Z. Pan, K. Zhang, Y. Hong, P. Zhu, and Z. Wu, “Use of fractal zone plates for transmission X-ray microscopy,” Anal. Bioanal. Chem. 404(5), 1303–1309 (2012).
[Crossref] [PubMed]

Zhang, Q.

Q. Zhang, J. Wang, M. Wang, J. Bu, S. Zhu, B. Z. Gao, and X. Yuan, “Depth of focus enhancement of a modified imaging quasi-fractal zone plate,” Opt. Laser Technol. 44(7), 2140–2144 (2012).
[Crossref] [PubMed]

Zhang, X.

S. Cheng, X. Zhang, W. Ma, and S. Tao, “Fractal zone plate beam based optical tweezers,” Sci. Rep. 6(1), 34492 (2016).
[Crossref] [PubMed]

Zhang, Y.

Zhu, P.

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Wu, J. Chen, Z. Pan, K. Zhang, Y. Hong, P. Zhu, and Z. Wu, “Use of fractal zone plates for transmission X-ray microscopy,” Anal. Bioanal. Chem. 404(5), 1303–1309 (2012).
[Crossref] [PubMed]

Zhu, S.

Q. Zhang, J. Wang, M. Wang, J. Bu, S. Zhu, B. Z. Gao, and X. Yuan, “Depth of focus enhancement of a modified imaging quasi-fractal zone plate,” Opt. Laser Technol. 44(7), 2140–2144 (2012).
[Crossref] [PubMed]

Anal. Bioanal. Chem. (1)

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Wu, J. Chen, Z. Pan, K. Zhang, Y. Hong, P. Zhu, and Z. Wu, “Use of fractal zone plates for transmission X-ray microscopy,” Anal. Bioanal. Chem. 404(5), 1303–1309 (2012).
[Crossref] [PubMed]

Appl. Opt. (3)

Eur. J. Phys. (1)

J. A. Monsoriu, M. H. Giménez, W. D. Furlan, J. C. Barreiro, and G. Saavedra, “Diffraction by m-bonacci gratings,” Eur. J. Phys. 36(6), 65005 (2015).
[Crossref]

IEEE Photonics J. (2)

V. Ferrando, A. Calatayud, P. Andrés, R. Torroba, W. D. Furlan, and J. A. Monsoriu, “Imaging properties of Kinoform Fibonacci lenses,” IEEE Photonics J. 6(1), 6500106 (2014).
[Crossref]

J. A. Monsoriu, A. Calatayud, L. Remón, W. D. Furlan, G. Saavedra, and P. Andrés, “Bifocal Fibonacci diffraction lenses,” IEEE Photonics J. 5(3), 3400106 (2013).
[Crossref]

J. Opt. Soc. Am. A (2)

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(3), 035003 (2013).
[Crossref]

Opt. Commun. (3)

J. A. Monsoriu, C. J. Zapata-Rodriguez, and W. D. Furlan, “Fractal axicons,” Opt. Commun. 263(1), 1–5 (2006).
[Crossref]

A. K. Yadav, S. Vashisth, H. Singh, and K. Singh, “A phase-image watermarking scheme in gyrator domain using devil’s vortex Fresnel lens as a phase mask,” Opt. Commun. 344, 172–180 (2015).
[Crossref]

H. Dai, J. Liu, S. Xuecheng, and Y. Dejin, “Programmable fractal zone plates (FraZPs) with foci finely tuned,” Opt. Commun. 281(22), 5515–5519 (2008).
[Crossref]

Opt. Express (6)

Opt. Laser Technol. (1)

Q. Zhang, J. Wang, M. Wang, J. Bu, S. Zhu, B. Z. Gao, and X. Yuan, “Depth of focus enhancement of a modified imaging quasi-fractal zone plate,” Opt. Laser Technol. 44(7), 2140–2144 (2012).
[Crossref] [PubMed]

Opt. Lett. (6)

Sci. Rep. (2)

S. Cheng, X. Zhang, W. Ma, and S. Tao, “Fractal zone plate beam based optical tweezers,” Sci. Rep. 6(1), 34492 (2016).
[Crossref] [PubMed]

K. Wu and G. P. Wang, “Two-dimensional Fibonacci grating for far-field super-resolution imaging,” Sci. Rep. 6(1), 38651 (2016).
[Crossref] [PubMed]

Other (1)

T. Noe, T. Piezas, and E. W. Weisstein, “Fibonacci n-Step Number,” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/Fibonaccin-StepNumber .

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Figures (5)

Fig. 1
Fig. 1 Scheme for the construction of the radial profile of a tribonacci zone plate from the sequence t 3,5 ={ 1010101101010 } .
Fig. 2
Fig. 2 a) Diffractive Tribonacci (m=3) and (b) Tetranacci (m=4) lenses designed for S=8 . The number of zones in (a) and (b) are N 3,8 =81 and N 4,8 =108 , respectively.
Fig. 3
Fig. 3 Normalized axial irradiance versus the normalized reduced axial coordinate produced by the (a) diffractive Tribonacci and (b) Tetranacci lenses shown in Fig. 2.
Fig. 4
Fig. 4 Experimental setup. L1 and L4 are 100 mm focal distance lenses. L2 and L3 are 200 mm focal distance lenses. BS is a beam splitter, D is an iris diaphragm, and PL a linear polarizer. The translation stage shifts the camera in order to get images along z-axis (see the main text for details).
Fig. 5
Fig. 5 Twin images obtained with the m-bonacci lenses shown in Fig. 2.

Equations (5)

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φ m =  lim S ( N m,S N m,S1 )
( φ m ) m i=1 m ( φ m ) mi =0
τ m =  lim S ( N m,S N m,S+1 N m,S )= 1 φ m 1  .
q m,S ( ζ )= l=1 N m,S+1 t m,S,l  rect(ζl+1/2),
I( u )=4π u 2 | 0 1 q( ζ )exp(i 2 π u ζ)dζ | 2

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