Abstract

We present a new family of Zone Plates (ZPs) designed using the Thue-Morse sequence. The focusing and imaging properties of these aperiodic diffractive lenses coined Thue-Morse Zone Plates (TMZPs) are examined. It is demonstrated that TMZPs produce a pair of self-similar and equally intense foci along the optical axis. As a consequence of this property, under broadband illumination, a TMZP produces two foci with an extended depth of focus and a strong reduction of the chromatic aberration compared with conventional periodic ZPs. This distinctive optical characteristic is experimentally confirmed.

© 2015 Optical Society of America

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References

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  1. J. Ojeda-Castañeda and C. Gómez-Reino, Selected Papers on Zone Plates (SPIE Optical Engineering Press, 1996), vol. MS128.
  2. Y. Wang, W. Yun, and C. Jacobsen, “Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,” Nature 424, 50–53 (2003).
    [Crossref] [PubMed]
  3. S. Wang, X. C. Zhang, M. P. Maley, M. F. Hundley, L. N. Bulaevskii, A. E. Koshelev, and A. J. Taylor, “Terahertz tomographic imaging with a Fresnel lens,” Opt. Photonics News 13, 58 (2002).
    [Crossref]
  4. E. Maciá, “The role of aperiodic order in science and technology,” Rep. Prog. Phys. 69, 397–441 (2006).
    [Crossref]
  5. G. Saavedra, W. D. Furlan, and J. A. Monsoriu, “Fractal zone plates,” Opt. Lett. 28, 971–973 (2003).
    [Crossref] [PubMed]
  6. J. A. Monsoriu, A. Calatayud, L. Remón, W. D. Furlan, G. Saavedra, and P. Andrés, “Bifocal Fibonacci diffractive lenses,” IEEE Photonics J. 5, 3400106 (2013).
    [Crossref]
  7. W. D. Furlan, G. Saavedra, and J. A. Monsoriu, “White-light imaging with fractal zone plates,” Opt. Lett. 32, 2109–2111 (2007).
    [Crossref] [PubMed]
  8. X. Ge, Z. Wang, K. Gao, D. Wang, Z. Wu, J. Chen, K. Zhang, Y. Hong, P. Zhu, and Z. Wu, “Effects of the condenser fractal zone plate in a transmission X-ray microscope,” Radiat. Phys. Chem. 95, 424–427 (2014).
    [Crossref]
  9. 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]
  10. 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, 2140–2144 (2012).
    [Crossref]
  11. Q. Q. Zhang, J. G. Wang, M. W. Wang, J. Bu, S. W. Zhu, R. Wang, B. Z. Gao, and X.-C. Yuan, “A modified fractal zone plate with extended depth of focus in spectral domain optical coherence tomography,” J. Opt. 13, 055301 (2011).
    [Crossref]
  12. Y. J. Liu, H. T. Dai, X. W. Sun, and T. J. Huang, “Electrically switchable phase-type fractal zone plates and fractal photon sieves,” Opt. Express 17, 12418 (2009).
    [Crossref] [PubMed]
  13. Y. Fu, W. Zhou, and L. Lim, “Propagation properties of plasmonic micro-zone plates with and without fractals,” Appl. Phys. B 90, 421–425 (2008).
    [Crossref]
  14. 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, 6500106 (2014).
    [Crossref]
  15. C. W. Tsao, Y. H. Cheng, and W. J. Hsueh, “Localized modes in one-dimensional symmetric Thue-Morse quasicrystals,” Opt. Express 22, 24378–24383 (2014).
    [Crossref] [PubMed]
  16. W. J. Hsueh, C. H. Chang, and C. T. Lin, “Exciton photoluminescence in resonant quasi-periodic Thue-Morse quantum wells,” Opt. Lett. 39, 489–492 (2014).
    [Crossref] [PubMed]
  17. J. A. Monsoriu, R. A. Depine, and E. Silvestre, “Non-Bragg band gaps in 1D metamaterial aperiodic multilayers,”J. Eur. Opt. Soc. 2, 07002 (2007).
    [Crossref]
  18. H. Huang, D. Liu, H. Zhang, and X. Kong, “Electronic transport and shot noise in Thue-Morse sequence graphene superlattice,” J. Appl. Phys. 113, 043702 (2013).
    [Crossref]
  19. F. Giménez, W. D. Furlan, A. Calatayud, and J. A. Monsoriu, “Multifractal zone plates,” J. Opt. Soc. Am. A 27, 1851–1855 (2010).
    [Crossref]
  20. D. Pascale, A Review of RGB Color Spaces … from xyY to RGB (The BabelColor Company, 2003).
  21. X. Ge, Z. Wang, K. Gao, D. Wang, Z. Z. Wu, J. Chen, Z. Pan, K. Zhang, Y. Hong, and P. Zhu, “Use of fractal zone plates for transmission X-ray microscopy,” Anal. Bioanal. Chem. 404, 1303–1309 (2012).
    [Crossref] [PubMed]
  22. D. Keum and K.-H. Jeong, “Artificial compound eye with fractal zone plate arrays,” in Proceedings of IEEE Conference on Optical MEMS and Nanophotonics (IEEE, 2013), pp. 31–32.
  23. R. Verma, M. K. Sharma, V. Banerjee, and P. Senthilkumaran, “Robustness of Cantor diffractals,” Opt. Express 21, 7951–7956 (2013).
    [Crossref] [PubMed]
  24. N. Gao, H. Li, X. Zhu, Y. Hua, and C. Xie, “Quasi-periodic gratings: diffraction orders accelerate along curves,” Opt. Lett. 38, 2829–2831 (2013).
    [Crossref] [PubMed]
  25. Y. J. Liu, H. Liu, E. S. P. Leong, C. C. Chum, and J. H. Teng, “Fractal holey metal microlenses with significantly suppressed side lobes and high-order diffractions in focusing,” Adv. Opt. Mater. 2, 487–492 (2014).
    [Crossref]

2014 (5)

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Wu, J. Chen, K. Zhang, Y. Hong, P. Zhu, and Z. Wu, “Effects of the condenser fractal zone plate in a transmission X-ray microscope,” Radiat. Phys. Chem. 95, 424–427 (2014).
[Crossref]

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, 6500106 (2014).
[Crossref]

C. W. Tsao, Y. H. Cheng, and W. J. Hsueh, “Localized modes in one-dimensional symmetric Thue-Morse quasicrystals,” Opt. Express 22, 24378–24383 (2014).
[Crossref] [PubMed]

W. J. Hsueh, C. H. Chang, and C. T. Lin, “Exciton photoluminescence in resonant quasi-periodic Thue-Morse quantum wells,” Opt. Lett. 39, 489–492 (2014).
[Crossref] [PubMed]

Y. J. Liu, H. Liu, E. S. P. Leong, C. C. Chum, and J. H. Teng, “Fractal holey metal microlenses with significantly suppressed side lobes and high-order diffractions in focusing,” Adv. Opt. Mater. 2, 487–492 (2014).
[Crossref]

2013 (5)

R. Verma, M. K. Sharma, V. Banerjee, and P. Senthilkumaran, “Robustness of Cantor diffractals,” Opt. Express 21, 7951–7956 (2013).
[Crossref] [PubMed]

N. Gao, H. Li, X. Zhu, Y. Hua, and C. Xie, “Quasi-periodic gratings: diffraction orders accelerate along curves,” Opt. Lett. 38, 2829–2831 (2013).
[Crossref] [PubMed]

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

H. Huang, D. Liu, H. Zhang, and X. Kong, “Electronic transport and shot noise in Thue-Morse sequence graphene superlattice,” J. Appl. Phys. 113, 043702 (2013).
[Crossref]

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]

2012 (2)

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, 2140–2144 (2012).
[Crossref]

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

2011 (1)

Q. Q. Zhang, J. G. Wang, M. W. Wang, J. Bu, S. W. Zhu, R. Wang, B. Z. Gao, and X.-C. Yuan, “A modified fractal zone plate with extended depth of focus in spectral domain optical coherence tomography,” J. Opt. 13, 055301 (2011).
[Crossref]

2010 (1)

2009 (1)

2008 (1)

Y. Fu, W. Zhou, and L. Lim, “Propagation properties of plasmonic micro-zone plates with and without fractals,” Appl. Phys. B 90, 421–425 (2008).
[Crossref]

2007 (2)

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

J. A. Monsoriu, R. A. Depine, and E. Silvestre, “Non-Bragg band gaps in 1D metamaterial aperiodic multilayers,”J. Eur. Opt. Soc. 2, 07002 (2007).
[Crossref]

2006 (1)

E. Maciá, “The role of aperiodic order in science and technology,” Rep. Prog. Phys. 69, 397–441 (2006).
[Crossref]

2003 (2)

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

Y. Wang, W. Yun, and C. Jacobsen, “Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,” Nature 424, 50–53 (2003).
[Crossref] [PubMed]

2002 (1)

S. Wang, X. C. Zhang, M. P. Maley, M. F. Hundley, L. N. Bulaevskii, A. E. Koshelev, and A. J. Taylor, “Terahertz tomographic imaging with a Fresnel lens,” Opt. Photonics News 13, 58 (2002).
[Crossref]

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, 6500106 (2014).
[Crossref]

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

Banerjee, V.

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, 2140–2144 (2012).
[Crossref]

Q. Q. Zhang, J. G. Wang, M. W. Wang, J. Bu, S. W. Zhu, R. Wang, B. Z. Gao, and X.-C. Yuan, “A modified fractal zone plate with extended depth of focus in spectral domain optical coherence tomography,” J. Opt. 13, 055301 (2011).
[Crossref]

Bulaevskii, L. N.

S. Wang, X. C. Zhang, M. P. Maley, M. F. Hundley, L. N. Bulaevskii, A. E. Koshelev, and A. J. Taylor, “Terahertz tomographic imaging with a Fresnel lens,” Opt. Photonics News 13, 58 (2002).
[Crossref]

Calatayud, A.

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, 6500106 (2014).
[Crossref]

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

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

Chang, C. H.

Chen, J.

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Wu, J. Chen, K. Zhang, Y. Hong, P. Zhu, and Z. Wu, “Effects of the condenser fractal zone plate in a transmission X-ray microscope,” Radiat. Phys. Chem. 95, 424–427 (2014).
[Crossref]

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

Cheng, Y. H.

Chum, C. C.

Y. J. Liu, H. Liu, E. S. P. Leong, C. C. Chum, and J. H. Teng, “Fractal holey metal microlenses with significantly suppressed side lobes and high-order diffractions in focusing,” Adv. Opt. Mater. 2, 487–492 (2014).
[Crossref]

Dai, H. T.

Depine, R. A.

J. A. Monsoriu, R. A. Depine, and E. Silvestre, “Non-Bragg band gaps in 1D metamaterial aperiodic multilayers,”J. Eur. Opt. Soc. 2, 07002 (2007).
[Crossref]

Ferrando, V.

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, 6500106 (2014).
[Crossref]

Fu, Y.

Y. Fu, W. Zhou, and L. Lim, “Propagation properties of plasmonic micro-zone plates with and without fractals,” Appl. Phys. B 90, 421–425 (2008).
[Crossref]

Furlan, W. D.

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, 6500106 (2014).
[Crossref]

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

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

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]

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, 2140–2144 (2012).
[Crossref]

Q. Q. Zhang, J. G. Wang, M. W. Wang, J. Bu, S. W. Zhu, R. Wang, B. Z. Gao, and X.-C. Yuan, “A modified fractal zone plate with extended depth of focus in spectral domain optical coherence tomography,” J. Opt. 13, 055301 (2011).
[Crossref]

Gao, K.

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Wu, J. Chen, K. Zhang, Y. Hong, P. Zhu, and Z. Wu, “Effects of the condenser fractal zone plate in a transmission X-ray microscope,” Radiat. Phys. Chem. 95, 424–427 (2014).
[Crossref]

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

Gao, N.

Ge, X.

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Wu, J. Chen, K. Zhang, Y. Hong, P. Zhu, and Z. Wu, “Effects of the condenser fractal zone plate in a transmission X-ray microscope,” Radiat. Phys. Chem. 95, 424–427 (2014).
[Crossref]

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

Giménez, F.

Gómez-Reino, C.

J. Ojeda-Castañeda and C. Gómez-Reino, Selected Papers on Zone Plates (SPIE Optical Engineering Press, 1996), vol. MS128.

Hong, Y.

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Wu, J. Chen, K. Zhang, Y. Hong, P. Zhu, and Z. Wu, “Effects of the condenser fractal zone plate in a transmission X-ray microscope,” Radiat. Phys. Chem. 95, 424–427 (2014).
[Crossref]

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

Hsueh, W. J.

Hua, Y.

Huang, H.

H. Huang, D. Liu, H. Zhang, and X. Kong, “Electronic transport and shot noise in Thue-Morse sequence graphene superlattice,” J. Appl. Phys. 113, 043702 (2013).
[Crossref]

Huang, T. J.

Hundley, M. F.

S. Wang, X. C. Zhang, M. P. Maley, M. F. Hundley, L. N. Bulaevskii, A. E. Koshelev, and A. J. Taylor, “Terahertz tomographic imaging with a Fresnel lens,” Opt. Photonics News 13, 58 (2002).
[Crossref]

Jacobsen, C.

Y. Wang, W. Yun, and C. Jacobsen, “Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,” Nature 424, 50–53 (2003).
[Crossref] [PubMed]

Jeong, K.-H.

D. Keum and K.-H. Jeong, “Artificial compound eye with fractal zone plate arrays,” in Proceedings of IEEE Conference on Optical MEMS and Nanophotonics (IEEE, 2013), pp. 31–32.

Keum, D.

D. Keum and K.-H. Jeong, “Artificial compound eye with fractal zone plate arrays,” in Proceedings of IEEE Conference on Optical MEMS and Nanophotonics (IEEE, 2013), pp. 31–32.

Kong, X.

H. Huang, D. Liu, H. Zhang, and X. Kong, “Electronic transport and shot noise in Thue-Morse sequence graphene superlattice,” J. Appl. Phys. 113, 043702 (2013).
[Crossref]

Koshelev, A. E.

S. Wang, X. C. Zhang, M. P. Maley, M. F. Hundley, L. N. Bulaevskii, A. E. Koshelev, and A. J. Taylor, “Terahertz tomographic imaging with a Fresnel lens,” Opt. Photonics News 13, 58 (2002).
[Crossref]

Leong, E. S. P.

Y. J. Liu, H. Liu, E. S. P. Leong, C. C. Chum, and J. H. Teng, “Fractal holey metal microlenses with significantly suppressed side lobes and high-order diffractions in focusing,” Adv. Opt. Mater. 2, 487–492 (2014).
[Crossref]

Li, H.

Lim, L.

Y. Fu, W. Zhou, and L. Lim, “Propagation properties of plasmonic micro-zone plates with and without fractals,” Appl. Phys. B 90, 421–425 (2008).
[Crossref]

Lin, C. T.

Liu, D.

H. Huang, D. Liu, H. Zhang, and X. Kong, “Electronic transport and shot noise in Thue-Morse sequence graphene superlattice,” J. Appl. Phys. 113, 043702 (2013).
[Crossref]

Liu, H.

Y. J. Liu, H. Liu, E. S. P. Leong, C. C. Chum, and J. H. Teng, “Fractal holey metal microlenses with significantly suppressed side lobes and high-order diffractions in focusing,” Adv. Opt. Mater. 2, 487–492 (2014).
[Crossref]

Liu, Y. J.

Y. J. Liu, H. Liu, E. S. P. Leong, C. C. Chum, and J. H. Teng, “Fractal holey metal microlenses with significantly suppressed side lobes and high-order diffractions in focusing,” Adv. Opt. Mater. 2, 487–492 (2014).
[Crossref]

Y. J. Liu, H. T. Dai, X. W. Sun, and T. J. Huang, “Electrically switchable phase-type fractal zone plates and fractal photon sieves,” Opt. Express 17, 12418 (2009).
[Crossref] [PubMed]

Maciá, E.

E. Maciá, “The role of aperiodic order in science and technology,” Rep. Prog. Phys. 69, 397–441 (2006).
[Crossref]

Maley, M. P.

S. Wang, X. C. Zhang, M. P. Maley, M. F. Hundley, L. N. Bulaevskii, A. E. Koshelev, and A. J. Taylor, “Terahertz tomographic imaging with a Fresnel lens,” Opt. Photonics News 13, 58 (2002).
[Crossref]

Monsoriu, J. A.

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, 6500106 (2014).
[Crossref]

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

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

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

J. A. Monsoriu, R. A. Depine, and E. Silvestre, “Non-Bragg band gaps in 1D metamaterial aperiodic multilayers,”J. Eur. Opt. Soc. 2, 07002 (2007).
[Crossref]

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

Ojeda-Castañeda, J.

J. Ojeda-Castañeda and C. Gómez-Reino, Selected Papers on Zone Plates (SPIE Optical Engineering Press, 1996), vol. MS128.

Pan, Z.

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

Pascale, D.

D. Pascale, A Review of RGB Color Spaces … from xyY to RGB (The BabelColor Company, 2003).

Remón, L.

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

Saavedra, G.

Senthilkumaran, P.

Sharma, M. K.

Silvestre, E.

J. A. Monsoriu, R. A. Depine, and E. Silvestre, “Non-Bragg band gaps in 1D metamaterial aperiodic multilayers,”J. Eur. Opt. Soc. 2, 07002 (2007).
[Crossref]

Sun, X. W.

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]

Taylor, A. J.

S. Wang, X. C. Zhang, M. P. Maley, M. F. Hundley, L. N. Bulaevskii, A. E. Koshelev, and A. J. Taylor, “Terahertz tomographic imaging with a Fresnel lens,” Opt. Photonics News 13, 58 (2002).
[Crossref]

Teng, J. H.

Y. J. Liu, H. Liu, E. S. P. Leong, C. C. Chum, and J. H. Teng, “Fractal holey metal microlenses with significantly suppressed side lobes and high-order diffractions in focusing,” Adv. Opt. Mater. 2, 487–492 (2014).
[Crossref]

Torroba, R.

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, 6500106 (2014).
[Crossref]

Tsao, C. W.

Verma, R.

Wang, D.

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Wu, J. Chen, K. Zhang, Y. Hong, P. Zhu, and Z. Wu, “Effects of the condenser fractal zone plate in a transmission X-ray microscope,” Radiat. Phys. Chem. 95, 424–427 (2014).
[Crossref]

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Z. Wu, J. Chen, Z. Pan, K. Zhang, Y. Hong, and P. Zhu, “Use of fractal zone plates for transmission X-ray microscopy,” Anal. Bioanal. Chem. 404, 1303–1309 (2012).
[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, 2140–2144 (2012).
[Crossref]

Wang, J. G.

Q. Q. Zhang, J. G. Wang, M. W. Wang, J. Bu, S. W. Zhu, R. Wang, B. Z. Gao, and X.-C. Yuan, “A modified fractal zone plate with extended depth of focus in spectral domain optical coherence tomography,” J. Opt. 13, 055301 (2011).
[Crossref]

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, 2140–2144 (2012).
[Crossref]

Wang, M. W.

Q. Q. Zhang, J. G. Wang, M. W. Wang, J. Bu, S. W. Zhu, R. Wang, B. Z. Gao, and X.-C. Yuan, “A modified fractal zone plate with extended depth of focus in spectral domain optical coherence tomography,” J. Opt. 13, 055301 (2011).
[Crossref]

Wang, R.

Q. Q. Zhang, J. G. Wang, M. W. Wang, J. Bu, S. W. Zhu, R. Wang, B. Z. Gao, and X.-C. Yuan, “A modified fractal zone plate with extended depth of focus in spectral domain optical coherence tomography,” J. Opt. 13, 055301 (2011).
[Crossref]

Wang, S.

S. Wang, X. C. Zhang, M. P. Maley, M. F. Hundley, L. N. Bulaevskii, A. E. Koshelev, and A. J. Taylor, “Terahertz tomographic imaging with a Fresnel lens,” Opt. Photonics News 13, 58 (2002).
[Crossref]

Wang, Y.

Y. Wang, W. Yun, and C. Jacobsen, “Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,” Nature 424, 50–53 (2003).
[Crossref] [PubMed]

Wang, Z.

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Wu, J. Chen, K. Zhang, Y. Hong, P. Zhu, and Z. Wu, “Effects of the condenser fractal zone plate in a transmission X-ray microscope,” Radiat. Phys. Chem. 95, 424–427 (2014).
[Crossref]

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

Wu, Z.

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Wu, J. Chen, K. Zhang, Y. Hong, P. Zhu, and Z. Wu, “Effects of the condenser fractal zone plate in a transmission X-ray microscope,” Radiat. Phys. Chem. 95, 424–427 (2014).
[Crossref]

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Wu, J. Chen, K. Zhang, Y. Hong, P. Zhu, and Z. Wu, “Effects of the condenser fractal zone plate in a transmission X-ray microscope,” Radiat. Phys. Chem. 95, 424–427 (2014).
[Crossref]

Wu, Z. Z.

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Z. Wu, J. Chen, Z. Pan, K. Zhang, Y. Hong, and P. Zhu, “Use of fractal zone plates for transmission X-ray microscopy,” Anal. Bioanal. Chem. 404, 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, 035003 (2013).
[Crossref]

Xie, C.

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]

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.

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, 2140–2144 (2012).
[Crossref]

Yuan, X.-C.

Q. Q. Zhang, J. G. Wang, M. W. Wang, J. Bu, S. W. Zhu, R. Wang, B. Z. Gao, and X.-C. Yuan, “A modified fractal zone plate with extended depth of focus in spectral domain optical coherence tomography,” J. Opt. 13, 055301 (2011).
[Crossref]

Yun, W.

Y. Wang, W. Yun, and C. Jacobsen, “Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,” Nature 424, 50–53 (2003).
[Crossref] [PubMed]

Zhang, H.

H. Huang, D. Liu, H. Zhang, and X. Kong, “Electronic transport and shot noise in Thue-Morse sequence graphene superlattice,” J. Appl. Phys. 113, 043702 (2013).
[Crossref]

Zhang, K.

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Wu, J. Chen, K. Zhang, Y. Hong, P. Zhu, and Z. Wu, “Effects of the condenser fractal zone plate in a transmission X-ray microscope,” Radiat. Phys. Chem. 95, 424–427 (2014).
[Crossref]

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Z. Wu, J. Chen, Z. Pan, K. Zhang, Y. Hong, and P. Zhu, “Use of fractal zone plates for transmission X-ray microscopy,” Anal. Bioanal. Chem. 404, 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, 2140–2144 (2012).
[Crossref]

Zhang, Q. Q.

Q. Q. Zhang, J. G. Wang, M. W. Wang, J. Bu, S. W. Zhu, R. Wang, B. Z. Gao, and X.-C. Yuan, “A modified fractal zone plate with extended depth of focus in spectral domain optical coherence tomography,” J. Opt. 13, 055301 (2011).
[Crossref]

Zhang, X. C.

S. Wang, X. C. Zhang, M. P. Maley, M. F. Hundley, L. N. Bulaevskii, A. E. Koshelev, and A. J. Taylor, “Terahertz tomographic imaging with a Fresnel lens,” Opt. Photonics News 13, 58 (2002).
[Crossref]

Zhou, W.

Y. Fu, W. Zhou, and L. Lim, “Propagation properties of plasmonic micro-zone plates with and without fractals,” Appl. Phys. B 90, 421–425 (2008).
[Crossref]

Zhu, P.

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Wu, J. Chen, K. Zhang, Y. Hong, P. Zhu, and Z. Wu, “Effects of the condenser fractal zone plate in a transmission X-ray microscope,” Radiat. Phys. Chem. 95, 424–427 (2014).
[Crossref]

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Z. Wu, J. Chen, Z. Pan, K. Zhang, Y. Hong, and P. Zhu, “Use of fractal zone plates for transmission X-ray microscopy,” Anal. Bioanal. Chem. 404, 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, 2140–2144 (2012).
[Crossref]

Zhu, S. W.

Q. Q. Zhang, J. G. Wang, M. W. Wang, J. Bu, S. W. Zhu, R. Wang, B. Z. Gao, and X.-C. Yuan, “A modified fractal zone plate with extended depth of focus in spectral domain optical coherence tomography,” J. Opt. 13, 055301 (2011).
[Crossref]

Zhu, X.

Adv. Opt. Mater. (1)

Y. J. Liu, H. Liu, E. S. P. Leong, C. C. Chum, and J. H. Teng, “Fractal holey metal microlenses with significantly suppressed side lobes and high-order diffractions in focusing,” Adv. Opt. Mater. 2, 487–492 (2014).
[Crossref]

Anal. Bioanal. Chem. (1)

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

Appl. Phys. B (1)

Y. Fu, W. Zhou, and L. Lim, “Propagation properties of plasmonic micro-zone plates with and without fractals,” Appl. Phys. B 90, 421–425 (2008).
[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, 6500106 (2014).
[Crossref]

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

J. Appl. Phys. (1)

H. Huang, D. Liu, H. Zhang, and X. Kong, “Electronic transport and shot noise in Thue-Morse sequence graphene superlattice,” J. Appl. Phys. 113, 043702 (2013).
[Crossref]

J. Eur. Opt. Soc. (1)

J. A. Monsoriu, R. A. Depine, and E. Silvestre, “Non-Bragg band gaps in 1D metamaterial aperiodic multilayers,”J. Eur. Opt. Soc. 2, 07002 (2007).
[Crossref]

J. Opt. (1)

Q. Q. Zhang, J. G. Wang, M. W. Wang, J. Bu, S. W. Zhu, R. Wang, B. Z. Gao, and X.-C. Yuan, “A modified fractal zone plate with extended depth of focus in spectral domain optical coherence tomography,” J. Opt. 13, 055301 (2011).
[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 (1)

Y. Wang, W. Yun, and C. Jacobsen, “Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,” Nature 424, 50–53 (2003).
[Crossref] [PubMed]

Opt. Express (3)

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, 2140–2144 (2012).
[Crossref]

Opt. Lett. (4)

Opt. Photonics News (1)

S. Wang, X. C. Zhang, M. P. Maley, M. F. Hundley, L. N. Bulaevskii, A. E. Koshelev, and A. J. Taylor, “Terahertz tomographic imaging with a Fresnel lens,” Opt. Photonics News 13, 58 (2002).
[Crossref]

Radiat. Phys. Chem. (1)

X. Ge, Z. Wang, K. Gao, D. Wang, Z. Wu, J. Chen, K. Zhang, Y. Hong, P. Zhu, and Z. Wu, “Effects of the condenser fractal zone plate in a transmission X-ray microscope,” Radiat. Phys. Chem. 95, 424–427 (2014).
[Crossref]

Rep. Prog. Phys. (1)

E. Maciá, “The role of aperiodic order in science and technology,” Rep. Prog. Phys. 69, 397–441 (2006).
[Crossref]

Other (3)

J. Ojeda-Castañeda and C. Gómez-Reino, Selected Papers on Zone Plates (SPIE Optical Engineering Press, 1996), vol. MS128.

D. Pascale, A Review of RGB Color Spaces … from xyY to RGB (The BabelColor Company, 2003).

D. Keum and K.-H. Jeong, “Artificial compound eye with fractal zone plate arrays,” in Proceedings of IEEE Conference on Optical MEMS and Nanophotonics (IEEE, 2013), pp. 31–32.

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Figures (5)

Fig. 1
Fig. 1 a) Geometrical construction of the TM sequence up to order S = 4. b) TMZP of order S = 6 and its equivalent periodic ZP.
Fig. 2
Fig. 2 Normalized axial irradiance provided by TMZPs of orders S = 4, 5, and 6, and their respective equivalent periodic ZPs.
Fig. 3
Fig. 3 a) Normalized axial irradiance for different wavelengths in the visible range, b) Normalized axial illuminance, and c) chromaticity of the different foci for the TMZP of order S = 6 and its equivalent periodic ZP.
Fig. 4
Fig. 4 Scheme of the experimental setup and the polychromatic PSFs provided by the simulated TMZP of order S = 6 and its equivalent periodic ZP.
Fig. 5
Fig. 5 Captured RGB images provided by the printed TMZP of order S7 and its equivalent periodic ZP. The images are captured at the focal length which corresponds to every focus and around these focal planes (±10%)

Equations (5)

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

q ( ζ ) = j = 1 2 S t S , j rect [ ζ ( j 1 / 2 ) d S d S ] .
I ( u ) = 4 π u 2 | 0 1 q ( ζ ) exp ( i 2 π u ζ ) d ζ | 2 ,
I ( u ) = 4 π 2 u 2 d S 2 sinc 2 [ d S u ] | j = 1 2 S t S , j e i 2 π u j d S | 2 .
X ( z ) = λ 1 λ 2 I ( z ; λ ) S ( λ ) x ˜ d λ , Y ( z ) = λ 1 λ 2 I ( z ; λ ) S ( λ ) y ˜ d λ , Z ( z ) = λ 1 λ 2 I ( z ; λ ) S ( λ ) z ˜ d λ ,
x = X X + Y + Z , y = Y X + Y + Z .

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