Abstract

A zone plate lens utilizing a refractive instead of diffractive approach is presented for broadband operation. By utilizing transformation optics, we compress the conventional hyperbolic lens into a flat one with a few zone plates made of all-dielectric materials. Such a transformed lens maintains the broadband performance of the original lens, thus providing a superior alternative to the diffractive Fresnel element which is inherently narrow band.

©2011 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
  15. R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
    [Crossref] [PubMed]
  16. J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
    [Crossref] [PubMed]
  17. E. Kallos, C. Argyropoulos, and Y. Hao, “Ground-plane quasicloaking for free space,” Phys. Rev. A 79(6), 063825 (2009).
    [Crossref]
  18. D. Bao, E. Kallos, W. X. Tang, C. Argyropoulos, Y. Hao, and T. J. Cui, “A broadband simplified free space cloak realized by nonmagnetic dielectric cylinders,” Front. Phys. China 5(3), 319–323 (2010).
    [Crossref]
  19. H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1(3), 21 (2010).
    [Crossref] [PubMed]
  20. H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010).
    [Crossref] [PubMed]
  21. N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
    [Crossref]
  22. W. Tang, C. Argyropoulos, E. Kallos, W. Song, and Y. Hao, “Discrete coordinate transformation for designing all-dielectric flat antennas,” IEEE Trans. Antenn. Propag. 58(12), 3795–3804 (2010).
    [Crossref]
  23. F. Kong, B. I. Wu, J. A. Kong, J. T. Huangfu, S. Xi, and H. S. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91(25), 253509 (2007).
    [Crossref]
  24. D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express 17(19), 16535–16542 (2009).
    [Crossref] [PubMed]
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  26. D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(3), 036617 (2005).
    [Crossref] [PubMed]

2010 (5)

D. Bao, E. Kallos, W. X. Tang, C. Argyropoulos, Y. Hao, and T. J. Cui, “A broadband simplified free space cloak realized by nonmagnetic dielectric cylinders,” Front. Phys. China 5(3), 319–323 (2010).
[Crossref]

H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1(3), 21 (2010).
[Crossref] [PubMed]

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010).
[Crossref] [PubMed]

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
[Crossref]

W. Tang, C. Argyropoulos, E. Kallos, W. Song, and Y. Hao, “Discrete coordinate transformation for designing all-dielectric flat antennas,” IEEE Trans. Antenn. Propag. 58(12), 3795–3804 (2010).
[Crossref]

2009 (4)

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[Crossref] [PubMed]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[Crossref] [PubMed]

E. Kallos, C. Argyropoulos, and Y. Hao, “Ground-plane quasicloaking for free space,” Phys. Rev. A 79(6), 063825 (2009).
[Crossref]

D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express 17(19), 16535–16542 (2009).
[Crossref] [PubMed]

2008 (2)

A. V. Kildishev and V. M. Shalaev, “Engineering space for light via transformation optics,” Opt. Lett. 33(1), 43–45 (2008).
[Crossref]

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[Crossref] [PubMed]

2007 (2)

F. Kong, B. I. Wu, J. A. Kong, J. T. Huangfu, S. Xi, and H. S. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91(25), 253509 (2007).
[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]

2006 (5)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14(21), 9794–9804 (2006).
[Crossref] [PubMed]

A. Petosa, A. Ittipiboon, and S. Thirakoune, “Investigation on arrays of perforated dielectric Fresnel lenses,” IEE Proc., Microw. Antennas Propag. 153(3), 270–276 (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(3), 031105 (2006).
[Crossref]

2005 (1)

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(3), 036617 (2005).
[Crossref] [PubMed]

2004 (1)

2003 (2)

A. Petosa and A. Ittipiboon, “Design and performance of a perforated dielectric Fresnel lens,” IEE Proc., Microw. Antennas Propag. 150(5), 309–314 (2003).
[Crossref]

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

Alieva, T.

Argyropoulos, C.

D. Bao, E. Kallos, W. X. Tang, C. Argyropoulos, Y. Hao, and T. J. Cui, “A broadband simplified free space cloak realized by nonmagnetic dielectric cylinders,” Front. Phys. China 5(3), 319–323 (2010).
[Crossref]

W. Tang, C. Argyropoulos, E. Kallos, W. Song, and Y. Hao, “Discrete coordinate transformation for designing all-dielectric flat antennas,” IEEE Trans. Antenn. Propag. 58(12), 3795–3804 (2010).
[Crossref]

E. Kallos, C. Argyropoulos, and Y. Hao, “Ground-plane quasicloaking for free space,” Phys. Rev. A 79(6), 063825 (2009).
[Crossref]

Bao, D.

D. Bao, E. Kallos, W. X. Tang, C. Argyropoulos, Y. Hao, and T. J. Cui, “A broadband simplified free space cloak realized by nonmagnetic dielectric cylinders,” Front. Phys. China 5(3), 319–323 (2010).
[Crossref]

Bartal, G.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[Crossref] [PubMed]

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(3), 031105 (2006).
[Crossref]

Calvo, M. L.

Chen, H. S.

F. Kong, B. I. Wu, J. A. Kong, J. T. Huangfu, S. Xi, and H. S. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91(25), 253509 (2007).
[Crossref]

Chin, J. Y.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[Crossref] [PubMed]

Cui, T. J.

D. Bao, E. Kallos, W. X. Tang, C. Argyropoulos, Y. Hao, and T. J. Cui, “A broadband simplified free space cloak realized by nonmagnetic dielectric cylinders,” Front. Phys. China 5(3), 319–323 (2010).
[Crossref]

H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1(3), 21 (2010).
[Crossref] [PubMed]

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010).
[Crossref] [PubMed]

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[Crossref] [PubMed]

Davis, J. A.

Furlan, W. D.

Hao, Y.

D. Bao, E. Kallos, W. X. Tang, C. Argyropoulos, Y. Hao, and T. J. Cui, “A broadband simplified free space cloak realized by nonmagnetic dielectric cylinders,” Front. Phys. China 5(3), 319–323 (2010).
[Crossref]

W. Tang, C. Argyropoulos, E. Kallos, W. Song, and Y. Hao, “Discrete coordinate transformation for designing all-dielectric flat antennas,” IEEE Trans. Antenn. Propag. 58(12), 3795–3804 (2010).
[Crossref]

E. Kallos, C. Argyropoulos, and Y. Hao, “Ground-plane quasicloaking for free space,” Phys. Rev. A 79(6), 063825 (2009).
[Crossref]

Huangfu, J. T.

F. Kong, B. I. Wu, J. A. Kong, J. T. Huangfu, S. Xi, and H. S. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91(25), 253509 (2007).
[Crossref]

Ittipiboon, A.

A. Petosa, A. Ittipiboon, and S. Thirakoune, “Investigation on arrays of perforated dielectric Fresnel lenses,” IEE Proc., Microw. Antennas Propag. 153(3), 270–276 (2006).
[Crossref]

A. Petosa and A. Ittipiboon, “Design and performance of a perforated dielectric Fresnel lens,” IEE Proc., Microw. Antennas Propag. 150(5), 309–314 (2003).
[Crossref]

Ji, C.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[Crossref] [PubMed]

Kallos, E.

W. Tang, C. Argyropoulos, E. Kallos, W. Song, and Y. Hao, “Discrete coordinate transformation for designing all-dielectric flat antennas,” IEEE Trans. Antenn. Propag. 58(12), 3795–3804 (2010).
[Crossref]

D. Bao, E. Kallos, W. X. Tang, C. Argyropoulos, Y. Hao, and T. J. Cui, “A broadband simplified free space cloak realized by nonmagnetic dielectric cylinders,” Front. Phys. China 5(3), 319–323 (2010).
[Crossref]

E. Kallos, C. Argyropoulos, and Y. Hao, “Ground-plane quasicloaking for free space,” Phys. Rev. A 79(6), 063825 (2009).
[Crossref]

Kildishev, A. V.

Kong, F.

F. Kong, B. I. Wu, J. A. Kong, J. T. Huangfu, S. Xi, and H. S. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91(25), 253509 (2007).
[Crossref]

Kong, J. A.

F. Kong, B. I. Wu, J. A. Kong, J. T. Huangfu, S. Xi, and H. S. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91(25), 253509 (2007).
[Crossref]

Koschny, Th.

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(3), 036617 (2005).
[Crossref] [PubMed]

Kundtz, N.

Leonhardt, U.

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref] [PubMed]

Li, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[Crossref] [PubMed]

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[Crossref] [PubMed]

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(3), 031105 (2006).
[Crossref]

Liu, R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[Crossref] [PubMed]

Ma, H. F.

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010).
[Crossref] [PubMed]

H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1(3), 21 (2010).
[Crossref] [PubMed]

Martín-Romo, J. A.

Mock, J. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[Crossref] [PubMed]

Monsoriu, J. A.

Pendry, J. B.

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[Crossref] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14(21), 9794–9804 (2006).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

Petosa, A.

A. Petosa, A. Ittipiboon, and S. Thirakoune, “Investigation on arrays of perforated dielectric Fresnel lenses,” IEE Proc., Microw. Antennas Propag. 153(3), 270–276 (2006).
[Crossref]

A. Petosa and A. Ittipiboon, “Design and performance of a perforated dielectric Fresnel lens,” IEE Proc., Microw. Antennas Propag. 150(5), 309–314 (2003).
[Crossref]

Ramirez, L.

Roberts, D. A.

Saavedra, G.

Schurig, D.

Shalaev, V. M.

Smith, D. R.

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
[Crossref]

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[Crossref] [PubMed]

D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express 17(19), 16535–16542 (2009).
[Crossref] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14(21), 9794–9804 (2006).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(3), 036617 (2005).
[Crossref] [PubMed]

Song, W.

W. Tang, C. Argyropoulos, E. Kallos, W. Song, and Y. Hao, “Discrete coordinate transformation for designing all-dielectric flat antennas,” IEEE Trans. Antenn. Propag. 58(12), 3795–3804 (2010).
[Crossref]

Soukoulis, C. M.

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(3), 036617 (2005).
[Crossref] [PubMed]

Tang, W.

W. Tang, C. Argyropoulos, E. Kallos, W. Song, and Y. Hao, “Discrete coordinate transformation for designing all-dielectric flat antennas,” IEEE Trans. Antenn. Propag. 58(12), 3795–3804 (2010).
[Crossref]

Tang, W. X.

D. Bao, E. Kallos, W. X. Tang, C. Argyropoulos, Y. Hao, and T. J. Cui, “A broadband simplified free space cloak realized by nonmagnetic dielectric cylinders,” Front. Phys. China 5(3), 319–323 (2010).
[Crossref]

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(3), 031105 (2006).
[Crossref]

Thirakoune, S.

A. Petosa, A. Ittipiboon, and S. Thirakoune, “Investigation on arrays of perforated dielectric Fresnel lenses,” IEE Proc., Microw. Antennas Propag. 153(3), 270–276 (2006).
[Crossref]

Valentine, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[Crossref] [PubMed]

Vier, D. C.

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(3), 036617 (2005).
[Crossref] [PubMed]

Wu, B. I.

F. Kong, B. I. Wu, J. A. Kong, J. T. Huangfu, S. Xi, and H. S. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91(25), 253509 (2007).
[Crossref]

Xi, S.

F. Kong, B. I. Wu, J. A. Kong, J. T. Huangfu, S. Xi, and H. S. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91(25), 253509 (2007).
[Crossref]

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(3), 031105 (2006).
[Crossref]

Zentgraf, T.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[Crossref] [PubMed]

Zhang, X.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[Crossref] [PubMed]

Appl. Phys. Lett. (2)

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(3), 031105 (2006).
[Crossref]

F. Kong, B. I. Wu, J. A. Kong, J. T. Huangfu, S. Xi, and H. S. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91(25), 253509 (2007).
[Crossref]

Front. Phys. China (1)

D. Bao, E. Kallos, W. X. Tang, C. Argyropoulos, Y. Hao, and T. J. Cui, “A broadband simplified free space cloak realized by nonmagnetic dielectric cylinders,” Front. Phys. China 5(3), 319–323 (2010).
[Crossref]

IEE Proc., Microw. Antennas Propag. (2)

A. Petosa, A. Ittipiboon, and S. Thirakoune, “Investigation on arrays of perforated dielectric Fresnel lenses,” IEE Proc., Microw. Antennas Propag. 153(3), 270–276 (2006).
[Crossref]

A. Petosa and A. Ittipiboon, “Design and performance of a perforated dielectric Fresnel lens,” IEE Proc., Microw. Antennas Propag. 150(5), 309–314 (2003).
[Crossref]

IEEE Trans. Antenn. Propag. (1)

W. Tang, C. Argyropoulos, E. Kallos, W. Song, and Y. Hao, “Discrete coordinate transformation for designing all-dielectric flat antennas,” IEEE Trans. Antenn. Propag. 58(12), 3795–3804 (2010).
[Crossref]

Nat. Commun. (2)

H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1(3), 21 (2010).
[Crossref] [PubMed]

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010).
[Crossref] [PubMed]

Nat. Mater. (2)

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
[Crossref]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. A (1)

E. Kallos, C. Argyropoulos, and Y. Hao, “Ground-plane quasicloaking for free space,” Phys. Rev. A 79(6), 063825 (2009).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(3), 036617 (2005).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

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Figures (4)
Fig. 1
Fig. 1 Configuration of the quarter wave Fresnel lens. The demonstration phase-correcting Fresnel lens working at 30 GHz is chosen from [3], with D = 63.5   mm , F = D / 4 , t = 9   mm , ε 1 = 2.48 , ε 2 = 5.8 , ε 3 = 45.4 , ε 4 = 3.43 . (a) Top view. (b) Lateral view. (c) Ray tracing through every sub-zone of the phase-correcting Fresnel lens (magnified picture of the blue dashed box in (b)) .

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Fig. 2
Fig. 2 Schematic showing of the transformed zone plate lens design using the selective-sampled transformation technique. (a) 2D hyperbolic lens with nearly orthogonal mapping. The parameters are: D = 63.5   mm , F = D / 4 , t = 9   mm . (b) 2D flat lens with the permittivity map consisting of 110 × 20 blocks. (c) 2D flat lens with the permittivity map consisting of 22 × 4 blocks. The four layers have heights of 1.4mm, 3mm, 3mm and 1.6mm respectively in the z ^ direction, and the 1st to 10th blocks have the width of 3mm in x ^ direction with the 11th block having a width of 1.75mm (d) 3D transformed zone plate lens.

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Fig. 3
Fig. 3 The radiation patterns of the conventional 3D hyperbolic lens, 3D phase-correcting Fresnel lens in [3] and 3D transformed zone plate lens at (a) 20 GHz, (b) 30 GHz, (c) 40 GHz. (d) The comparison of the bandwidth performance of 3D phase-correcting Fresnel lens and 3D transformed zone plate lens from 20GHz to 40GHz.

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Fig. 4
Fig. 4 Graphical representation of the relationship between the effective permittivity and the perforation. The host medium chosen here is ε r 1 = 5.8 , and the filling materials is air ε r 2 a i r = 1 or ε r 2 h i g h = 36.7 . d refers to the hole diameter, and l refers to the length of side of the unit cell. l = 1   mm is subwavelength scaled in order to make the effective media more homogeneous. (a) Perforated host medium with square unit topology. (b) The effective permittivity achieved from the square unit topology at 30 GHz as d is varied. The maximum value is 24.11, while the minimum value is 1.68. (c) Frequency response from 20 to 40 GHz of the effective perforated medium. (d) Magnified picture of the frequency response in (c) around the effective permittivity equal to 2.62. (e) Frequency response from 20 to 40 GHz of the perforated medium filled with high dielectric material. (f) Magnified picture of the frequency response in (e) around the effective permittivity equal to 15.02. (The curves at different frequencies are very similar, and in (c), (d), (e), (f) clearly overlapped. This represents, for our purposes, dipersionless effective media. The parameter retrieval in (b), (c), (d), (f), and (e) assumes the unit cell to be periodically infinite. In practice, the finiteness of the structure will result in slight changes in effective permittivity.)

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Tables (2)

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Table 1 Relative Permittivity Values of the Transformed Zone Plate Lens

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Table 2 Perforation Size on Every Unit with Unit Side Length l = 1 mm a

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Equations (7)

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r i = 2 i F λ 0 / P + ( i λ 0 / P ) 2
t = λ 0 / ( P ( ε i − ε i − 1 ) )
2 π [ ( o b ) + ( b b ' ) ε 1 ] / λ 0 = 2 π [ ( o c ) + ( c c ' ) ε 2 ] / λ 0
R n = 2 n F λ 0 + ( n λ 0 ) 2
2 π [ ( o a ) + ( a a ' ) ε 1 ] / λ 0 = 2 π [ ( o b ) + ( b b ' ) ε 1 ] / λ 0 − 2 π / P
ε ¯ ¯ ' = J ε ¯ ¯ J T det ( J )
μ ¯ ¯ ' = J μ ¯ ¯ J T det ( J )

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