Abstract

We describe a design methodology for modifying the refractive index profile of graded-index optical instruments that incorporate singularities or zeros in their refractive index. The process maintains the device performance whilst resulting in graded profiles that are all-dielectric, do not require materials with unrealistic values, and that are impedance matched to the bounding medium. This is achieved by transmuting the singularities (or zeros) using the formalism of transformation optics, but with an additional boundary condition requiring the gradient of the co-ordinate transformation be continuous. This additional boundary condition ensures that the device is impedance matched to the bounding medium when the spatially varying permittivity and permeability profiles are scaled to realizable values. We demonstrate the method in some detail for an Eaton lens, before describing the profiles for an “invisible disc” and “multipole” lenses.

© 2013 Optical Society of America

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  1. U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006).
    [CrossRef] [PubMed]
  2. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
    [CrossRef] [PubMed]
  3. U. Leonhardt and T. G. Philbin, Geometry and Light: The Science of Invisibility (Dover, 2010).
  4. K. B. Nathan, D. R. Smith, and J. B. Pendry, “Electromagnetic design with transformation optics,” Proc. IEEE99(10), 1622–1633 (2011).
    [CrossRef]
  5. H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater.9(5), 387–396 (2010).
    [CrossRef] [PubMed]
  6. W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett.91(11), 111105 (2007).
    [CrossRef]
  7. U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science323(5910), 110–112 (2009).
    [CrossRef] [PubMed]
  8. J. Li and J. B. Pendry, “Hiding under the carpet: A new strategy for cloaking,” Phys. Rev. Lett.101(20), 203901 (2008).
    [CrossRef] [PubMed]
  9. R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323(5912), 366–369 (2009).
    [CrossRef] [PubMed]
  10. J. Perczel, T. Tyc, and U. Leonhardt, “Invisibility cloaking without superluminal propagation,” New J. Phys.13(8), 083007 (2011).
    [CrossRef]
  11. J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation optics and subwavelength control of light,” Science337(6094), 549–552 (2012).
    [CrossRef] [PubMed]
  12. P.-H. Tichit, S. N. Burokur, and A. De Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys.105(10), 104912 (2009).
    [CrossRef]
  13. Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett.95(19), 193506 (2009).
    [CrossRef]
  14. M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostructures6(1), 87–95 (2008).
    [CrossRef]
  15. R. K. Luneburg, Mathematical Theory of Optics (Univ. of California Press, 1964).
  16. J. E. Eaton, “On spherically symmetric lenses,” Trans. IRE Antennas Propag.4, 66–71 (1952).
  17. J. C. Maxwell, “Problems,” Cambridge Dublin Math. J.8, 188–189 (1854).
  18. N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater.9(2), 129–132 (2010).
    [CrossRef] [PubMed]
  19. T. Driscoll, G. Lipworth, J. Hunt, N. Landy, N. Kundtz, D. N. Basov, and D. R. Smith, “Performance of a three dimensional transformation-optical-flattened Lüneburg lens,” Opt. Express20(12), 13262–13273 (2012).
    [CrossRef] [PubMed]
  20. A. Demetriadou and Y. Hao, “Slim Luneburg Lens for Antenna Applications,” Opt. Express19(21), 19925–19934 (2011).
    [CrossRef] [PubMed]
  21. R. Yang, W. Tang, and Y. Hao, “A broadband zone plate lens from transformation optics,” Opt. Express19(13), 12348–12355 (2011).
    [CrossRef] [PubMed]
  22. N. Engheta and R. W. Ziolkowski, Metamaterials: Physics and Engineering Explorations (Wiley & Sons, 2006).
  23. C. M. Soukoulis and M. Wegener, “Materials science. Optical metamaterials--more bulky and less lossy,” Science330(6011), 1633–1634 (2010).
    [CrossRef] [PubMed]
  24. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science305(5685), 788–792 (2004).
    [CrossRef] [PubMed]
  25. A. N. Lagarkov and K. N. Rozanov, “High-frequency behavior of magnetic composites,” J. Magn. Magn. Mater.321(14), 2082–2092 (2009).
    [CrossRef]
  26. T. Tsutaoka, “Frequency dispersion of complex permeability in Mn–Zn and Ni–Zn spinel ferrites and their composite materials,” J. Appl. Phys.93(5), 2789–2796 (2003).
    [CrossRef]
  27. O. Acher, “Copper vs. iron: Microwave magnetism in the metamaterial age,” J. Magn. Magn. Mater.321(14), 2093–2101 (2009).
    [CrossRef]
  28. D. Bao, K. Z. Rajab, Y. Hao, E. Kallos, W. Tang, C. Argyropoulos, Y. Piao, and S. Yang, “All-dielectric invisibility cloaks made of BaTiO 3 -loaded polyurethane foam,” New J. Phys.13(10), 103023 (2011).
    [CrossRef]
  29. N. I. Landy, N. Kundtz, and D. R. Smith, “Designing three-dimensional transformation optical media using quasiconformal coordinate transformations,” Phys. Rev. Lett.105(19), 193902 (2010).
    [CrossRef] [PubMed]
  30. A. J. Danner, T. Tyc, and U. Leonhardt, “Controlling birefringence in dielectrics,” Nat. Photonics5(6), 357–359 (2011).
    [CrossRef]
  31. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314(5801), 977–980 (2006).
    [CrossRef] [PubMed]
  32. Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater.8(8), 639–642 (2009).
    [CrossRef] [PubMed]
  33. T. Tyc and U. Leonhardt, “Transmutation of singularities in optical instruments,” New J. Phys.10(11), 115038 (2008).
    [CrossRef]
  34. J. Perczel, C. Garci-Meca, and U. Leonhardt, “Partial transmutation of singularities in optical instruments,” J. Opt.13(7), 075103 (2011).
    [CrossRef]
  35. D. F. Sievenpiper, E. Yablonovitch, J. N. Winn, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “3D metallo-dielectric photonic crystals with strong capacitative coupling,” Phys. Rev. Lett.80, 2829–2832 (1998).
    [CrossRef]
  36. J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett.94(19), 197401 (2005).
    [CrossRef] [PubMed]
  37. B. Wood and J. B. Pendry, “Metamaterials at zero frequency,” J. Phys. Condens. Matter19(7), 076208 (2007).
    [CrossRef] [PubMed]
  38. Y. N. Demkov and V. N. Ostrovsky, “Internal symmetry of the Maxwell “fish-eye” problem and the Fock group for the Hydrogen atom,” Sov. Phys. JETP33, 1083 (1971).
  39. T. Tyc, L. Herzánová, M. Šarbot, and K. Bering, “Absolute instruments and perfect imaging in geometrical optics,” New J. Phys.13(11), 115004 (2011).
    [CrossRef]
  40. P. Benítez, J. C. Miñano, and J. C. González, “Perfect focusing of scalar wave fields in three dimensions,” Opt. Express18(8), 7650–7663 (2010).
    [CrossRef] [PubMed]

2012 (2)

2011 (8)

K. B. Nathan, D. R. Smith, and J. B. Pendry, “Electromagnetic design with transformation optics,” Proc. IEEE99(10), 1622–1633 (2011).
[CrossRef]

J. Perczel, T. Tyc, and U. Leonhardt, “Invisibility cloaking without superluminal propagation,” New J. Phys.13(8), 083007 (2011).
[CrossRef]

D. Bao, K. Z. Rajab, Y. Hao, E. Kallos, W. Tang, C. Argyropoulos, Y. Piao, and S. Yang, “All-dielectric invisibility cloaks made of BaTiO 3 -loaded polyurethane foam,” New J. Phys.13(10), 103023 (2011).
[CrossRef]

A. J. Danner, T. Tyc, and U. Leonhardt, “Controlling birefringence in dielectrics,” Nat. Photonics5(6), 357–359 (2011).
[CrossRef]

J. Perczel, C. Garci-Meca, and U. Leonhardt, “Partial transmutation of singularities in optical instruments,” J. Opt.13(7), 075103 (2011).
[CrossRef]

T. Tyc, L. Herzánová, M. Šarbot, and K. Bering, “Absolute instruments and perfect imaging in geometrical optics,” New J. Phys.13(11), 115004 (2011).
[CrossRef]

R. Yang, W. Tang, and Y. Hao, “A broadband zone plate lens from transformation optics,” Opt. Express19(13), 12348–12355 (2011).
[CrossRef] [PubMed]

A. Demetriadou and Y. Hao, “Slim Luneburg Lens for Antenna Applications,” Opt. Express19(21), 19925–19934 (2011).
[CrossRef] [PubMed]

2010 (5)

P. Benítez, J. C. Miñano, and J. C. González, “Perfect focusing of scalar wave fields in three dimensions,” Opt. Express18(8), 7650–7663 (2010).
[CrossRef] [PubMed]

N. I. Landy, N. Kundtz, and D. R. Smith, “Designing three-dimensional transformation optical media using quasiconformal coordinate transformations,” Phys. Rev. Lett.105(19), 193902 (2010).
[CrossRef] [PubMed]

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater.9(5), 387–396 (2010).
[CrossRef] [PubMed]

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

C. M. Soukoulis and M. Wegener, “Materials science. Optical metamaterials--more bulky and less lossy,” Science330(6011), 1633–1634 (2010).
[CrossRef] [PubMed]

2009 (7)

A. N. Lagarkov and K. N. Rozanov, “High-frequency behavior of magnetic composites,” J. Magn. Magn. Mater.321(14), 2082–2092 (2009).
[CrossRef]

P.-H. Tichit, S. N. Burokur, and A. De Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys.105(10), 104912 (2009).
[CrossRef]

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett.95(19), 193506 (2009).
[CrossRef]

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323(5912), 366–369 (2009).
[CrossRef] [PubMed]

U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science323(5910), 110–112 (2009).
[CrossRef] [PubMed]

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater.8(8), 639–642 (2009).
[CrossRef] [PubMed]

O. Acher, “Copper vs. iron: Microwave magnetism in the metamaterial age,” J. Magn. Magn. Mater.321(14), 2093–2101 (2009).
[CrossRef]

2008 (3)

T. Tyc and U. Leonhardt, “Transmutation of singularities in optical instruments,” New J. Phys.10(11), 115038 (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]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostructures6(1), 87–95 (2008).
[CrossRef]

2007 (2)

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett.91(11), 111105 (2007).
[CrossRef]

B. Wood and J. B. Pendry, “Metamaterials at zero frequency,” J. Phys. Condens. Matter19(7), 076208 (2007).
[CrossRef] [PubMed]

2006 (3)

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

2005 (1)

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett.94(19), 197401 (2005).
[CrossRef] [PubMed]

2004 (1)

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science305(5685), 788–792 (2004).
[CrossRef] [PubMed]

2003 (1)

T. Tsutaoka, “Frequency dispersion of complex permeability in Mn–Zn and Ni–Zn spinel ferrites and their composite materials,” J. Appl. Phys.93(5), 2789–2796 (2003).
[CrossRef]

1998 (1)

D. F. Sievenpiper, E. Yablonovitch, J. N. Winn, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “3D metallo-dielectric photonic crystals with strong capacitative coupling,” Phys. Rev. Lett.80, 2829–2832 (1998).
[CrossRef]

1971 (1)

Y. N. Demkov and V. N. Ostrovsky, “Internal symmetry of the Maxwell “fish-eye” problem and the Fock group for the Hydrogen atom,” Sov. Phys. JETP33, 1083 (1971).

1952 (1)

J. E. Eaton, “On spherically symmetric lenses,” Trans. IRE Antennas Propag.4, 66–71 (1952).

1854 (1)

J. C. Maxwell, “Problems,” Cambridge Dublin Math. J.8, 188–189 (1854).

Acher, O.

O. Acher, “Copper vs. iron: Microwave magnetism in the metamaterial age,” J. Magn. Magn. Mater.321(14), 2093–2101 (2009).
[CrossRef]

Argyropoulos, C.

D. Bao, K. Z. Rajab, Y. Hao, E. Kallos, W. Tang, C. Argyropoulos, Y. Piao, and S. Yang, “All-dielectric invisibility cloaks made of BaTiO 3 -loaded polyurethane foam,” New J. Phys.13(10), 103023 (2011).
[CrossRef]

Aubry, A.

J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation optics and subwavelength control of light,” Science337(6094), 549–552 (2012).
[CrossRef] [PubMed]

Bao, D.

D. Bao, K. Z. Rajab, Y. Hao, E. Kallos, W. Tang, C. Argyropoulos, Y. Piao, and S. Yang, “All-dielectric invisibility cloaks made of BaTiO 3 -loaded polyurethane foam,” New J. Phys.13(10), 103023 (2011).
[CrossRef]

Basov, D. N.

Benítez, P.

Bering, K.

T. Tyc, L. Herzánová, M. Šarbot, and K. Bering, “Absolute instruments and perfect imaging in geometrical optics,” New J. Phys.13(11), 115004 (2011).
[CrossRef]

Burokur, S. N.

P.-H. Tichit, S. N. Burokur, and A. De Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys.105(10), 104912 (2009).
[CrossRef]

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett.91(11), 111105 (2007).
[CrossRef]

Catrysse, P. B.

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett.94(19), 197401 (2005).
[CrossRef] [PubMed]

Chan, C. T.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater.9(5), 387–396 (2010).
[CrossRef] [PubMed]

Chen, H.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater.9(5), 387–396 (2010).
[CrossRef] [PubMed]

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett.95(19), 193506 (2009).
[CrossRef]

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett.91(11), 111105 (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,” Science323(5912), 366–369 (2009).
[CrossRef] [PubMed]

Cui, T. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323(5912), 366–369 (2009).
[CrossRef] [PubMed]

Cummer, S. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostructures6(1), 87–95 (2008).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Danner, A. J.

A. J. Danner, T. Tyc, and U. Leonhardt, “Controlling birefringence in dielectrics,” Nat. Photonics5(6), 357–359 (2011).
[CrossRef]

De Lustrac, A.

P.-H. Tichit, S. N. Burokur, and A. De Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys.105(10), 104912 (2009).
[CrossRef]

Demetriadou, A.

Demkov, Y. N.

Y. N. Demkov and V. N. Ostrovsky, “Internal symmetry of the Maxwell “fish-eye” problem and the Fock group for the Hydrogen atom,” Sov. Phys. JETP33, 1083 (1971).

Driscoll, T.

Eaton, J. E.

J. E. Eaton, “On spherically symmetric lenses,” Trans. IRE Antennas Propag.4, 66–71 (1952).

Fan, S.

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett.94(19), 197401 (2005).
[CrossRef] [PubMed]

D. F. Sievenpiper, E. Yablonovitch, J. N. Winn, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “3D metallo-dielectric photonic crystals with strong capacitative coupling,” Phys. Rev. Lett.80, 2829–2832 (1998).
[CrossRef]

Garci-Meca, C.

J. Perczel, C. Garci-Meca, and U. Leonhardt, “Partial transmutation of singularities in optical instruments,” J. Opt.13(7), 075103 (2011).
[CrossRef]

González, J. C.

Hao, Y.

D. Bao, K. Z. Rajab, Y. Hao, E. Kallos, W. Tang, C. Argyropoulos, Y. Piao, and S. Yang, “All-dielectric invisibility cloaks made of BaTiO 3 -loaded polyurethane foam,” New J. Phys.13(10), 103023 (2011).
[CrossRef]

R. Yang, W. Tang, and Y. Hao, “A broadband zone plate lens from transformation optics,” Opt. Express19(13), 12348–12355 (2011).
[CrossRef] [PubMed]

A. Demetriadou and Y. Hao, “Slim Luneburg Lens for Antenna Applications,” Opt. Express19(21), 19925–19934 (2011).
[CrossRef] [PubMed]

Herzánová, L.

T. Tyc, L. Herzánová, M. Šarbot, and K. Bering, “Absolute instruments and perfect imaging in geometrical optics,” New J. Phys.13(11), 115004 (2011).
[CrossRef]

Huangfu, J.

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett.95(19), 193506 (2009).
[CrossRef]

Hunt, J.

Ji, C.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323(5912), 366–369 (2009).
[CrossRef] [PubMed]

Joannopoulos, J. D.

D. F. Sievenpiper, E. Yablonovitch, J. N. Winn, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “3D metallo-dielectric photonic crystals with strong capacitative coupling,” Phys. Rev. Lett.80, 2829–2832 (1998).
[CrossRef]

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Kallos, E.

D. Bao, K. Z. Rajab, Y. Hao, E. Kallos, W. Tang, C. Argyropoulos, Y. Piao, and S. Yang, “All-dielectric invisibility cloaks made of BaTiO 3 -loaded polyurethane foam,” New J. Phys.13(10), 103023 (2011).
[CrossRef]

Kildishev, A. V.

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett.91(11), 111105 (2007).
[CrossRef]

Kundtz, N.

T. Driscoll, G. Lipworth, J. Hunt, N. Landy, N. Kundtz, D. N. Basov, and D. R. Smith, “Performance of a three dimensional transformation-optical-flattened Lüneburg lens,” Opt. Express20(12), 13262–13273 (2012).
[CrossRef] [PubMed]

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

N. I. Landy, N. Kundtz, and D. R. Smith, “Designing three-dimensional transformation optical media using quasiconformal coordinate transformations,” Phys. Rev. Lett.105(19), 193902 (2010).
[CrossRef] [PubMed]

Lagarkov, A. N.

A. N. Lagarkov and K. N. Rozanov, “High-frequency behavior of magnetic composites,” J. Magn. Magn. Mater.321(14), 2082–2092 (2009).
[CrossRef]

Landy, N.

Landy, N. I.

N. I. Landy, N. Kundtz, and D. R. Smith, “Designing three-dimensional transformation optical media using quasiconformal coordinate transformations,” Phys. Rev. Lett.105(19), 193902 (2010).
[CrossRef] [PubMed]

Leonhardt, U.

J. Perczel, T. Tyc, and U. Leonhardt, “Invisibility cloaking without superluminal propagation,” New J. Phys.13(8), 083007 (2011).
[CrossRef]

J. Perczel, C. Garci-Meca, and U. Leonhardt, “Partial transmutation of singularities in optical instruments,” J. Opt.13(7), 075103 (2011).
[CrossRef]

A. J. Danner, T. Tyc, and U. Leonhardt, “Controlling birefringence in dielectrics,” Nat. Photonics5(6), 357–359 (2011).
[CrossRef]

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater.8(8), 639–642 (2009).
[CrossRef] [PubMed]

U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science323(5910), 110–112 (2009).
[CrossRef] [PubMed]

T. Tyc and U. Leonhardt, “Transmutation of singularities in optical instruments,” New J. Phys.10(11), 115038 (2008).
[CrossRef]

U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

Li, J.

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

Lipworth, G.

Liu, R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323(5912), 366–369 (2009).
[CrossRef] [PubMed]

Luo, Y.

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett.95(19), 193506 (2009).
[CrossRef]

Ma, Y. G.

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater.8(8), 639–642 (2009).
[CrossRef] [PubMed]

Maier, S. A.

J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation optics and subwavelength control of light,” Science337(6094), 549–552 (2012).
[CrossRef] [PubMed]

Maxwell, J. C.

J. C. Maxwell, “Problems,” Cambridge Dublin Math. J.8, 188–189 (1854).

Milton, G. W.

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett.91(11), 111105 (2007).
[CrossRef]

Miñano, J. C.

Mock, J. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323(5912), 366–369 (2009).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Nathan, K. B.

K. B. Nathan, D. R. Smith, and J. B. Pendry, “Electromagnetic design with transformation optics,” Proc. IEEE99(10), 1622–1633 (2011).
[CrossRef]

Ong, C. K.

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater.8(8), 639–642 (2009).
[CrossRef] [PubMed]

Ostrovsky, V. N.

Y. N. Demkov and V. N. Ostrovsky, “Internal symmetry of the Maxwell “fish-eye” problem and the Fock group for the Hydrogen atom,” Sov. Phys. JETP33, 1083 (1971).

Pendry, J. B.

J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation optics and subwavelength control of light,” Science337(6094), 549–552 (2012).
[CrossRef] [PubMed]

K. B. Nathan, D. R. Smith, and J. B. Pendry, “Electromagnetic design with transformation optics,” Proc. IEEE99(10), 1622–1633 (2011).
[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]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostructures6(1), 87–95 (2008).
[CrossRef]

B. Wood and J. B. Pendry, “Metamaterials at zero frequency,” J. Phys. Condens. Matter19(7), 076208 (2007).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science305(5685), 788–792 (2004).
[CrossRef] [PubMed]

Perczel, J.

J. Perczel, T. Tyc, and U. Leonhardt, “Invisibility cloaking without superluminal propagation,” New J. Phys.13(8), 083007 (2011).
[CrossRef]

J. Perczel, C. Garci-Meca, and U. Leonhardt, “Partial transmutation of singularities in optical instruments,” J. Opt.13(7), 075103 (2011).
[CrossRef]

Piao, Y.

D. Bao, K. Z. Rajab, Y. Hao, E. Kallos, W. Tang, C. Argyropoulos, Y. Piao, and S. Yang, “All-dielectric invisibility cloaks made of BaTiO 3 -loaded polyurethane foam,” New J. Phys.13(10), 103023 (2011).
[CrossRef]

Rahm, M.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostructures6(1), 87–95 (2008).
[CrossRef]

Rajab, K. Z.

D. Bao, K. Z. Rajab, Y. Hao, E. Kallos, W. Tang, C. Argyropoulos, Y. Piao, and S. Yang, “All-dielectric invisibility cloaks made of BaTiO 3 -loaded polyurethane foam,” New J. Phys.13(10), 103023 (2011).
[CrossRef]

Ran, L.

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett.95(19), 193506 (2009).
[CrossRef]

Roberts, D. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostructures6(1), 87–95 (2008).
[CrossRef]

Rozanov, K. N.

A. N. Lagarkov and K. N. Rozanov, “High-frequency behavior of magnetic composites,” J. Magn. Magn. Mater.321(14), 2082–2092 (2009).
[CrossRef]

Šarbot, M.

T. Tyc, L. Herzánová, M. Šarbot, and K. Bering, “Absolute instruments and perfect imaging in geometrical optics,” New J. Phys.13(11), 115004 (2011).
[CrossRef]

Schurig, D.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostructures6(1), 87–95 (2008).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Shalaev, V. M.

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett.91(11), 111105 (2007).
[CrossRef]

Shen, J. T.

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett.94(19), 197401 (2005).
[CrossRef] [PubMed]

Sheng, P.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater.9(5), 387–396 (2010).
[CrossRef] [PubMed]

Sievenpiper, D. F.

D. F. Sievenpiper, E. Yablonovitch, J. N. Winn, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “3D metallo-dielectric photonic crystals with strong capacitative coupling,” Phys. Rev. Lett.80, 2829–2832 (1998).
[CrossRef]

Smith, D. R.

T. Driscoll, G. Lipworth, J. Hunt, N. Landy, N. Kundtz, D. N. Basov, and D. R. Smith, “Performance of a three dimensional transformation-optical-flattened Lüneburg lens,” Opt. Express20(12), 13262–13273 (2012).
[CrossRef] [PubMed]

J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation optics and subwavelength control of light,” Science337(6094), 549–552 (2012).
[CrossRef] [PubMed]

K. B. Nathan, D. R. Smith, and J. B. Pendry, “Electromagnetic design with transformation optics,” Proc. IEEE99(10), 1622–1633 (2011).
[CrossRef]

N. I. Landy, N. Kundtz, and D. R. Smith, “Designing three-dimensional transformation optical media using quasiconformal coordinate transformations,” Phys. Rev. Lett.105(19), 193902 (2010).
[CrossRef] [PubMed]

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

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323(5912), 366–369 (2009).
[CrossRef] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostructures6(1), 87–95 (2008).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science305(5685), 788–792 (2004).
[CrossRef] [PubMed]

Soukoulis, C. M.

C. M. Soukoulis and M. Wegener, “Materials science. Optical metamaterials--more bulky and less lossy,” Science330(6011), 1633–1634 (2010).
[CrossRef] [PubMed]

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Tang, W.

D. Bao, K. Z. Rajab, Y. Hao, E. Kallos, W. Tang, C. Argyropoulos, Y. Piao, and S. Yang, “All-dielectric invisibility cloaks made of BaTiO 3 -loaded polyurethane foam,” New J. Phys.13(10), 103023 (2011).
[CrossRef]

R. Yang, W. Tang, and Y. Hao, “A broadband zone plate lens from transformation optics,” Opt. Express19(13), 12348–12355 (2011).
[CrossRef] [PubMed]

Tichit, P.-H.

P.-H. Tichit, S. N. Burokur, and A. De Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys.105(10), 104912 (2009).
[CrossRef]

Tsutaoka, T.

T. Tsutaoka, “Frequency dispersion of complex permeability in Mn–Zn and Ni–Zn spinel ferrites and their composite materials,” J. Appl. Phys.93(5), 2789–2796 (2003).
[CrossRef]

Tyc, T.

A. J. Danner, T. Tyc, and U. Leonhardt, “Controlling birefringence in dielectrics,” Nat. Photonics5(6), 357–359 (2011).
[CrossRef]

J. Perczel, T. Tyc, and U. Leonhardt, “Invisibility cloaking without superluminal propagation,” New J. Phys.13(8), 083007 (2011).
[CrossRef]

T. Tyc, L. Herzánová, M. Šarbot, and K. Bering, “Absolute instruments and perfect imaging in geometrical optics,” New J. Phys.13(11), 115004 (2011).
[CrossRef]

U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science323(5910), 110–112 (2009).
[CrossRef] [PubMed]

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater.8(8), 639–642 (2009).
[CrossRef] [PubMed]

T. Tyc and U. Leonhardt, “Transmutation of singularities in optical instruments,” New J. Phys.10(11), 115038 (2008).
[CrossRef]

Villeneuve, P. R.

D. F. Sievenpiper, E. Yablonovitch, J. N. Winn, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “3D metallo-dielectric photonic crystals with strong capacitative coupling,” Phys. Rev. Lett.80, 2829–2832 (1998).
[CrossRef]

Wegener, M.

C. M. Soukoulis and M. Wegener, “Materials science. Optical metamaterials--more bulky and less lossy,” Science330(6011), 1633–1634 (2010).
[CrossRef] [PubMed]

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science305(5685), 788–792 (2004).
[CrossRef] [PubMed]

Winn, J. N.

D. F. Sievenpiper, E. Yablonovitch, J. N. Winn, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “3D metallo-dielectric photonic crystals with strong capacitative coupling,” Phys. Rev. Lett.80, 2829–2832 (1998).
[CrossRef]

Wood, B.

B. Wood and J. B. Pendry, “Metamaterials at zero frequency,” J. Phys. Condens. Matter19(7), 076208 (2007).
[CrossRef] [PubMed]

Yablonovitch, E.

D. F. Sievenpiper, E. Yablonovitch, J. N. Winn, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “3D metallo-dielectric photonic crystals with strong capacitative coupling,” Phys. Rev. Lett.80, 2829–2832 (1998).
[CrossRef]

Yang, R.

Yang, S.

D. Bao, K. Z. Rajab, Y. Hao, E. Kallos, W. Tang, C. Argyropoulos, Y. Piao, and S. Yang, “All-dielectric invisibility cloaks made of BaTiO 3 -loaded polyurethane foam,” New J. Phys.13(10), 103023 (2011).
[CrossRef]

Zhang, J.

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett.95(19), 193506 (2009).
[CrossRef]

Appl. Phys. Lett. (2)

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett.91(11), 111105 (2007).
[CrossRef]

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett.95(19), 193506 (2009).
[CrossRef]

Cambridge Dublin Math. J. (1)

J. C. Maxwell, “Problems,” Cambridge Dublin Math. J.8, 188–189 (1854).

J. Appl. Phys. (2)

P.-H. Tichit, S. N. Burokur, and A. De Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys.105(10), 104912 (2009).
[CrossRef]

T. Tsutaoka, “Frequency dispersion of complex permeability in Mn–Zn and Ni–Zn spinel ferrites and their composite materials,” J. Appl. Phys.93(5), 2789–2796 (2003).
[CrossRef]

J. Magn. Magn. Mater. (2)

O. Acher, “Copper vs. iron: Microwave magnetism in the metamaterial age,” J. Magn. Magn. Mater.321(14), 2093–2101 (2009).
[CrossRef]

A. N. Lagarkov and K. N. Rozanov, “High-frequency behavior of magnetic composites,” J. Magn. Magn. Mater.321(14), 2082–2092 (2009).
[CrossRef]

J. Opt. (1)

J. Perczel, C. Garci-Meca, and U. Leonhardt, “Partial transmutation of singularities in optical instruments,” J. Opt.13(7), 075103 (2011).
[CrossRef]

J. Phys. Condens. Matter (1)

B. Wood and J. B. Pendry, “Metamaterials at zero frequency,” J. Phys. Condens. Matter19(7), 076208 (2007).
[CrossRef] [PubMed]

Nat. Mater. (3)

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater.8(8), 639–642 (2009).
[CrossRef] [PubMed]

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

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater.9(5), 387–396 (2010).
[CrossRef] [PubMed]

Nat. Photonics (1)

A. J. Danner, T. Tyc, and U. Leonhardt, “Controlling birefringence in dielectrics,” Nat. Photonics5(6), 357–359 (2011).
[CrossRef]

New J. Phys. (4)

D. Bao, K. Z. Rajab, Y. Hao, E. Kallos, W. Tang, C. Argyropoulos, Y. Piao, and S. Yang, “All-dielectric invisibility cloaks made of BaTiO 3 -loaded polyurethane foam,” New J. Phys.13(10), 103023 (2011).
[CrossRef]

T. Tyc and U. Leonhardt, “Transmutation of singularities in optical instruments,” New J. Phys.10(11), 115038 (2008).
[CrossRef]

T. Tyc, L. Herzánová, M. Šarbot, and K. Bering, “Absolute instruments and perfect imaging in geometrical optics,” New J. Phys.13(11), 115004 (2011).
[CrossRef]

J. Perczel, T. Tyc, and U. Leonhardt, “Invisibility cloaking without superluminal propagation,” New J. Phys.13(8), 083007 (2011).
[CrossRef]

Opt. Express (4)

Photon. Nanostructures (1)

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostructures6(1), 87–95 (2008).
[CrossRef]

Phys. Rev. Lett. (4)

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. F. Sievenpiper, E. Yablonovitch, J. N. Winn, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “3D metallo-dielectric photonic crystals with strong capacitative coupling,” Phys. Rev. Lett.80, 2829–2832 (1998).
[CrossRef]

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett.94(19), 197401 (2005).
[CrossRef] [PubMed]

N. I. Landy, N. Kundtz, and D. R. Smith, “Designing three-dimensional transformation optical media using quasiconformal coordinate transformations,” Phys. Rev. Lett.105(19), 193902 (2010).
[CrossRef] [PubMed]

Proc. IEEE (1)

K. B. Nathan, D. R. Smith, and J. B. Pendry, “Electromagnetic design with transformation optics,” Proc. IEEE99(10), 1622–1633 (2011).
[CrossRef]

Science (8)

U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323(5912), 366–369 (2009).
[CrossRef] [PubMed]

U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science323(5910), 110–112 (2009).
[CrossRef] [PubMed]

J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation optics and subwavelength control of light,” Science337(6094), 549–552 (2012).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

C. M. Soukoulis and M. Wegener, “Materials science. Optical metamaterials--more bulky and less lossy,” Science330(6011), 1633–1634 (2010).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science305(5685), 788–792 (2004).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

Y. N. Demkov and V. N. Ostrovsky, “Internal symmetry of the Maxwell “fish-eye” problem and the Fock group for the Hydrogen atom,” Sov. Phys. JETP33, 1083 (1971).

Trans. IRE Antennas Propag. (1)

J. E. Eaton, “On spherically symmetric lenses,” Trans. IRE Antennas Propag.4, 66–71 (1952).

Other (3)

N. Engheta and R. W. Ziolkowski, Metamaterials: Physics and Engineering Explorations (Wiley & Sons, 2006).

R. K. Luneburg, Mathematical Theory of Optics (Univ. of California Press, 1964).

U. Leonhardt and T. G. Philbin, Geometry and Light: The Science of Invisibility (Dover, 2010).

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Figures (12)

Fig. 1
Fig. 1

Ray trajectories in a plane through a) a spherical Eaton lens, b) an impedance-matched transmuted spherical Eaton lens using the co-ordinate transformation in Eq. (2), c) a transmuted cylindrical Eaton lens with non-magnetic materials using the co-ordinate transformation in Eq. (10).

Fig. 2
Fig. 2

(a) The permittivity and permeability as a function of the radius for the transmuted spherical Eaton lens. (b) The permittivity and permeability as a function of the radius obtained using the same transmutation process, but in cylindrical co-ordinates (note the log scale).

Fig. 3
Fig. 3

The components of the refractive index tensor as a function of the radial distance for the transmuted cylindrical Eaton lens obtained using Eq. (6).

Fig. 4
Fig. 4

The relevant permittivity and permeability components as a function of the radial co-ordinate of a transmuted cylindrical Eaton lens for light polarised with the electric field in the { r,φ } plane.

Fig. 5
Fig. 5

Full wave numerical modeling (instantaneous total electric field) of transmuted cylindrical Eaton lenses. a) a scaled transmuted Eaton lens consisting of non-magnetic materials (in-plane polarisation) using the co-ordinate transformation given by Eq. (2) b) a transmuted Eaton lens consisting of non-magnetic materials using the modified co-ordinate transformation given by Eq. (8) (in-plane polarisation). c) The same as b), but for the out-of-plane polarisation.

Fig. 6
Fig. 6

The permittivity and permeability profiles of the modified transmuted Eaton lens (for light polarised with its electric field in the {r,φ} plane. Inset: the co-ordinate transformations of the transmuted and modified transmuted Eaton lenses.

Fig. 7
Fig. 7

Ray trajectories for an “invisible disc”. Any ray impinging upon the device exits as if the device were not present.

Fig. 8
Fig. 8

Left: The relevant components of the permittivity tensor for the transmuted invisible disc for light polarised with its electric field parallel to the {r,φ} plane z =1) . Right: Full wave numerical modeling (instantaneous total electric field) of the transmuted invisible disc.

Fig. 9
Fig. 9

Ray trajectories for refractive index profiles given by Eq. (14). Left:  l=0 , a monopolar mode, Center:  l=1 , a dipolar mode identical to the well-known Maxwell fish-eye lens, Right: l=2 , a quadrupolar mode.

Fig. 10
Fig. 10

The resulting permittivity profile and full wave modeling (instantaneous total electric field) of the transmuted monopolar lens ( l=0 ) for light polarised with its electric field in the {r,φ} plane z =1) . The wave components from a point source at the boundary that enter the device are re-focused back to the source.

Fig. 11
Fig. 11

The permittivity profile of the transmuted quadrupolar lens for light polarised with its E-field parallel to the {r,φ} plane z =1) . The original refractive index profile (Eq. (14)) is scaled by a factor of 2.4 to enable all relevant permittivity components to be greater than unity.

Fig. 12
Fig. 12

Full wave modeling (instantaneous total electric field) of the quadrupolar lens using the permittivity profile shown in Fig. 11 for light polarised with its electric field in the {r,φ} plane. Left: with a single point source placed at the radius of the device on the left. Right: with two point sources, one on the radius to the left of the device, and an additional one to the right.

Equations (14)

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

n( r )= 2 r 1   if r  1, and n( r )=1 if r > 1     
R( r )= f(r) N(b)  if rb, and R( r )=r if r>b 
f( r )= 0 r n( r' )dr' 0 1 n( r' )dr'   
ε k i = μ k i =n diag( r 2 R 2 dR dr ,   dr dR ,  dr dR )   
ε k i = μ k i =n diag( r R dR dr ,   R r dr dR ,  r R dr dR ) 
n'=diag( ε θ ε z ,  ε r ε z , ε r ε θ )= n diag( dr dR ,   r R , 1 )
 Electric field in the { r,φ }plane: n r = ε θ μ z  &  n θ = ε r μ z
Magnetic field in the{ r,φ }plane: n r = μ θ ε z  &  n θ = μ r ε z
ε > 1 0  μ <1 n 1
R( r )= f(r) N(b) +α r m ( rb )
dR dr trans | r=b = dR dr nontrans | r=b  
n( r )= ( Q 1 3Q ) 2
Q= 1 r + 1 r 2 + 1 27 3
n(r)= 2 r ( 2 l1 1 ) 1+ r 2 l

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