Abstract

An effective cylindrical cloak may be conceptualized as an assembly of adjacent local neighborhoods, each of which is made from a homogenized composite material (HCM). The HCM is required to be a certain uniaxial dielectric-magnetic material, characterized by positive-definite constitutive dyadics. It can arise from the homogenization of component materials that are remarkably simple in terms of their structure and constitutive relations. For example, the components can be two isotropic dielectric-magnetic materials, randomly distributed as oriented spheroidal particles. By carefully controlling the spheroidal shape of the component particles, a high degree of HCM anisotropy may be achieved which is necessary for the cloaking effect to be realized. The inverse Bruggeman formalism can provide estimates of the shape and constitutive parameters for the component materials, as well as their volume fractions.

© 2012 Optical Society of America

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  9. Y. Lai, H. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102, 093901 (2009).
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    [CrossRef]
  30. S. S. Jamaian and T. G. Mackay, “On limitations of the Bruggeman formalism for inverse homogenization,” J. Nanophoton. 4, 043510 (2010).
    [CrossRef]
  31. A. Alù, M. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
    [CrossRef]
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    [CrossRef]
  33. M. N. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla, “Enhanced lens by ϵ and μ near-zero metamaterial boosted by extraordinary optical transmission,” Phys. Rev. B 83, 115112 (2011).
    [CrossRef]
  34. A. Sihvola, S. Tretyakov, and A. de Baas, “Metamaterials with extreme material parameters,” J. Commun. Technol. Electron. 52, 986–990 (2007).
    [CrossRef]
  35. S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
    [CrossRef]
  36. T. G. Mackay and W. S. Weiglhofer, “Homogenization of biaxial composite materials: dissipative anisotropic properties,” J. Opt. A: Pure Appl. Opt. 2, 426–432 (2000).
    [CrossRef]

2011 (6)

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

H. Gao, B. Zhang, and G. Barbastathis, “Photonic cloak made of subwavelength dielectric elliptical rod arrays,” Opt. Commun. 284, 4820–4823 (2011).
[CrossRef]

T. H. Anderson, T. G. Mackay, and A. Lakhtakia, “Ray trajectories for Alcubierre spacetime,” J. Opt. 13, 055107 (2011).
[CrossRef]

T. G. Mackay and A. Lakhtakia, “Towards a realization of Schwarzschild-(anti-)de Sitter spacetime as a particulate metamaterial,” Phys. Rev. B 83, 195424 (2011).
[CrossRef]

T. G. Mackay, “Effective constitutive parameters of linear nanocomposites in the long-wavelength regime,” J. Nanophoton. 5, 051001 (2011).
[CrossRef]

M. N. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla, “Enhanced lens by ϵ and μ near-zero metamaterial boosted by extraordinary optical transmission,” Phys. Rev. B 83, 115112 (2011).
[CrossRef]

2010 (6)

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef]

T. G. Mackay and A. Lakhtakia, “Determination of constitutive and morphological parameters of columnar thin films by inverse homogenization,” J. Nanophoton. 4, 041535 (2010).
[CrossRef]

S. S. Jamaian and T. G. Mackay, “On limitations of the Bruggeman formalism for inverse homogenization,” J. Nanophoton. 4, 043510 (2010).
[CrossRef]

T. G. Mackay and A. Lakhtakia, “Towards a metamaterial simulation of a spinning cosmic string,” Phys. Lett. A 374, 2305–2308 (2010).
[CrossRef]

T. H. Anderson, T. G. Mackay, and A. Lakhtakia, “Ray trajectories for a spinning cosmic string and a manifestation of self-cloaking,” Phys. Lett. A 374, 4637–4641 (2010).
[CrossRef]

G. Milton, “Realizability of metamaterials with prescribed electric permittivity and magnetic permeability tensors,” New J. Phys. 12, 033035 (2010).
[CrossRef]

2009 (5)

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: application to optical cloaking,” Phys. Rev. Lett. 102, 213901 (2009).
[CrossRef]

B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, “Experimental verification of plasmonic cloaking at microwave frequencies with metamaterials,” Phys. Rev. Lett. 103, 153901 (2009).
[CrossRef]

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Cloaking devices, electromagnetic wormholes, and transformation optics,” SIAM Rev. 51, 3–33 (2009).
[CrossRef]

Y. Lai, H. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102, 093901 (2009).
[CrossRef]

M. Sluijter, D. K. De Boer, and H. P. Urbach, “Ray-optics analysis of inhomogeneous biaxially anisotropic media,” J. Opt. Soc. Am. A 26, 317–329 (2009).
[CrossRef]

2008 (1)

2007 (5)

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, “Ideal cylindrical cloak: perfect but sensitive to tiny perturbations,” Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef]

A. Alù, M. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[CrossRef]

G. Lovat, P. Burghignoli, F. Capolino, and D. R. Jackson, “Combinations of low/high permittivity and/or permeability substrates for highly directive planar metamaterial antennas,” IET Microw. Antennas Propagat. 1, 177–183 (2007).
[CrossRef]

A. Sihvola, S. Tretyakov, and A. de Baas, “Metamaterials with extreme material parameters,” J. Commun. Technol. Electron. 52, 986–990 (2007).
[CrossRef]

N. A. Nicorovici, G. W. Milton, R. C. McPhedran, and L. C. Botten, “Quasistatic cloaking of two-dimensional polarizable discrete systems by anomalous resonance,” Opt. Express 15, 6314–6323 (2007).
[CrossRef]

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,” Science 314, 977–980(2006).
[CrossRef]

R. A. Depine, M. E. Inchaussandague, and A. Lakhtakia, “Vector theory of diffraction by gratings made of a uniaxial dielectric-magnetic material exhibiting negative refraction,” J. Opt. Soc. Am. B 23, 514–528 (2006).
[CrossRef]

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

2005 (1)

T. G. Mackay, A. Lakhtakia, and S. Setiawan, “Gravitation and electromagnetic wave propagation with negative phase velocity,” New J. Phys. 7, 75 (2005).
[CrossRef]

2001 (2)

W. S. Weiglhofer, “On the inverse homogenization problem of linear composite materials,” Microw. Opt. Technol. Lett. 28, 421–423 (2001).
[CrossRef]

E. Cherkaev, “Inverse homogenization for evaluation of effective properties of a mixture,” Inverse Probl. 17, 1203–1218 (2001).
[CrossRef]

2000 (1)

T. G. Mackay and W. S. Weiglhofer, “Homogenization of biaxial composite materials: dissipative anisotropic properties,” J. Opt. A: Pure Appl. Opt. 2, 426–432 (2000).
[CrossRef]

1999 (1)

1982 (1)

1960 (1)

J. Plébanski, “Electromagnetic waves in gravitational fields,” Phys. Rev. 118, 1396–1408 (1960).
[CrossRef]

1957 (1)

G. V. Skrotskii, “The influence of gravitation on the propagation of light,” Sov. Phys. Dokl. 2, 226–229 (1957).

Alù, A.

B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, “Experimental verification of plasmonic cloaking at microwave frequencies with metamaterials,” Phys. Rev. Lett. 103, 153901 (2009).
[CrossRef]

A. Alù, M. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[CrossRef]

Anderson, T. H.

T. H. Anderson, T. G. Mackay, and A. Lakhtakia, “Ray trajectories for Alcubierre spacetime,” J. Opt. 13, 055107 (2011).
[CrossRef]

T. H. Anderson, T. G. Mackay, and A. Lakhtakia, “Ray trajectories for a spinning cosmic string and a manifestation of self-cloaking,” Phys. Lett. A 374, 4637–4641 (2010).
[CrossRef]

Barbastathis, G.

H. Gao, B. Zhang, and G. Barbastathis, “Photonic cloak made of subwavelength dielectric elliptical rod arrays,” Opt. Commun. 284, 4820–4823 (2011).
[CrossRef]

Beruete, M.

M. N. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla, “Enhanced lens by ϵ and μ near-zero metamaterial boosted by extraordinary optical transmission,” Phys. Rev. B 83, 115112 (2011).
[CrossRef]

Botten, L. C.

Burghignoli, P.

G. Lovat, P. Burghignoli, F. Capolino, and D. R. Jackson, “Combinations of low/high permittivity and/or permeability substrates for highly directive planar metamaterial antennas,” IET Microw. Antennas Propagat. 1, 177–183 (2007).
[CrossRef]

Campillo, I.

M. N. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla, “Enhanced lens by ϵ and μ near-zero metamaterial boosted by extraordinary optical transmission,” Phys. Rev. B 83, 115112 (2011).
[CrossRef]

Capolino, F.

G. Lovat, P. Burghignoli, F. Capolino, and D. R. Jackson, “Combinations of low/high permittivity and/or permeability substrates for highly directive planar metamaterial antennas,” IET Microw. Antennas Propagat. 1, 177–183 (2007).
[CrossRef]

Chan, C. T.

Y. Lai, H. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102, 093901 (2009).
[CrossRef]

Chandezon, J.

Chen, H.

Y. Lai, H. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102, 093901 (2009).
[CrossRef]

Cherkaev, E.

E. Cherkaev, “Inverse homogenization for evaluation of effective properties of a mixture,” Inverse Probl. 17, 1203–1218 (2001).
[CrossRef]

Chettiar, U. K.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef]

Cornet, G.

Cummer, S. A.

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,” Science 314, 977–980(2006).
[CrossRef]

de Baas, A.

A. Sihvola, S. Tretyakov, and A. de Baas, “Metamaterials with extreme material parameters,” J. Commun. Technol. Electron. 52, 986–990 (2007).
[CrossRef]

De Boer, D. K.

Depine, R. A.

Drachev, V. P.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef]

Dupuis, M. T.

Edwards, B.

B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, “Experimental verification of plasmonic cloaking at microwave frequencies with metamaterials,” Phys. Rev. Lett. 103, 153901 (2009).
[CrossRef]

Engheta, N.

B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, “Experimental verification of plasmonic cloaking at microwave frequencies with metamaterials,” Phys. Rev. Lett. 103, 153901 (2009).
[CrossRef]

A. Alù, M. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[CrossRef]

Gao, H.

H. Gao, B. Zhang, and G. Barbastathis, “Photonic cloak made of subwavelength dielectric elliptical rod arrays,” Opt. Commun. 284, 4820–4823 (2011).
[CrossRef]

Granet, G.

Greenleaf, A.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Cloaking devices, electromagnetic wormholes, and transformation optics,” SIAM Rev. 51, 3–33 (2009).
[CrossRef]

Inchaussandague, M. E.

Jackson, D. R.

G. Lovat, P. Burghignoli, F. Capolino, and D. R. Jackson, “Combinations of low/high permittivity and/or permeability substrates for highly directive planar metamaterial antennas,” IET Microw. Antennas Propagat. 1, 177–183 (2007).
[CrossRef]

Jamaian, S. S.

S. S. Jamaian and T. G. Mackay, “On limitations of the Bruggeman formalism for inverse homogenization,” J. Nanophoton. 4, 043510 (2010).
[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,” Science 314, 977–980(2006).
[CrossRef]

Kay, I. W.

M. Kline and I. W. Kay, Electromagnetic Theory and Geometric Optics (Interscience, 1965).

Kildishev, A. V.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef]

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: application to optical cloaking,” Phys. Rev. Lett. 102, 213901 (2009).
[CrossRef]

Kline, M.

M. Kline and I. W. Kay, Electromagnetic Theory and Geometric Optics (Interscience, 1965).

Kurylev, Y.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Cloaking devices, electromagnetic wormholes, and transformation optics,” SIAM Rev. 51, 3–33 (2009).
[CrossRef]

Lai, Y.

Y. Lai, H. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102, 093901 (2009).
[CrossRef]

Lakhtakia, A.

T. H. Anderson, T. G. Mackay, and A. Lakhtakia, “Ray trajectories for Alcubierre spacetime,” J. Opt. 13, 055107 (2011).
[CrossRef]

T. G. Mackay and A. Lakhtakia, “Towards a realization of Schwarzschild-(anti-)de Sitter spacetime as a particulate metamaterial,” Phys. Rev. B 83, 195424 (2011).
[CrossRef]

T. G. Mackay and A. Lakhtakia, “Towards a metamaterial simulation of a spinning cosmic string,” Phys. Lett. A 374, 2305–2308 (2010).
[CrossRef]

T. H. Anderson, T. G. Mackay, and A. Lakhtakia, “Ray trajectories for a spinning cosmic string and a manifestation of self-cloaking,” Phys. Lett. A 374, 4637–4641 (2010).
[CrossRef]

T. G. Mackay and A. Lakhtakia, “Determination of constitutive and morphological parameters of columnar thin films by inverse homogenization,” J. Nanophoton. 4, 041535 (2010).
[CrossRef]

R. A. Depine, M. E. Inchaussandague, and A. Lakhtakia, “Vector theory of diffraction by gratings made of a uniaxial dielectric-magnetic material exhibiting negative refraction,” J. Opt. Soc. Am. B 23, 514–528 (2006).
[CrossRef]

T. G. Mackay, A. Lakhtakia, and S. Setiawan, “Gravitation and electromagnetic wave propagation with negative phase velocity,” New J. Phys. 7, 75 (2005).
[CrossRef]

T. G. Mackay and A. Lakhtakia, Electromagnetic Anisotropy and Bianisotropy: A Field Guide (Word Scientific, 2010).

Lassas, M.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Cloaking devices, electromagnetic wormholes, and transformation optics,” SIAM Rev. 51, 3–33 (2009).
[CrossRef]

Leonhardt, U.

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

Li, L.

Lovat, G.

G. Lovat, P. Burghignoli, F. Capolino, and D. R. Jackson, “Combinations of low/high permittivity and/or permeability substrates for highly directive planar metamaterial antennas,” IET Microw. Antennas Propagat. 1, 177–183 (2007).
[CrossRef]

Mackay, T. G.

T. G. Mackay, “Effective constitutive parameters of linear nanocomposites in the long-wavelength regime,” J. Nanophoton. 5, 051001 (2011).
[CrossRef]

T. G. Mackay and A. Lakhtakia, “Towards a realization of Schwarzschild-(anti-)de Sitter spacetime as a particulate metamaterial,” Phys. Rev. B 83, 195424 (2011).
[CrossRef]

T. H. Anderson, T. G. Mackay, and A. Lakhtakia, “Ray trajectories for Alcubierre spacetime,” J. Opt. 13, 055107 (2011).
[CrossRef]

T. H. Anderson, T. G. Mackay, and A. Lakhtakia, “Ray trajectories for a spinning cosmic string and a manifestation of self-cloaking,” Phys. Lett. A 374, 4637–4641 (2010).
[CrossRef]

T. G. Mackay and A. Lakhtakia, “Towards a metamaterial simulation of a spinning cosmic string,” Phys. Lett. A 374, 2305–2308 (2010).
[CrossRef]

T. G. Mackay and A. Lakhtakia, “Determination of constitutive and morphological parameters of columnar thin films by inverse homogenization,” J. Nanophoton. 4, 041535 (2010).
[CrossRef]

S. S. Jamaian and T. G. Mackay, “On limitations of the Bruggeman formalism for inverse homogenization,” J. Nanophoton. 4, 043510 (2010).
[CrossRef]

T. G. Mackay, A. Lakhtakia, and S. Setiawan, “Gravitation and electromagnetic wave propagation with negative phase velocity,” New J. Phys. 7, 75 (2005).
[CrossRef]

T. G. Mackay and W. S. Weiglhofer, “Homogenization of biaxial composite materials: dissipative anisotropic properties,” J. Opt. A: Pure Appl. Opt. 2, 426–432 (2000).
[CrossRef]

T. G. Mackay and A. Lakhtakia, Electromagnetic Anisotropy and Bianisotropy: A Field Guide (Word Scientific, 2010).

Maystre, D.

McPhedran, R. C.

Milton, G.

G. Milton, “Realizability of metamaterials with prescribed electric permittivity and magnetic permeability tensors,” New J. Phys. 12, 033035 (2010).
[CrossRef]

Milton, G. W.

Mock, J. 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,” Science 314, 977–980(2006).
[CrossRef]

Navarro-Cía, M. N.

M. N. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla, “Enhanced lens by ϵ and μ near-zero metamaterial boosted by extraordinary optical transmission,” Phys. Rev. B 83, 115112 (2011).
[CrossRef]

Neff, C. W.

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, “Ideal cylindrical cloak: perfect but sensitive to tiny perturbations,” Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef]

Ni, X.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef]

Nicorovici, N. A.

Pendry, J. B.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[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,” Science 314, 977–980(2006).
[CrossRef]

Perczel, J.

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

Plébanski, J.

J. Plébanski, “Electromagnetic waves in gravitational fields,” Phys. Rev. 118, 1396–1408 (1960).
[CrossRef]

Plumey, J.-P.

Qiu, M.

W. Yan, M. Yan, Z. Ruan, and M. Qiu, “Influence of geometrical perturbation at inner boundaries of invisibility cloaks,” J. Opt. Soc. Am. A 25, 968–973 (2008).
[CrossRef]

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, “Ideal cylindrical cloak: perfect but sensitive to tiny perturbations,” Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef]

Ruan, Z.

W. Yan, M. Yan, Z. Ruan, and M. Qiu, “Influence of geometrical perturbation at inner boundaries of invisibility cloaks,” J. Opt. Soc. Am. A 25, 968–973 (2008).
[CrossRef]

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, “Ideal cylindrical cloak: perfect but sensitive to tiny perturbations,” Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef]

Salandrino, A.

A. Alù, M. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[CrossRef]

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[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,” Science 314, 977–980(2006).
[CrossRef]

Setiawan, S.

T. G. Mackay, A. Lakhtakia, and S. Setiawan, “Gravitation and electromagnetic wave propagation with negative phase velocity,” New J. Phys. 7, 75 (2005).
[CrossRef]

Shalaev, V. M.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef]

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: application to optical cloaking,” Phys. Rev. Lett. 102, 213901 (2009).
[CrossRef]

Sihvola, A.

A. Sihvola, S. Tretyakov, and A. de Baas, “Metamaterials with extreme material parameters,” J. Commun. Technol. Electron. 52, 986–990 (2007).
[CrossRef]

Silveirinha, M.

A. Alù, M. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[CrossRef]

Silveirinha, M. G.

B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, “Experimental verification of plasmonic cloaking at microwave frequencies with metamaterials,” Phys. Rev. Lett. 103, 153901 (2009).
[CrossRef]

Skrotskii, G. V.

G. V. Skrotskii, “The influence of gravitation on the propagation of light,” Sov. Phys. Dokl. 2, 226–229 (1957).

Sluijter, M.

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[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,” Science 314, 977–980(2006).
[CrossRef]

Smolyaninov, I. I.

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: application to optical cloaking,” Phys. Rev. Lett. 102, 213901 (2009).
[CrossRef]

Smolyaninova, V. N.

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: application to optical cloaking,” Phys. Rev. Lett. 102, 213901 (2009).
[CrossRef]

Sorolla, M.

M. N. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla, “Enhanced lens by ϵ and μ near-zero metamaterial boosted by extraordinary optical transmission,” Phys. Rev. B 83, 115112 (2011).
[CrossRef]

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,” Science 314, 977–980(2006).
[CrossRef]

Tretyakov, S.

A. Sihvola, S. Tretyakov, and A. de Baas, “Metamaterials with extreme material parameters,” J. Commun. Technol. Electron. 52, 986–990 (2007).
[CrossRef]

Tyc, T.

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

Uhlmann, G.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Cloaking devices, electromagnetic wormholes, and transformation optics,” SIAM Rev. 51, 3–33 (2009).
[CrossRef]

Urbach, H. P.

Weiglhofer, W. S.

W. S. Weiglhofer, “On the inverse homogenization problem of linear composite materials,” Microw. Opt. Technol. Lett. 28, 421–423 (2001).
[CrossRef]

T. G. Mackay and W. S. Weiglhofer, “Homogenization of biaxial composite materials: dissipative anisotropic properties,” J. Opt. A: Pure Appl. Opt. 2, 426–432 (2000).
[CrossRef]

Xiao, S.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef]

Yan, M.

W. Yan, M. Yan, Z. Ruan, and M. Qiu, “Influence of geometrical perturbation at inner boundaries of invisibility cloaks,” J. Opt. Soc. Am. A 25, 968–973 (2008).
[CrossRef]

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, “Ideal cylindrical cloak: perfect but sensitive to tiny perturbations,” Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef]

Yan, W.

Yuan, H.-K.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef]

Zhang, B.

H. Gao, B. Zhang, and G. Barbastathis, “Photonic cloak made of subwavelength dielectric elliptical rod arrays,” Opt. Commun. 284, 4820–4823 (2011).
[CrossRef]

Zhang, Z.-Q.

Y. Lai, H. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102, 093901 (2009).
[CrossRef]

Appl. Opt. (1)

IET Microw. Antennas Propagat. (1)

G. Lovat, P. Burghignoli, F. Capolino, and D. R. Jackson, “Combinations of low/high permittivity and/or permeability substrates for highly directive planar metamaterial antennas,” IET Microw. Antennas Propagat. 1, 177–183 (2007).
[CrossRef]

Inverse Probl. (1)

E. Cherkaev, “Inverse homogenization for evaluation of effective properties of a mixture,” Inverse Probl. 17, 1203–1218 (2001).
[CrossRef]

J. Commun. Technol. Electron. (1)

A. Sihvola, S. Tretyakov, and A. de Baas, “Metamaterials with extreme material parameters,” J. Commun. Technol. Electron. 52, 986–990 (2007).
[CrossRef]

J. Nanophoton. (3)

T. G. Mackay and A. Lakhtakia, “Determination of constitutive and morphological parameters of columnar thin films by inverse homogenization,” J. Nanophoton. 4, 041535 (2010).
[CrossRef]

S. S. Jamaian and T. G. Mackay, “On limitations of the Bruggeman formalism for inverse homogenization,” J. Nanophoton. 4, 043510 (2010).
[CrossRef]

T. G. Mackay, “Effective constitutive parameters of linear nanocomposites in the long-wavelength regime,” J. Nanophoton. 5, 051001 (2011).
[CrossRef]

J. Opt. (1)

T. H. Anderson, T. G. Mackay, and A. Lakhtakia, “Ray trajectories for Alcubierre spacetime,” J. Opt. 13, 055107 (2011).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

T. G. Mackay and W. S. Weiglhofer, “Homogenization of biaxial composite materials: dissipative anisotropic properties,” J. Opt. A: Pure Appl. Opt. 2, 426–432 (2000).
[CrossRef]

J. Opt. Soc. Am. (1)

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

J. Opt. Soc. Am. B (1)

Microw. Opt. Technol. Lett. (1)

W. S. Weiglhofer, “On the inverse homogenization problem of linear composite materials,” Microw. Opt. Technol. Lett. 28, 421–423 (2001).
[CrossRef]

Nature (1)

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef]

New J. Phys. (3)

T. G. Mackay, A. Lakhtakia, and S. Setiawan, “Gravitation and electromagnetic wave propagation with negative phase velocity,” New J. Phys. 7, 75 (2005).
[CrossRef]

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

G. Milton, “Realizability of metamaterials with prescribed electric permittivity and magnetic permeability tensors,” New J. Phys. 12, 033035 (2010).
[CrossRef]

Opt. Commun. (1)

H. Gao, B. Zhang, and G. Barbastathis, “Photonic cloak made of subwavelength dielectric elliptical rod arrays,” Opt. Commun. 284, 4820–4823 (2011).
[CrossRef]

Opt. Express (1)

Phys. Lett. A (2)

T. G. Mackay and A. Lakhtakia, “Towards a metamaterial simulation of a spinning cosmic string,” Phys. Lett. A 374, 2305–2308 (2010).
[CrossRef]

T. H. Anderson, T. G. Mackay, and A. Lakhtakia, “Ray trajectories for a spinning cosmic string and a manifestation of self-cloaking,” Phys. Lett. A 374, 4637–4641 (2010).
[CrossRef]

Phys. Rev. (1)

J. Plébanski, “Electromagnetic waves in gravitational fields,” Phys. Rev. 118, 1396–1408 (1960).
[CrossRef]

Phys. Rev. B (3)

M. N. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla, “Enhanced lens by ϵ and μ near-zero metamaterial boosted by extraordinary optical transmission,” Phys. Rev. B 83, 115112 (2011).
[CrossRef]

A. Alù, M. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[CrossRef]

T. G. Mackay and A. Lakhtakia, “Towards a realization of Schwarzschild-(anti-)de Sitter spacetime as a particulate metamaterial,” Phys. Rev. B 83, 195424 (2011).
[CrossRef]

Phys. Rev. Lett. (4)

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, “Ideal cylindrical cloak: perfect but sensitive to tiny perturbations,” Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef]

Y. Lai, H. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102, 093901 (2009).
[CrossRef]

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: application to optical cloaking,” Phys. Rev. Lett. 102, 213901 (2009).
[CrossRef]

B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, “Experimental verification of plasmonic cloaking at microwave frequencies with metamaterials,” Phys. Rev. Lett. 103, 153901 (2009).
[CrossRef]

Science (2)

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,” Science 314, 977–980(2006).
[CrossRef]

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

SIAM Rev. (1)

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Cloaking devices, electromagnetic wormholes, and transformation optics,” SIAM Rev. 51, 3–33 (2009).
[CrossRef]

Sov. Phys. Dokl. (1)

G. V. Skrotskii, “The influence of gravitation on the propagation of light,” Sov. Phys. Dokl. 2, 226–229 (1957).

Other (2)

M. Kline and I. W. Kay, Electromagnetic Theory and Geometric Optics (Interscience, 1965).

T. G. Mackay and A. Lakhtakia, Electromagnetic Anisotropy and Bianisotropy: A Field Guide (Word Scientific, 2010).

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Figures (4)

Fig. 1.
Fig. 1.

Constitutive parameters γ11 (solid red curve) and γ22 (dashed blue curve) plotted versus radial distance ρ.

Fig. 2.
Fig. 2.

Two-dimensional example of ray trajectories for ρc=1.1. Rays start at equally spaced locations along the line x¯(0)=M¯¯·(30,ν,0) with 12.5<ν<12.5 and where the rotation dyadic M¯¯=cosφ(x¯^x¯^+y¯^y¯^)sinφ(x¯^y¯^y¯^x¯^) with φ=π/4; and k¯(0) is directed along (1,1,0).

Fig. 3.
Fig. 3.

Three-dimensional example of ray trajectories for ρc=1.1. Rays start at equally spaced locations along the line x¯(0)=M¯¯·(30,ν,29) with 12.5<ν<12.5 and where the rotation dyadic M¯¯ is defined as in Fig. 2; and k¯(0) is directed along (1,1,1).

Fig. 4.
Fig. 4.

Constitutive parameter ϵbμb (solid red curves), shape parameter UbUa (dashed green curves), and the volume fraction fb (broken blue dashed curves) plotted versus radial distance ρ for (a) ϵaμa=0.01, (b) ϵaμa=0.1, and (c) ϵaμa=0.3.

Equations (8)

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

D¯(r¯)=ϵ0γ=(ρ)·E¯(r¯)B¯(r¯)=μ0γ=(ρ)·H¯(r¯)},ρ>ρc,
γ=(ρ)=γ11(ρ)(x¯^x¯^+z¯^z¯^)+γ22(ρ)y¯^y¯^
γ11(ρ)=ρ1ργ22(ρ)=ρρ1}.
H=detγ=(ρ)k¯·γ=(ρ)·k¯
dr¯dα=k¯Hdk¯dα=r¯H},
ν(x¯^x¯^+Uy¯^y¯^+z¯^z¯^)·r¯^,(=a,b),
τ=Br=τ11Br(x¯^x¯^+z¯^z¯^)+τ22Bry¯^y¯^,(τ=ϵ,μ).
Δ=[(ϵ11Brγ11γ11)2+(ϵ22Brγ22γ22)2+(μ11Brγ11γ11)2+(μ22Brγ22γ22)2]1/2

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