Abstract

A type of transformation media called α media is proposed by performing a direct transformation to the metric tensor of another kind of media, called seed media. Light rays in an α medium correlate to those in its seed medium through a simple displacement or rotation relation. Three types of commonly encountered anisotropic media are covered by the concept of α media: (1) media of slab shape, having continuous translational symmetry with respect to two Cartesian coordinate components; (2) media of cylindrical shape, having cylindrical rotational symmetry and continuous translational symmetry along the longitudinal direction; (3) media of spherical shape, having spherical rotational symmetry, with two principal axes along the symmetry directions, and with the material parameters in the same sign. Optical properties of such media can be effectively interpreted through recalling the properties of certain isotropic media, i.e., their seed media. Conversely, from simple isotropic media in which light trajectories are well known, one can design α media for manipulating light. Based on this fact, several optical devices, including frequency demultiplexers, beam splitters, focusing lenses, and radiation controllers, are designed and numerically verified. The famed invisibility cloak derived from a conventional coordinate transformation is revisited from the α media perspective.

© 2011 Optical Society of America

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  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
    [CrossRef] [PubMed]
  2. U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
    [CrossRef] [PubMed]
  3. U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8, 247 (2006).
    [CrossRef]
  4. U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt. 53, 69–152 (2009).
    [CrossRef]
  5. M. Yan, W. Yan, and M. Qiu, “Invisibility cloaking by coordinate transformation,” Prog. Opt. 52, 261–301 (2009).
    [CrossRef]
  6. Z. C. 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] [PubMed]
  7. H. S. Chen, B. I. Wu, B. L. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
    [CrossRef] [PubMed]
  8. 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] [PubMed]
  9. J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  13. W. Yan, M. Yan, and M. Qiu, “Achieving perfect imaging beyond passive and active obstacles by a transformed bilayer lens,” Phys. Rev. B 79, 161101 (2009).
    [CrossRef]
  14. M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78, 125113 (2008).
    [CrossRef]
  15. M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77, 035122 (2008).
    [CrossRef]
  16. Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Wang, and C. T. Chan, “Illusion optics: The optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
    [CrossRef] [PubMed]
  17. Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. 8, 639–642 (2009).
    [CrossRef] [PubMed]
  18. L. Bergamin, “Generalized transformation optics from triple spacetime metamaterials,” Phys. Rev. A 78, 043825 (2008).
    [CrossRef]

2009

U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt. 53, 69–152 (2009).
[CrossRef]

M. Yan, W. Yan, and M. Qiu, “Invisibility cloaking by coordinate transformation,” Prog. Opt. 52, 261–301 (2009).
[CrossRef]

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

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photon. 3, 461–463 (2009).
[CrossRef]

Y. Lai, H. Y. Chen, Z. Q. Wang, 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] [PubMed]

W. Yan, M. Yan, and M. Qiu, “Achieving perfect imaging beyond passive and active obstacles by a transformed bilayer lens,” Phys. Rev. B 79, 161101 (2009).
[CrossRef]

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Wang, and C. T. Chan, “Illusion optics: The optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (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, 639–642 (2009).
[CrossRef] [PubMed]

2008

L. Bergamin, “Generalized transformation optics from triple spacetime metamaterials,” Phys. Rev. A 78, 043825 (2008).
[CrossRef]

M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78, 125113 (2008).
[CrossRef]

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77, 035122 (2008).
[CrossRef]

2007

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

Z. C. 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] [PubMed]

H. S. Chen, B. I. Wu, B. L. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

2006

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] [PubMed]

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

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

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8, 247 (2006).
[CrossRef]

Bartal, G.

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

Bergamin, L.

L. Bergamin, “Generalized transformation optics from triple spacetime metamaterials,” Phys. Rev. A 78, 043825 (2008).
[CrossRef]

Cardenas, J.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photon. 3, 461–463 (2009).
[CrossRef]

Chan, C. T.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Wang, and C. T. Chan, “Illusion optics: The optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef] [PubMed]

Y. Lai, H. Y. Chen, Z. Q. Wang, 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] [PubMed]

Chen, H. S.

H. S. Chen, B. I. Wu, B. L. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

Chen, H. Y.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Wang, and C. T. Chan, “Illusion optics: The optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef] [PubMed]

Y. Lai, H. Y. Chen, Z. Q. Wang, 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] [PubMed]

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] [PubMed]

Gabrielli, L. H.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photon. 3, 461–463 (2009).
[CrossRef]

Greenleaf, A.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

Han, D. Z.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Wang, and C. T. Chan, “Illusion optics: The optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef] [PubMed]

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] [PubMed]

Kong, J. A.

H. S. Chen, B. I. Wu, B. L. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

Kurylev, Y.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

Lai, Y.

Y. Lai, H. Y. Chen, Z. Q. Wang, 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] [PubMed]

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Wang, and C. T. Chan, “Illusion optics: The optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef] [PubMed]

Lassas, M.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

Leonhardt, U.

U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt. 53, 69–152 (2009).
[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, 639–642 (2009).
[CrossRef] [PubMed]

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

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8, 247 (2006).
[CrossRef]

Li, J.

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

Lipson, M.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photon. 3, 461–463 (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, 639–642 (2009).
[CrossRef] [PubMed]

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] [PubMed]

Neff, C. W.

Z. C. 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] [PubMed]

Ng, J.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Wang, and C. T. Chan, “Illusion optics: The optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef] [PubMed]

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, 639–642 (2009).
[CrossRef] [PubMed]

Pendry, J. B.

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

Philbin, T. G.

U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt. 53, 69–152 (2009).
[CrossRef]

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8, 247 (2006).
[CrossRef]

Poitras, C. B.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photon. 3, 461–463 (2009).
[CrossRef]

Psaltis, D.

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77, 035122 (2008).
[CrossRef]

Qiu, M.

M. Yan, W. Yan, and M. Qiu, “Invisibility cloaking by coordinate transformation,” Prog. Opt. 52, 261–301 (2009).
[CrossRef]

W. Yan, M. Yan, and M. Qiu, “Achieving perfect imaging beyond passive and active obstacles by a transformed bilayer lens,” Phys. Rev. B 79, 161101 (2009).
[CrossRef]

M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78, 125113 (2008).
[CrossRef]

Z. C. 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] [PubMed]

Ruan, Z. C.

Z. C. 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] [PubMed]

Schurig, D.

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

Smith, D. R.

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] [PubMed]

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

Tsang, M.

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77, 035122 (2008).
[CrossRef]

Tyc, T.

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

Uhlmann, G.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

Valentine, J.

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

Wang, Z. Q.

Y. Lai, H. Y. Chen, Z. Q. Wang, 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] [PubMed]

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Wang, and C. T. Chan, “Illusion optics: The optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef] [PubMed]

Wu, B. I.

H. S. Chen, B. I. Wu, B. L. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

Xiao, J. J.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Wang, and C. T. Chan, “Illusion optics: The optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef] [PubMed]

Yan, M.

M. Yan, W. Yan, and M. Qiu, “Invisibility cloaking by coordinate transformation,” Prog. Opt. 52, 261–301 (2009).
[CrossRef]

W. Yan, M. Yan, and M. Qiu, “Achieving perfect imaging beyond passive and active obstacles by a transformed bilayer lens,” Phys. Rev. B 79, 161101 (2009).
[CrossRef]

M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78, 125113 (2008).
[CrossRef]

Z. C. 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] [PubMed]

Yan, W.

W. Yan, M. Yan, and M. Qiu, “Achieving perfect imaging beyond passive and active obstacles by a transformed bilayer lens,” Phys. Rev. B 79, 161101 (2009).
[CrossRef]

M. Yan, W. Yan, and M. Qiu, “Invisibility cloaking by coordinate transformation,” Prog. Opt. 52, 261–301 (2009).
[CrossRef]

M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78, 125113 (2008).
[CrossRef]

Zentgraf, T.

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

Zhang, B. L.

H. S. Chen, B. I. Wu, B. L. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

Zhang, X.

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

Nat. Mater.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (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, 639–642 (2009).
[CrossRef] [PubMed]

Nat. Photon.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photon. 3, 461–463 (2009).
[CrossRef]

New J. Phys.

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8, 247 (2006).
[CrossRef]

Phys. Rev. A

L. Bergamin, “Generalized transformation optics from triple spacetime metamaterials,” Phys. Rev. A 78, 043825 (2008).
[CrossRef]

Phys. Rev. B

W. Yan, M. Yan, and M. Qiu, “Achieving perfect imaging beyond passive and active obstacles by a transformed bilayer lens,” Phys. Rev. B 79, 161101 (2009).
[CrossRef]

M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78, 125113 (2008).
[CrossRef]

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77, 035122 (2008).
[CrossRef]

Phys. Rev. Lett.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Wang, and C. T. Chan, “Illusion optics: The optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef] [PubMed]

Z. C. 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] [PubMed]

H. S. Chen, B. I. Wu, B. L. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

Y. Lai, H. Y. Chen, Z. Q. Wang, 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] [PubMed]

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

Prog. Opt.

U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt. 53, 69–152 (2009).
[CrossRef]

M. Yan, W. Yan, and M. Qiu, “Invisibility cloaking by coordinate transformation,” Prog. Opt. 52, 261–301 (2009).
[CrossRef]

Science

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

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (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,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

Illustration of a light ray passing through three types of α media and the corresponding seed media. The material parameters of seed and α media are expressed in Eqs. (9, 10), respectively. (a1) and (b1) represent the seed medium and α medium, respectively, with the three principal axes being Cartesian axes, (a2) and (b2) represent the seed medium and α medium, respectively, with the three principal axes being cylindrical axes; (a3) and (b3) represent the seed medium and α medium, respectively, with the three principal axes being spherical axes. The background and the seed media are all set to be free space, and the parameter α is set to be a constant.

Fig. 2
Fig. 2

Simulated power flow for a current sheet, J = exp ( ( y 6 λ p ) 2 / ( 3 λ p ) 2 ) δ ( x 20 λ p ) z ^ , with two frequencies, ω 1 = 0.6 ω p and ω 2 = 0.65 ω p , interacting with a cylinder in free space. The cylinder has material parameters μ r = 1 , μ θ = 3 ω p 2 / ω 2 , and ϵ = 1 , and has a radius of 16 λ p , where λ p = 2 π c / ω p . The dashed circle represents the boundary of the cylinder. The solid curves represent the calculated light ray from Eq. (6) based on the light ray in the corresponding isotropic seed medium.

Fig. 3
Fig. 3

Simulated power flow for a current sheet, J = exp ( y 2 / ( 2 λ ) 2 ) δ ( x 11 λ p ) z ^ , at wavelength λ, interacting with a cylinder in free space. The cylinder has material parameters μ r = 3 , μ θ = 1 and ϵ = 1 , with a radius of 10 λ . The dashed circle represents the boundary of the cylinder. The solid curves represent the calculated light ray from Eq. (6) based on the light ray in the corresponding isotropic seed medium.

Fig. 4
Fig. 4

Illustration of light rays for a plane wave from the free space background interacting with a cylinder composed of (a) free space, (b) an α medium, which has the α-relation with free space, and α = 1 / 2 . In (b), the reflected rays are not plotted.

Fig. 5
Fig. 5

Simulated electric field intensity for a TE plane wave interacting with (a) a cylinder; (b) the half-cylinder. The cylinder has material parameters μ r = 2 , μ θ = 1 / 2 and ϵ = 1 / 2 , and has a radius of 10 λ . The background is free space. The dashed circle represents the boundary of the cylinder or the half-cylinder.

Fig. 6
Fig. 6

Simulated electric field distribution for a line current at r c = 4 λ and θ c = 0 interacting with a cylinder composed of a medium with (a1)  μ r = 2 , μ θ = 1 / 2 , and ϵ = 1 / 2 ; (a2)  μ r = 1 , μ θ = 1 / 4 , and ϵ = 1 ; (b1)  μ r = 4 / 3 , μ θ = 3 / 4 , and ϵ = 3 / 4 ; (b2)  μ r = 1 , μ θ = 9 / 16 , and ϵ = 1 . The normalized radiation power for (a1) and (a2) is plotted in (a3). The normalized radiation power for (b1) and (b2) is plotted in (b3). The cylinder has a radius of 8 λ . The dashed line in (a1), (a2), b(1) and (b2), represents the boundary of the cylinder. The dotted line in all figures represents the boundary of the radiation range from our theory.

Fig. 7
Fig. 7

Illustration of light rays passing through (a) an isotropic shell with a refractive index of b b a r a r ; (b) a cylindrical invisibility cloak with material parameters from Eq. (12). The invisibility cloak in (b) has the α-relation with the isotropic shell in (a). The background is free space.

Tables (1)

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Table 1 α-Relation between a Diagonal Anisotropic Medium and an Isotropic Medium a

Equations (28)

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g α = diag [ α , 1 , 1 ] g s diag [ α , 1 , 1 ] ,
ϵ s = μ s = ± det ( g s ) det ( g c ) h ( g s ) 1 g c h 1 ,
ϵ α = μ α = ± det ( g α ) det ( g c ) h ( g α ) 1 g c h 1 ,
x 1 = f 1 ( σ ) , x 2 = f 2 ( σ ) , x 3 = f 3 ( σ ) ,
x 1 = f 1 ( σ ) , x 2 = σ 1 σ α ( x 1 ) d f 2 ( σ ) d σ d σ + f 2 ( σ 1 ) , x 3 = σ 1 σ α ( x 1 ) d f 3 ( σ ) d σ d σ + f 3 ( σ 1 ) ,
x 1 = f 1 ( σ ) , x 2 = α f 2 ( σ ) α f 2 ( σ 1 ) + f 2 ( σ 1 ) , x 3 = α f 3 ( σ ) α f 3 ( σ 1 ) + f 3 ( σ 1 ) .
Δ x 1 α = Δ x 1 s , Δ x 2 α = α Δ x 2 s , Δ x 3 α = α Δ x 3 s ,
Δ ϕ α = α Δ ϕ s .
ϵ s = μ s = n ,
ϵ α = μ α = n diag [ 1 / α , α , α ] ,
Δ θ α ( ω ) = μ θ ( ω ) μ r Δ θ s .
ϵ r = μ r = r a r , ϵ θ = μ θ = r r a , ϵ z = μ z = ( b b a ) 2 r a r ,
n = b b a r a r , α = r r a .
s = d s = L d σ ,
L = g i j d x i d σ d x j d σ .
d d σ L ( d x i / d σ ) = L x i = 0.
d d σ g 1 i s d f i ( σ ) d σ L s 1 2 L s g i j s x 1 d f i ( σ ) d σ d f j ( σ ) d σ = 0.
A 1 = α ( x 1 ) ( d d σ g 1 i s d f i ( σ ) d σ L s 1 2 L s g i j s x 1 d f i ( σ ) d σ d f j ( σ ) d σ ) .
H = g s i j k i s k j s = ω 2 c 2 ,
d x i d τ = 2 g s i j k j s ,
d k i d τ = d g s j l d x i k j s k l s .
k i s k j s = g i l s d x l d σ g j l s d x l d σ .
k i α k j α = g i l α d x l d σ g j l α d x l d σ .
k 1 α k 3 α = α k 1 s k 3 s , k 2 α k 3 α = k 2 s k 3 s .
k 1 α = α k 1 s , k 2 α = k 2 s , k 3 α = k 3 s .
Δ ϕ = ω c σ 1 σ 2 L d σ .
Δ ϕ s = ω c σ 1 σ 2 L s d σ , Δ ϕ α = ω c σ 1 σ 2 α ( x 1 ) L s d σ .
Δ ϕ α = α Δ ϕ s ,

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