Abstract

We studied the scattering from the simplified cylindrical cloaks analytically at both normal and oblique incidences. We found that these simplified cylindrical cloaks may produce a larger scattering at nonnormal incidences than that from an object without any cloak, making this object more “visible”. Even at normal incidence, the high-order transformation with impedance matched at the outer boundary can produce stronger scattering than the linear simplified one without matched impedance. This is due to the inefficiency of guided waves close to the inner boundary. Therefore, a square root transformation can improve scattering by guiding waves away from the inner boundary.

© 2008 Optical Society of America

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    [CrossRef]
  5. A. Greenleaf, M. Lassas, and G. Uhlmann, "Anisotropic conductivities that cannot be detected by EIT," Physiol. Meas. 24, 413-419 (2003).
    [CrossRef] [PubMed]
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2008 (5)

2007 (9)

H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic Wave Interactions with a Metamaterial Cloak," Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

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] [PubMed]

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, "Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect," Opt. Lett. 32, 1069-1071 (2007).
[CrossRef] [PubMed]

Y. Huang, Y. Feng, and T. Jiang, "Electromagnetic cloaking by layered structure of homogeneous isotropic materials," Opt. Express 15, 11133-11141 (2007).
[CrossRef] [PubMed]

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, "Improvement of cylindrical cloaking with the SHS lining," Opt. Express 15, 12717-12734 (2007).
[CrossRef] [PubMed]

M. Yan, Z. Chao, and M. Qiu, "Scattering characteristics of simplified cylindrical invisibility cloaks," Opt. Express 15, 17772-17782 (2007).
[CrossRef] [PubMed]

Q1. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 063904 (2007).
[CrossRef]

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

M. Yan, Z. Chao, and M. Qiu, "Cylindrical Invisibility Cloak with Simplified Material Parameters is Inherently Visible," Phys. Rev. Lett. 99, 233901 (2007).
[CrossRef]

2006 (7)

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]

G. W. Milton and N. A. P. Nicorovici, "On the cloaking effects associated with anomalous localized resonance," Proc. R. Soc. London A 462, 3027 (2006).
[CrossRef]

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).
[CrossRef]

N. A. P. 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 (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] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794-9804 (2006).
[CrossRef] [PubMed]

2005 (1)

A. Alu and N. Engheta, "Achiveing transparency with plasmonic and metamaterial coatings," Phys. Rev. E 72, 016623 (2005).
[CrossRef]

2003 (1)

A. Greenleaf, M. Lassas, and G. Uhlmann, "Anisotropic conductivities that cannot be detected by EIT," Physiol. Meas. 24, 413-419 (2003).
[CrossRef] [PubMed]

Alu, A.

A. Alu and N. Engheta, "Achiveing transparency with plasmonic and metamaterial coatings," Phys. Rev. E 72, 016623 (2005).
[CrossRef]

Blanchard, C.

Botten, L. C.

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Designs for optical cloaking with high-order transformations," Opt. Express 16, 5444-5452 (2008).
[CrossRef] [PubMed]

Q1. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 063904 (2007).
[CrossRef]

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

Chao, Z.

M. Yan, Z. Chao, and M. Qiu, "Cylindrical Invisibility Cloak with Simplified Material Parameters is Inherently Visible," Phys. Rev. Lett. 99, 233901 (2007).
[CrossRef]

M. Yan, Z. Chao, and M. Qiu, "Scattering characteristics of simplified cylindrical invisibility cloaks," Opt. Express 15, 17772-17782 (2007).
[CrossRef] [PubMed]

Chen, H.

S. Xi, H. Chen, B. I. Wu, B. Zhang, J. Huangfu, D. Wang, and J. A. Kong, "Effects of different transformations on the performance of cylindrical cloaks," J. Electrom. Waves and Appl. 22, 1489-1497 (2008).
[CrossRef]

B. Zhang, H. Chen, B. I. Wu, and J. A. Kong, "Extraordinary Surface Voltage Effect in the Invisibility Cloak with an Active Device Inside," Phys. Rev. Lett. 100, 063904 (2008).
[CrossRef] [PubMed]

H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic Wave Interactions with a Metamaterial Cloak," Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Designs for optical cloaking with high-order transformations," Opt. Express 16, 5444-5452 (2008).
[CrossRef] [PubMed]

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

Q1. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 063904 (2007).
[CrossRef]

Cummer, S. A.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (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] [PubMed]

Engheta, N.

A. Alu and N. Engheta, "Achiveing transparency with plasmonic and metamaterial coatings," Phys. Rev. E 72, 016623 (2005).
[CrossRef]

Enoch, S.

Farhat, M.

Feng, Y.

Greenleaf, A.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, "Improvement of cylindrical cloaking with the SHS lining," Opt. Express 15, 12717-12734 (2007).
[CrossRef] [PubMed]

A. Greenleaf, M. Lassas, and G. Uhlmann, "Anisotropic conductivities that cannot be detected by EIT," Physiol. Meas. 24, 413-419 (2003).
[CrossRef] [PubMed]

Guenneau, S.

Huang, Y.

Huangfu, J.

S. Xi, H. Chen, B. I. Wu, B. Zhang, J. Huangfu, D. Wang, and J. A. Kong, "Effects of different transformations on the performance of cylindrical cloaks," J. Electrom. Waves and Appl. 22, 1489-1497 (2008).
[CrossRef]

Jiang, T.

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]

Kildishev, A. V.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Designs for optical cloaking with high-order transformations," Opt. Express 16, 5444-5452 (2008).
[CrossRef] [PubMed]

Q1. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 063904 (2007).
[CrossRef]

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

Kong, J. A.

B. Zhang, H. Chen, B. I. Wu, and J. A. Kong, "Extraordinary Surface Voltage Effect in the Invisibility Cloak with an Active Device Inside," Phys. Rev. Lett. 100, 063904 (2008).
[CrossRef] [PubMed]

S. Xi, H. Chen, B. I. Wu, B. Zhang, J. Huangfu, D. Wang, and J. A. Kong, "Effects of different transformations on the performance of cylindrical cloaks," J. Electrom. Waves and Appl. 22, 1489-1497 (2008).
[CrossRef]

C. Blanchard, J. Porti, B. I. Wu, J. A. Morente, A. Salinas, and J. A. Kong, "Time domain simulation of electromagnetic cloaking structures with TLM method," Opt. Express 16, 6461-6470 (2008).
[CrossRef] [PubMed]

H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic Wave Interactions with a Metamaterial Cloak," Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

Kurylev, Y.

Lassas, M.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, "Improvement of cylindrical cloaking with the SHS lining," Opt. Express 15, 12717-12734 (2007).
[CrossRef] [PubMed]

A. Greenleaf, M. Lassas, and G. Uhlmann, "Anisotropic conductivities that cannot be detected by EIT," Physiol. Meas. 24, 413-419 (2003).
[CrossRef] [PubMed]

Leonhardt, U.

U. Leonhardt, "Optical Conformal Mapping," Science 312, 1777-1780 (2006).
[CrossRef] [PubMed]

McPhedran, R. C.

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, 111105 (2007).
[CrossRef]

G. W. Milton and N. A. P. Nicorovici, "On the cloaking effects associated with anomalous localized resonance," Proc. R. Soc. London A 462, 3027 (2006).
[CrossRef]

N. A. P. 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 (2006).
[CrossRef]

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]

Morente, J. A.

Movchan, A. B.

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] [PubMed]

Nicolet, A.

Nicorovici, N. A. P.

N. A. P. 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 (2006).
[CrossRef]

G. W. Milton and N. A. P. Nicorovici, "On the cloaking effects associated with anomalous localized resonance," Proc. R. Soc. London A 462, 3027 (2006).
[CrossRef]

Pendry, J. B.

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, "Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect," Opt. Lett. 32, 1069-1071 (2007).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling Electromagnetic Fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (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] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794-9804 (2006).
[CrossRef] [PubMed]

Popa, B.-I.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).
[CrossRef]

Porti, J.

Qiu, M.

M. Yan, Z. Chao, and M. Qiu, "Scattering characteristics of simplified cylindrical invisibility cloaks," Opt. Express 15, 17772-17782 (2007).
[CrossRef] [PubMed]

M. Yan, Z. Chao, and M. Qiu, "Cylindrical Invisibility Cloak with Simplified Material Parameters is Inherently Visible," Phys. Rev. Lett. 99, 233901 (2007).
[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] [PubMed]

Ruan, Z.

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] [PubMed]

Salinas, A.

Schurig, D.

D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794-9804 (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]

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling Electromagnetic Fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

Shalaev, V. M.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Designs for optical cloaking with high-order transformations," Opt. Express 16, 5444-5452 (2008).
[CrossRef] [PubMed]

Q1. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 063904 (2007).
[CrossRef]

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

Smith, D. R.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling Electromagnetic Fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794-9804 (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]

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]

Uhlmann, G.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, "Improvement of cylindrical cloaking with the SHS lining," Opt. Express 15, 12717-12734 (2007).
[CrossRef] [PubMed]

A. Greenleaf, M. Lassas, and G. Uhlmann, "Anisotropic conductivities that cannot be detected by EIT," Physiol. Meas. 24, 413-419 (2003).
[CrossRef] [PubMed]

Wang, D.

S. Xi, H. Chen, B. I. Wu, B. Zhang, J. Huangfu, D. Wang, and J. A. Kong, "Effects of different transformations on the performance of cylindrical cloaks," J. Electrom. Waves and Appl. 22, 1489-1497 (2008).
[CrossRef]

Wu, B. I.

S. Xi, H. Chen, B. I. Wu, B. Zhang, J. Huangfu, D. Wang, and J. A. Kong, "Effects of different transformations on the performance of cylindrical cloaks," J. Electrom. Waves and Appl. 22, 1489-1497 (2008).
[CrossRef]

C. Blanchard, J. Porti, B. I. Wu, J. A. Morente, A. Salinas, and J. A. Kong, "Time domain simulation of electromagnetic cloaking structures with TLM method," Opt. Express 16, 6461-6470 (2008).
[CrossRef] [PubMed]

B. Zhang, H. Chen, B. I. Wu, and J. A. Kong, "Extraordinary Surface Voltage Effect in the Invisibility Cloak with an Active Device Inside," Phys. Rev. Lett. 100, 063904 (2008).
[CrossRef] [PubMed]

H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic Wave Interactions with a Metamaterial Cloak," Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

Xi, S.

S. Xi, H. Chen, B. I. Wu, B. Zhang, J. Huangfu, D. Wang, and J. A. Kong, "Effects of different transformations on the performance of cylindrical cloaks," J. Electrom. Waves and Appl. 22, 1489-1497 (2008).
[CrossRef]

Yan, M.

M. Yan, Z. Chao, and M. Qiu, "Cylindrical Invisibility Cloak with Simplified Material Parameters is Inherently Visible," Phys. Rev. Lett. 99, 233901 (2007).
[CrossRef]

M. Yan, Z. Chao, and M. Qiu, "Scattering characteristics of simplified cylindrical invisibility cloaks," Opt. Express 15, 17772-17782 (2007).
[CrossRef] [PubMed]

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] [PubMed]

Zhang, B.

B. Zhang, H. Chen, B. I. Wu, and J. A. Kong, "Extraordinary Surface Voltage Effect in the Invisibility Cloak with an Active Device Inside," Phys. Rev. Lett. 100, 063904 (2008).
[CrossRef] [PubMed]

S. Xi, H. Chen, B. I. Wu, B. Zhang, J. Huangfu, D. Wang, and J. A. Kong, "Effects of different transformations on the performance of cylindrical cloaks," J. Electrom. Waves and Appl. 22, 1489-1497 (2008).
[CrossRef]

H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic Wave Interactions with a Metamaterial Cloak," Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

Zolla, F.

Appl. Phys. Lett. (1)

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

J. Electrom. Waves and Appl. (1)

S. Xi, H. Chen, B. I. Wu, B. Zhang, J. Huangfu, D. Wang, and J. A. Kong, "Effects of different transformations on the performance of cylindrical cloaks," J. Electrom. Waves and Appl. 22, 1489-1497 (2008).
[CrossRef]

Nat. Photonics (1)

Q1. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 063904 (2007).
[CrossRef]

Opt. Express (8)

Opt. Lett. (1)

Phys. Rev. E (2)

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).
[CrossRef]

A. Alu and N. Engheta, "Achiveing transparency with plasmonic and metamaterial coatings," Phys. Rev. E 72, 016623 (2005).
[CrossRef]

Phys. Rev. Lett. (4)

H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic Wave Interactions with a Metamaterial Cloak," Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

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] [PubMed]

M. Yan, Z. Chao, and M. Qiu, "Cylindrical Invisibility Cloak with Simplified Material Parameters is Inherently Visible," Phys. Rev. Lett. 99, 233901 (2007).
[CrossRef]

B. Zhang, H. Chen, B. I. Wu, and J. A. Kong, "Extraordinary Surface Voltage Effect in the Invisibility Cloak with an Active Device Inside," Phys. Rev. Lett. 100, 063904 (2008).
[CrossRef] [PubMed]

Physiol. Meas. (1)

A. Greenleaf, M. Lassas, and G. Uhlmann, "Anisotropic conductivities that cannot be detected by EIT," Physiol. Meas. 24, 413-419 (2003).
[CrossRef] [PubMed]

Proc. R. Soc. London A (1)

G. W. Milton and N. A. P. Nicorovici, "On the cloaking effects associated with anomalous localized resonance," Proc. R. Soc. London A 462, 3027 (2006).
[CrossRef]

Science (3)

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]

Other (4)

B. Zhang, H. Chen, B. I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101(R) (2007).
[CrossRef]

A. Sihvola, "Peculiarities in the dielectric response of negative-permittivity scatterers," Prog. Electromagn. Res.pier- 66, 191-198 (2006).
[CrossRef]

H. Chen, Z. Liang, P. Yao, X. Jiang, H. Ma, and C. T. Chan, "Extending the bandwidth of electromagnetic cloaks," Phys. Rev. B 76, 241104(R) (2007).
[CrossRef]

W. C. Chew, Waves and Fields in inhomogeneous Media, 2nd ed, (IEEE Press, 1995).

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Figures (3)

Fig. 1.
Fig. 1.

(Color online) Electric field distribution of different simplified cylindrical cloaks illuminated by a vertically polarized and normally incident plane wave. Only scattered field is plotted outside of the cloak. R 2=1.5λ 0=2.08R 1. (a) Linear simplified cloak; (b) Impedance matched linear simplified cloak; (c) Impedance matched quadratic simplified cloak; (d) Impedance matched square root simplified cloak. From (a) to (d), the normalized RCS is 0.299, 0.125, 0.360 and 0.034, respectively.

Fig. 2.
Fig. 2.

(Color online) Comparison of the far-field differential normalized RCS of different simplified cylindrical cloaks illuminated by a vertically polarized and normally incident plane wave. R 2=1.5λ 0=2.08R 1.

Fig. 3.
Fig. 3.

(Color online) Dependance of normalized RCS (normalized to 2R 2) on incident angles for different simplified cloaks. R 2=1.5λ 0=2.08R 1.

Equations (8)

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s × = [ 0 z ρ ϕ z 0 0 ρ ϕ 0 0 ] and ρ × = [ 0 0 0 0 0 ρ 0 ρ ρ ρ 0 ]
ρ × E ¯ s + s × E ¯ ρ = i ω ( μ ϕ ϕ ̂ ϕ ̂ + μ z z ̂ z ̂ ) · H ¯ s ;
s × E ¯ s = i ω μ ρ H ¯ ρ ;
ρ × H ¯ s + s × H ¯ ρ = i ω ( ε ϕ ϕ ̂ ϕ ̂ + ε z z ̂ z ̂ ) · E ¯ s ;
s × H ¯ s = i ω ε ρ E ¯ ρ .
ρ [ E z E ϕ H z H ϕ ] = [ 0 0 ink z ω ε ρ ρ i ω μ ϕ + ik z 2 ω ε ρ 0 1 ρ i ω μ z in 2 ω ε ρ ρ 2 ink z ω ε ρ ρ ink z ω μ ρ ρ i ω ε ϕ ik z 2 ω μ ρ 0 0 i ω ε z + in 2 ω μ ρ ρ 2 ink z ω μ ρ ρ 0 1 ρ ] · [ E z E ϕ H z H ϕ ] .
V ¯ ( ρ j + 1 ) V ¯ ( ρ j ) = Δ ρ T = ( ρ j ) · V ¯ ( ρ j )
V ¯ ( R 2 ) = [ j = 1 N ( I = + Δ ρ T = ( ρ j ) ) ] · V ¯ ( R 1 )

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