Abstract

Based on the concept of complementary media, we propose a novel design which can enhance the electromagnetic wave scattering cross section of an object so that it looks like a scatterer bigger than the scale of the device. Such a “superscatterer” is realized by coating a negative refractive material shell on a perfect electrical conductor cylinder. The scattering field is analytically obtained by Mie scattering theory, and confirmed by full-wave simulations numerically. Such a device can be regarded as a cylindrical concave mirror for all angles.

© 2008 Optical Society of America

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  1. U. Leonhardt, "Optical Conformal Mapping," Science 312, 1777-80 (2006).
    [CrossRef] [PubMed]
  2. J. B. Pendry, D. Schurig, and D. R. Smith,"Controlling Electromagnetic Fields," Science 312, 1780-1782 (2006).
    [CrossRef] [PubMed]
  3. A. Greenleaf, M. Lassas, and G. Uhlmann, Physiol. Meas. "Anisotropic conductivities that cannot be detected by EIT, " Physiol. Meas. 24, 413-9 (2003).
    [CrossRef] [PubMed]
  4. 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]
  5. A. Al`u and N. Engheta,"Achieving transparency with plasmonic and metamaterial coatings," Phys. Rev. E 72, 016623 (2005).
    [CrossRef]
  6. 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]
  7. Z. Jacob, L. A. Alekseyev, and E. Narimanov, "Optical Hyperlens: Far-field imaging beyond the diffraction limit," Opt. Express 14, 8247-56 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  12. 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]
  13. X. H. Zhang, H. Y. Chen, X. D. Luo, and H. R. Ma,"Transformation media that turn a narrow slit into a large window," Opt. Express 16, 11764-8 (2008).
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    [CrossRef]
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    [CrossRef]
  18. J. B. Pendry,"Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85, 3966 (2000).
    [CrossRef] [PubMed]
  19. J. B. Pendry and S. A. Ramakrishna,"Focusing light using negative refraction," J. Phys.: Condens. Matter 15,6345-64 (2003).
    [CrossRef]
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2008 (2)

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 Maxwells equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[CrossRef]

X. H. Zhang, H. Y. Chen, X. D. Luo, and H. R. Ma,"Transformation media that turn a narrow slit into a large window," Opt. Express 16, 11764-8 (2008).
[CrossRef] [PubMed]

2007 (4)

H. Y. Chen and C. T. Chan,"Transformation media that rotate electromagnetic fields," Appl. Phys. Lett. 90, 241105 (2007).
[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]

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]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photon. 1, 224-7 (2007).
[CrossRef]

2006 (6)

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]

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

Z. Jacob, L. A. Alekseyev, and E. Narimanov, "Optical Hyperlens: Far-field imaging beyond the diffraction limit," Opt. Express 14, 8247-56 (2006).
[CrossRef] [PubMed]

U. Leonhardt, "Optical Conformal Mapping," Science 312, 1777-80 (2006).
[CrossRef] [PubMed]

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]

2005 (2)

A. Al`u and N. Engheta,"Achieving transparency with plasmonic and metamaterial coatings," Phys. Rev. E 72, 016623 (2005).
[CrossRef]

G.W. Milton, N. A. Nicorovici, R. C. McPhedran and V. A. Podolskiy,"A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance," Proc. R. Soc. London, Ser. A 461, 3999-4034 (2005).
[CrossRef]

2003 (2)

J. B. Pendry and S. A. Ramakrishna,"Focusing light using negative refraction," J. Phys.: Condens. Matter 15,6345-64 (2003).
[CrossRef]

A. Greenleaf, M. Lassas, and G. Uhlmann, Physiol. Meas. "Anisotropic conductivities that cannot be detected by EIT, " Physiol. Meas. 24, 413-9 (2003).
[CrossRef] [PubMed]

2000 (1)

J. B. Pendry,"Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

1994 (1)

N. A. Nicorovici, R. C. McPhedran, and G. W. Milton,"Optical and dielectric properties of partially resonant composites," Phys. Rev. B 49, 8479 (1994).
[CrossRef]

1968 (1)

V. G. Veselago,"The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Alekseyev, L. A.

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photon. 1, 224-7 (2007).
[CrossRef]

Chan, C. T.

H. Y. Chen and C. T. Chan,"Transformation media that rotate electromagnetic fields," Appl. Phys. Lett. 90, 241105 (2007).
[CrossRef]

Chen, H.

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]

Chen, H. Y.

X. H. Zhang, H. Y. Chen, X. D. Luo, and H. R. Ma,"Transformation media that turn a narrow slit into a large window," Opt. Express 16, 11764-8 (2008).
[CrossRef] [PubMed]

H. Y. Chen and C. T. Chan,"Transformation media that rotate electromagnetic fields," Appl. Phys. Lett. 90, 241105 (2007).
[CrossRef]

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photon. 1, 224-7 (2007).
[CrossRef]

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 Maxwells equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[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]

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]

Greenleaf, A.

A. Greenleaf, M. Lassas, and G. Uhlmann, Physiol. Meas. "Anisotropic conductivities that cannot be detected by EIT, " Physiol. Meas. 24, 413-9 (2003).
[CrossRef] [PubMed]

Jacob, Z.

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, "Optical cloaking with metamaterials," Nat. Photon. 1, 224-7 (2007).
[CrossRef]

Kong, J. A.

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]

Lassas, M.

A. Greenleaf, M. Lassas, and G. Uhlmann, Physiol. Meas. "Anisotropic conductivities that cannot be detected by EIT, " Physiol. Meas. 24, 413-9 (2003).
[CrossRef] [PubMed]

Leonhardt, U.

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

U. Leonhardt, "Optical Conformal Mapping," Science 312, 1777-80 (2006).
[CrossRef] [PubMed]

Luo, X. D.

Ma, H. R.

McPhedran, R. C.

G.W. Milton, N. A. Nicorovici, R. C. McPhedran and V. A. Podolskiy,"A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance," Proc. R. Soc. London, Ser. A 461, 3999-4034 (2005).
[CrossRef]

N. A. Nicorovici, R. C. McPhedran, and G. W. Milton,"Optical and dielectric properties of partially resonant composites," Phys. Rev. B 49, 8479 (1994).
[CrossRef]

Milton, G. W.

N. A. Nicorovici, R. C. McPhedran, and G. W. Milton,"Optical and dielectric properties of partially resonant composites," Phys. Rev. B 49, 8479 (1994).
[CrossRef]

Milton, G.W.

G.W. Milton, N. A. Nicorovici, R. C. McPhedran and V. A. Podolskiy,"A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance," Proc. R. Soc. London, Ser. A 461, 3999-4034 (2005).
[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]

Narimanov, E.

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]

Nicorovici, N. A.

G.W. Milton, N. A. Nicorovici, R. C. McPhedran and V. A. Podolskiy,"A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance," Proc. R. Soc. London, Ser. A 461, 3999-4034 (2005).
[CrossRef]

N. A. Nicorovici, R. C. McPhedran, and G. W. Milton,"Optical and dielectric properties of partially resonant composites," Phys. Rev. B 49, 8479 (1994).
[CrossRef]

Pendry, J. B.

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 Maxwells equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[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]

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]

J. B. Pendry and S. A. Ramakrishna,"Focusing light using negative refraction," J. Phys.: Condens. Matter 15,6345-64 (2003).
[CrossRef]

J. B. Pendry,"Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Philbin, T. G.

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

Podolskiy, V. A.

G.W. Milton, N. A. Nicorovici, R. C. McPhedran and V. A. Podolskiy,"A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance," Proc. R. Soc. London, Ser. A 461, 3999-4034 (2005).
[CrossRef]

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]

Qiu, M.

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]

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 Maxwells equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[CrossRef]

Ramakrishna, S. A.

J. B. Pendry and S. A. Ramakrishna,"Focusing light using negative refraction," J. Phys.: Condens. Matter 15,6345-64 (2003).
[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 Maxwells equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[CrossRef]

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]

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 Maxwells equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[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]

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]

Shalaev, V. M.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photon. 1, 224-7 (2007).
[CrossRef]

Smith, D. R.

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 Maxwells equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[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]

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]

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, M. Lassas, and G. Uhlmann, Physiol. Meas. "Anisotropic conductivities that cannot be detected by EIT, " Physiol. Meas. 24, 413-9 (2003).
[CrossRef] [PubMed]

Veselago, V. G.

V. G. Veselago,"The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Wu, B.-I.

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]

Yan, M.

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.

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]

Zhang, X. H.

Appl. Phys. Lett. (1)

H. Y. Chen and C. T. Chan,"Transformation media that rotate electromagnetic fields," Appl. Phys. Lett. 90, 241105 (2007).
[CrossRef]

J. Phys.: Condens. Matter (1)

J. B. Pendry and S. A. Ramakrishna,"Focusing light using negative refraction," J. Phys.: Condens. Matter 15,6345-64 (2003).
[CrossRef]

Nat. Photon. (1)

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photon. 1, 224-7 (2007).
[CrossRef]

New J. Phys. (1)

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

Opt. Express (2)

Photon. Nanostruct.: Fundam. Applic. (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 Maxwells equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[CrossRef]

Phys. Rev. B (1)

N. A. Nicorovici, R. C. McPhedran, and G. W. Milton,"Optical and dielectric properties of partially resonant composites," Phys. Rev. B 49, 8479 (1994).
[CrossRef]

Phys. Rev. E (2)

A. Al`u and N. Engheta,"Achieving transparency with plasmonic and metamaterial coatings," Phys. Rev. E 72, 016623 (2005).
[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]

Phys. Rev. Lett. (3)

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]

J. B. Pendry,"Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Physiol. Meas. (1)

A. Greenleaf, M. Lassas, and G. Uhlmann, Physiol. Meas. "Anisotropic conductivities that cannot be detected by EIT, " Physiol. Meas. 24, 413-9 (2003).
[CrossRef] [PubMed]

Proc. R. Soc. London, Ser. A (1)

G.W. Milton, N. A. Nicorovici, R. C. McPhedran and V. A. Podolskiy,"A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance," Proc. R. Soc. London, Ser. A 461, 3999-4034 (2005).
[CrossRef]

Science (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] [PubMed]

U. Leonhardt, "Optical Conformal Mapping," Science 312, 1777-80 (2006).
[CrossRef] [PubMed]

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

Sov. Phys. Usp. (1)

V. G. Veselago,"The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Other (2)

G. W. Milton, N. P. Nicorovici, R. C. McPhedran, K. Cherednichenko, and Z. Jacob,"Solutions in folded geometries, and associated cloaking due to anomalous resonance," arXiv:0804.3903.

A.D. Yaghjian and S. Maci,"Alternative Derivation of Electromagnetic Cloaks and Concentrators," arXiv:0710.2933.

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Figures (4)

Fig. 1.
Fig. 1.

(a) The schematic demonstration of the behavior of a beam propagates in a complementary media and PEC boundary. (b) The behavior is extended to the 2D case, where a superscatterer is formed with its effective size shown by the dashed line.

Fig. 2.
Fig. 2.

A simple function f(r) satisfies the condition of Fig.1(b)

Fig. 3.
Fig. 3.

Snapshot of the total electric field. (a) is the total electric field induced by PEC cylinder with radius R 3=0.3m and (b) is the total electric field induced by the designed device (the radius of virtual cylinder is 0.3m)

Fig. 4.
Fig. 4.

A Gaussian beam in free space is shown in (a). (b) and (c) are the scattering and total fields induced by the superscatterer (the radius of the virtual cylinder is 0.6m), respectively.

Equations (12)

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ε = = ε 0 [ ε r ( r ) r ̂ r ̂ + ε θ ( r ) θ ̂ θ ̂ + ε z ( r ) z ̂ z ̂ ] , μ = = μ 0 [ μ r ( r ) r ̂ r ̂ + μ θ ( r ) θ ̂ θ ̂ + μ z ( r ) z ̂ z ̂ ] .
1 ε z 1 r r ( r μ θ E z r ) + 1 ε z 1 r 2 θ ( 1 μ r E z θ ) + k 0 2 E z = 0 ,
1 ε z 1 r u u ( r μ θ u F u ) + 1 ε z 1 r 2 θ ( 1 μ r F θ ) + k 0 2 F = 0 ,
ε r = μ r = u r 1 u = f ( r ) r 1 f ( r ) ,
ε θ = μ θ = r u u = r f ( r ) f ( r ) ,
ε z = μ z = u r u = f ( r ) r f ( r ) .
E z ( r , θ ) = { 0 , r < R 1 , Σ m ( α m i J m ( k 0 f ( r ) ) + α m s H m ( 1 ) ( k 0 f ( r ) ) ) exp ( im θ ) , R 1 < r < R 2 , Σ m ( β m i J m ( k 0 r ) + β m s H m ( 1 ) ( k 0 r ) ) exp ( im θ ) , r > R 2 .
α m i J m ( k 0 f ( R 1 ) ) + α m s H m ( 1 ) ( k 0 f ( R 1 ) ) = 0 ,
α m i J m ( k 0 f ( R 2 ) ) + α m s H m ( 1 ) ( k 0 f ( R 2 ) ) = β m i J m ( k 0 R 2 ) + β m s H m ( 1 ) ( k 0 R 2 ) ,
f ( R 2 ) R 2 [ α m i J m ( k 0 f ( R 2 ) ) + α m s H m ( 1 ) ( k 0 f ( R 2 ) ) ] = β m i J m ( k 0 R 2 ) + β m s H m ( 1 ) ( k 0 R 2 ) ,
α m s α m i = β m s β m i = J m ( k 0 f ( R 1 ) ) H m ( 1 ) ( k 0 f ( R 1 ) ) , m = 0 , ± 1 , ± 2 , . . . .
f ( r ) = { b 0 ( R 2 r ) ( R 2 R 1 ) + R 2 , R 1 < r < R 2 , r , r > R 2 .

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