Abstract

Constitutive parameters for simplified cylindrical cloaks have been developed such that εzµθ and εzµr match those of the ideal cylindrical cloak. Although they are not perfect, simplified cylindrical cloaks have been shown to inherit many of the power-bending properties of the ideal cloak. However, energy is transmitted into simplified cloaks’ hidden regions. Here, we develop a constraint equation that can be used to determine how closely field behavior within the simplified cylindrical cloak matches that of the ideal cloak. The deviation from this controlling equation can be reduced by controlling the cloak’s parameter value, µθ. As the deviation from our constraint equation is decreased, the field transmitted into the cloak’s hidden region is reduced, resulting in less energy impinging on the cloaked object. This results in a smaller scattered field due to the presence of the cloaked object. However, the resulting impedance mismatch at r=b results in a significant scattered field by the cloak itself. Thus, we have found when using cylindrical cloaks that satisfy the ideal values of εzµθ and εzµr for scattering width reduction, it is more important to have a matched impedance at r=b than to have a smaller field transmitted into the cloak’s hidden region. However, such cloaks’ scattering widths can vary significantly as a function of the object in the hidden region. A cloak with a matched impedance at r=b and that satisfies specific values for εzµθ and µ θ performs reasonably well in terms of scattering width reduction in certain angular regions while being independent of the object in the hidden region.

© 2008 Optical Society of America

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  1. A. Alù and N. Engheta, "Achieving transparency with plasmonic and metamaterial coatings," Phys. Rev. E 72, 016623 (2005).
    [CrossRef]
  2. A. Alù and N. Engheta, "Plasmonic materials in transparency and cloaking problems: mechanism, robustnuss, and physical insights," Opt. Express 15, 3318-3332 (2007).
    [CrossRef] [PubMed]
  3. M. G. Silveirinha, A. Alù and N. Engheta, "Parallel-plate metamaterials for cloaking structures," Phys. Rev. E 75, 036603 (2007)
    [CrossRef]
  4. U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
    [CrossRef] [PubMed]
  5. J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
    [CrossRef] [PubMed]
  6. S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).
    [CrossRef]
  7. H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
    [CrossRef]
  8. D. Kwon and D. Werner, "Two-dimensional eccentric elliptic electromagnetic cloaks," Appl. Phys. Lett. 92, 013505 (2008).
    [CrossRef]
  9. 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 coordiante transformations of Maxwell’s equations," Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
    [CrossRef]
  10. 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]
  11. 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]
  12. H. Chen, B. I. W, B. Zhang, and J. A. Kong, "Electromagnetic wave interactions with a metamaterial cloak," Phys. Rev. Lett. 99, 063903 (2007).
    [CrossRef] [PubMed]
  13. G. Isić, R. Gajić, B. Novaković, Z. V. Popović, and K. Hingerl, "Radiation and scattering from imperfect cylindrical electromagnetic cloaks," Opt. Express 16, 1413-1422 (2008).
    [CrossRef] [PubMed]
  14. 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]
  15. M. Yan, Z. Ruan, and M. Qiu, "Cylindrical invisibility cloak with simplified material parameters is inherently visible," Phys. Rev. Lett. 99, 233901 (2007).
    [CrossRef]
  16. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 224-227 (2007).
    [CrossRef]
  17. W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, "Nonmagnetic cloak with minimized scattering," Appl. Phys. Lett. 91, 111107 (2007).
    [CrossRef]
  18. M. Yan, Z. Ruan, and M. Qiu, "Scattering characteristics of simplified cylindrical invisibility cloaks," Opt. Express 15, 17772-17782 (2007).
    [CrossRef] [PubMed]

2008

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

D. Kwon and D. Werner, "Two-dimensional eccentric elliptic electromagnetic cloaks," Appl. Phys. Lett. 92, 013505 (2008).
[CrossRef]

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 coordiante transformations of Maxwell’s equations," Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

G. Isić, R. Gajić, B. Novaković, Z. V. Popović, and K. Hingerl, "Radiation and scattering from imperfect cylindrical electromagnetic cloaks," Opt. Express 16, 1413-1422 (2008).
[CrossRef] [PubMed]

2007

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]

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

M. Yan, Z. Ruan, and M. Qiu, "Cylindrical invisibility cloak with simplified material parameters is inherently visible," Phys. Rev. Lett. 99, 233901 (2007).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 224-227 (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, 111107 (2007).
[CrossRef]

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

A. Alù and N. Engheta, "Plasmonic materials in transparency and cloaking problems: mechanism, robustnuss, and physical insights," Opt. Express 15, 3318-3332 (2007).
[CrossRef] [PubMed]

M. G. Silveirinha, A. Alù and N. Engheta, "Parallel-plate metamaterials for cloaking structures," Phys. Rev. E 75, 036603 (2007)
[CrossRef]

2006

U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
[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. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).
[CrossRef]

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]

2005

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

Alù, A.

A. Alù and N. Engheta, "Plasmonic materials in transparency and cloaking problems: mechanism, robustnuss, and physical insights," Opt. Express 15, 3318-3332 (2007).
[CrossRef] [PubMed]

M. G. Silveirinha, A. Alù and N. Engheta, "Parallel-plate metamaterials for cloaking structures," Phys. Rev. E 75, 036603 (2007)
[CrossRef]

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

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 224-227 (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, 111107 (2007).
[CrossRef]

Chen, B.

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

Chen, H.

H. Chen, B. I. W, 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, V. M. Shalaev, and G. W. Milton, "Nonmagnetic cloak with minimized scattering," Appl. Phys. Lett. 91, 111107 (2007).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 224-227 (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 coordiante transformations of Maxwell’s equations," Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. 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. Alù and N. Engheta, "Plasmonic materials in transparency and cloaking problems: mechanism, robustnuss, and physical insights," Opt. Express 15, 3318-3332 (2007).
[CrossRef] [PubMed]

M. G. Silveirinha, A. Alù and N. Engheta, "Parallel-plate metamaterials for cloaking structures," Phys. Rev. E 75, 036603 (2007)
[CrossRef]

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

Gajic, R.

Hingerl, K.

Isic, G.

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. Photonics 1, 224-227 (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, 111107 (2007).
[CrossRef]

Kwon, D.

D. Kwon and D. Werner, "Two-dimensional eccentric elliptic electromagnetic cloaks," Appl. Phys. Lett. 92, 013505 (2008).
[CrossRef]

Leonhardt, U.

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

Ma, H.

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

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, 111107 (2007).
[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]

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]

Novakovic, B.

Pendry, J.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).
[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 coordiante transformations of Maxwell’s equations," Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

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]

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]

Popa, B. I.

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

Popovic, Z. V.

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]

M. Yan, Z. Ruan, and M. Qiu, "Cylindrical invisibility cloak with simplified material parameters is inherently visible," Phys. Rev. Lett. 99, 233901 (2007).
[CrossRef]

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

Qu, S.

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

Rahm, M.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordiante transformations of Maxwell’s equations," Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[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 coordiante transformations of Maxwell’s equations," Photonics Nanostruct. Fundam. Appl. 6, 87 (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]

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

M. Yan, Z. Ruan, and M. Qiu, "Cylindrical invisibility cloak with simplified material parameters is inherently visible," Phys. Rev. Lett. 99, 233901 (2007).
[CrossRef]

Schurig, D.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordiante transformations of Maxwell’s equations," Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

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]

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. 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, V. M. Shalaev, and G. W. Milton, "Nonmagnetic cloak with minimized scattering," Appl. Phys. Lett. 91, 111107 (2007).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 224-227 (2007).
[CrossRef]

Silveirinha, M. G.

M. G. Silveirinha, A. Alù and N. Engheta, "Parallel-plate metamaterials for cloaking structures," Phys. Rev. E 75, 036603 (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 coordiante transformations of Maxwell’s equations," Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

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]

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. 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]

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]

Wang, J.

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

Werner, D.

D. Kwon and D. Werner, "Two-dimensional eccentric elliptic electromagnetic cloaks," Appl. Phys. Lett. 92, 013505 (2008).
[CrossRef]

Xu, Z.

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

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]

M. Yan, Z. Ruan, and M. Qiu, "Cylindrical invisibility cloak with simplified material parameters is inherently visible," Phys. Rev. Lett. 99, 233901 (2007).
[CrossRef]

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

Zhang, J.

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

Appl. Phys. Lett.

D. Kwon and D. Werner, "Two-dimensional eccentric elliptic electromagnetic cloaks," Appl. Phys. Lett. 92, 013505 (2008).
[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, 111107 (2007).
[CrossRef]

Nat. Photonics

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 224-227 (2007).
[CrossRef]

Opt. Express

Photonics Nanostruct. Fundam. Appl.

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 coordiante transformations of Maxwell’s equations," Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

Phys. Rev. A

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

Phys. Rev. E

A. Alù 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. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).
[CrossRef]

M. G. Silveirinha, A. Alù and N. Engheta, "Parallel-plate metamaterials for cloaking structures," Phys. Rev. E 75, 036603 (2007)
[CrossRef]

Phys. Rev. Lett.

M. Yan, Z. Ruan, 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]

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

Science

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, 1777-1780 (2006).
[CrossRef] [PubMed]

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

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Figures (14)

Fig. 1.
Fig. 1.

Cylindrical cloak geometry. For this effort, a=λ and b=. Additionally, plane wave incidence is assumed throughout with the wave travelling in the x̂ direction (i.e. θi =180°).

Fig. 2.
Fig. 2.

Scattered electric field magnitude for a simplified cylindrical cloak that has (a) nothing in its hidden region, (b) PEC cylinder with radius a in the hidden region, and (c) square PEC of side length a in the hidden region.

Fig. 3.
Fig. 3.

Scattering from a simplified cloak. The blue line is the scattering width for an uncloaked PEC normalized by its maximum field value, the green line shows the scattering width for an empty simplified cloak normalized by the maximum value for the scattered field from an uncloaked PEC, the red line is the scattering width for a simplified cloak with a PEC cylinder of radius a in the hidden region normalized using the same factor, and the black line is the scattering width for the cloak with a square PEC in the hidden region, also normalized by the same factor.

Fig. 4.
Fig. 4.

Scattering width difference for a simplified cloak with a PEC cylinder and a PEC square in the hidden region.

Fig. 5.
Fig. 5.

Scattered electric field magnitude for an improved simplified cylindrical cloak with material parameters put forth [18]. The cloak in image (a) has nothing in its hidden region, image (b) results are for a cloak with a PEC cylinder of radius a in the hidden region, and image (c) results are for a cloak with a square PEC of side length a in the hidden region.

Fig. 6.
Fig. 6.

Normalized scattering widths from an improved simplified cloak. The blue line is the normalized scattering width for an uncloaked PEC, the green line shows the normalized scattering width for an empty simplified cloak with the improved constitutive parameter set, the red line is normalized scattering width for the same cloak but with with a PEC cylinder of radius a in the hidden region, and the black line is the normalized scattering width for the cloak with a square PEC in the hidden region.

Fig. 7.
Fig. 7.

Scattering width difference for an improved simplified cloak with a PEC cylinder and a square PEC in the hidden region.

Fig. 8.
Fig. 8.

The calculated values for the left-hand side of Eq. (16) using non-ideal values for µ θ . The larger the value, the larger the deviation from satisfying the ideal parameter constraint. The red line is for µ θ =1, the green line is for μ θ = b b a , the cyan line is for μ θ = b a b , and the black line is for μ θ = ( b a b ) 3 .

Fig. 9.
Fig. 9.

Scattering width difference for a cloak with parameters shown in Eq. (17) with a PEC cylinder and a square PEC in the hidden region.

Fig. 10.
Fig. 10.

Scattering width difference for a cloak with parameters shown in Eq. (18) with a PEC cylinder and a square PEC in the hidden region.

Fig. 11.
Fig. 11.

Electric field magnitude in the hidden region for four different cloaks. Image (a) is for the cloak with material parameters shown in Eq. (15), (b) is for the cloak with material parameters shown in Eq. (8), (c) is for the cloak with material parameters shown in Eq. (17), and (d) is for the cloak with material parameters shown in Eq. (18).

Fig. 12.
Fig. 12.

Scattering widths for cloaks with a PEC cylinder of radius a in the hidden region. The blue line is the normalized scattering width for an uncloaked PEC, the red line is the normalized scattering width for cloak with the simplified parameter set (Eq. (8)), the green line is the scattering width for a cloak with the improved parameter set (15), and the cyan and black lines are the scattering widths for cloaks with parameter sets shown in Eqs. (17) and (18) respectively.

Fig. 13.
Fig. 13.

Scattered electric field magnitude for a cylindrical cloak with parameters shown in Eq. (19) that has (a) nothing in its hidden region, (b) PEC cylinder with radius a in the hidden region, and (c) square PEC of side length a in the hidden region.

Fig. 14.
Fig. 14.

Normalized scattering width from cloaks. The blue line is the scattering width for an uncloaked PEC, the red and green lines are the scattering widths for the improved cloak with parameters put forth in [18] and shown in Eq. (15) with a PEC cylinder and square PEC in the hidden region. The cyan and black lines are the same but for a cloak with material parameters shown in Eq. (19).

Tables (1)

Tables Icon

Table 1. Hidden Region Total Energy and Impedance at r=b for Different Cloaks

Equations (19)

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ε r = μ r = r a r , ε θ = μ θ = r r a , ε z = μ z = r a r ( b b a ) 2
H r = 1 j ω μ r r E z θ
H θ = 1 j ω μ θ E z r
E z = 1 j ω ε z r [ ( r H θ ) r H r θ ]
1 ε z r [ r ( r μ θ E z r ) ] + 1 ε z r 2 θ ( 1 μ r E z θ ) + k o 2 E z = 0
1 ε z μ θ 2 E z r 2 + [ 1 ε z μ θ 1 r μ θ ε z μ θ 2 ] E z r + 1 ε z μ r 1 r 2 2 E z θ 2 + k o 2 E z = 0
( b a b ) 2 2 E z r 2 + ( b a b ) 2 1 r a E z r + ( b a b ) 2 ( 1 r a ) 2 2 E z θ 2 + k o 2 E z = 0
μ r = ( r a r ) 2 , μ θ = 1 , ε z = ( b b a ) 2
( b a b ) 2 2 E z r 2 + ( b a b ) 2 1 r E z r + ( b a b ) 2 ( 1 r a ) 2 2 E z θ 2 + k o 2 E z = 0
1 ε z μ θ = ( b a b ) 2
1 ε z μ r = ( b a b ) 2 ( r r a ) 2
1 ε z μ θ 1 r μ θ ε z μ θ 2 = 1 r a ( b a b ) 2
Z ideal = μ θ ε z r = b = 1
Z simp = μ θ ε z r = b = 0.5
μ r = ( r a r ) 2 b b a , μ θ = b b a , ε z = b b a
μ θ + μ θ a r ( r a ) = 0
μ r = ( r a r ) 2 b a b , μ θ = b a b , ε z = ( b b a ) 3
μ r = ( r a r ) 2 ( b a b ) 3 , μ θ = ( b a b ) 3 , ε z = ( b b a ) 5
μ r = 0.5 , μ θ = r r a , ε z = r a r ( b b a ) 2

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