Abstract

We model electromagnetic cloaking of a spherical or cylindrical nanoparticle enclosed by an optically anisotropic and optically inhomogeneous symmetric shell, by examining its electric response in a quasi-static uniform electric field. When the components of the shell permittivity are radially anisotropic and power-law dependent (ε~rm) whereris distance to the shell center, and m a positive or negative exponent which can be varied), the problem is analytically tractable. Formulas are calculated for the degree of cloaking in the general case, allowing the determination of a dielectric condition for the shells to be used as an invisibility cloak. Ideal cloaking is known to require that homogeneous shells exhibit an infinite ratio of tangential and radial components of the shell permittivity, but for radially inhomogeneous shells ideal cloaking can occur even for finite values of this ratio.

© 2015 Optical Society of America

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References

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  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
    [Crossref] [PubMed]
  2. D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14(21), 9794–9804 (2006).
    [Crossref] [PubMed]
  3. U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
    [Crossref] [PubMed]
  4. D. Schurig, J. B. Pendry, and D. R. Smith, “Transformation-designed optical elements,” Opt. Express 15(22), 14772–14782 (2007).
    [Crossref] [PubMed]
  5. V. M. Shalaev, “Physics. Transforming light,” Science 322(5900), 384–386 (2008).
    [Crossref] [PubMed]
  6. P. Zhang, Y. Jin, and S. He, “Cloaking an object on a dielectric half-space,” Opt. Express 16(5), 3161–3166 (2008).
    [Crossref] [PubMed]
  7. U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt. 53, 69–152 (2009).
    [Crossref]
  8. H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
    [Crossref] [PubMed]
  9. A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016623 (2005).
    [Crossref] [PubMed]
  10. M. G. Silveirinha, A. Alù, and N. Engheta, “Parallel-plate metamaterials for cloaking structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(3), 036603 (2007).
    [Crossref] [PubMed]
  11. L. Gao, T. H. Fung, K. W. Yu, and C. W. Qiu, “Electromagnetic transparency by coated spheres with radial anisotropy,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(4), 046609 (2008).
    [Crossref] [PubMed]
  12. Y. Ni, L. Gao, and C.-W. Qiu, “Achieving invisibility of homogeneous cylindrically anisotropic cylinders,” Plasmonics 5(3), 251–258 (2010).
    [Crossref]
  13. C. W. Qiu, L. Hu, X. Xu, and Y. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4), 047602 (2009).
    [Crossref] [PubMed]
  14. S. Tricarico, F. Bilotti, and L. Vegni, “Scattering cancellation by metamaterial cylindrical multilayers,” J. Eur. Opt. Soc. 4, 09021 (2009).
    [Crossref]
  15. G. W. Milton and N.-A. P. Nicorovici, “On the cloaking effects associated with anomalous localized resonance,” Proc. R. Soc. Lond. A 462(2074), 3027–3059 (2006).
    [Crossref]
  16. 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(10), 6314–6323 (2007).
    [Crossref] [PubMed]
  17. C.-W. Qiu, A. Novitsky, H. Ma, and S. Qu, “Electromagnetic interaction of arbitrary radial-dependent anisotropic spheres and improved invisibility for nonlinear-transformation-based cloaks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(1), 016604 (2009).
    [Crossref] [PubMed]
  18. H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99(6), 063903 (2007).
    [Crossref] [PubMed]
  19. D. K. Cohoon, “An exact solution of Mie type for scattering by a multilayer anisotropic sphere,” J. Electromag. Wave. 3(5), 421–448 (1989).
    [Crossref]
  20. H. Kettunen, H. Wallén, and A. Sihvola, “Cloaking and magnifying using radial anisotropy,” J. Appl. Phys. 114(4), 044110 (2013).
    [Crossref]
  21. H. Wallén, H. Kettunen, and A. Sihvola, “Anomalous absorption, plasmonic resonances, and invisibility of radially anisotropic spheres,” Radio Sci. 50(1), 18–28 (2015).
    [Crossref]
  22. A. Sihvola, “Particular properties of the dielectric response of negative-permittivity scatterers,” PIERS Online 3(3), 246–247 (2007).
    [Crossref]

2015 (1)

H. Wallén, H. Kettunen, and A. Sihvola, “Anomalous absorption, plasmonic resonances, and invisibility of radially anisotropic spheres,” Radio Sci. 50(1), 18–28 (2015).
[Crossref]

2013 (1)

H. Kettunen, H. Wallén, and A. Sihvola, “Cloaking and magnifying using radial anisotropy,” J. Appl. Phys. 114(4), 044110 (2013).
[Crossref]

2010 (2)

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref] [PubMed]

Y. Ni, L. Gao, and C.-W. Qiu, “Achieving invisibility of homogeneous cylindrically anisotropic cylinders,” Plasmonics 5(3), 251–258 (2010).
[Crossref]

2009 (4)

C. W. Qiu, L. Hu, X. Xu, and Y. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4), 047602 (2009).
[Crossref] [PubMed]

S. Tricarico, F. Bilotti, and L. Vegni, “Scattering cancellation by metamaterial cylindrical multilayers,” J. Eur. Opt. Soc. 4, 09021 (2009).
[Crossref]

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

C.-W. Qiu, A. Novitsky, H. Ma, and S. Qu, “Electromagnetic interaction of arbitrary radial-dependent anisotropic spheres and improved invisibility for nonlinear-transformation-based cloaks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(1), 016604 (2009).
[Crossref] [PubMed]

2008 (3)

L. Gao, T. H. Fung, K. W. Yu, and C. W. Qiu, “Electromagnetic transparency by coated spheres with radial anisotropy,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(4), 046609 (2008).
[Crossref] [PubMed]

V. M. Shalaev, “Physics. Transforming light,” Science 322(5900), 384–386 (2008).
[Crossref] [PubMed]

P. Zhang, Y. Jin, and S. He, “Cloaking an object on a dielectric half-space,” Opt. Express 16(5), 3161–3166 (2008).
[Crossref] [PubMed]

2007 (5)

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(10), 6314–6323 (2007).
[Crossref] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Transformation-designed optical elements,” Opt. Express 15(22), 14772–14782 (2007).
[Crossref] [PubMed]

A. Sihvola, “Particular properties of the dielectric response of negative-permittivity scatterers,” PIERS Online 3(3), 246–247 (2007).
[Crossref]

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99(6), 063903 (2007).
[Crossref] [PubMed]

M. G. Silveirinha, A. Alù, and N. Engheta, “Parallel-plate metamaterials for cloaking structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(3), 036603 (2007).
[Crossref] [PubMed]

2006 (4)

G. W. Milton and N.-A. P. Nicorovici, “On the cloaking effects associated with anomalous localized resonance,” Proc. R. Soc. Lond. A 462(2074), 3027–3059 (2006).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (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(21), 9794–9804 (2006).
[Crossref] [PubMed]

2005 (1)

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016623 (2005).
[Crossref] [PubMed]

1989 (1)

D. K. Cohoon, “An exact solution of Mie type for scattering by a multilayer anisotropic sphere,” J. Electromag. Wave. 3(5), 421–448 (1989).
[Crossref]

Alù, A.

M. G. Silveirinha, A. Alù, and N. Engheta, “Parallel-plate metamaterials for cloaking structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(3), 036603 (2007).
[Crossref] [PubMed]

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016623 (2005).
[Crossref] [PubMed]

Bilotti, F.

S. Tricarico, F. Bilotti, and L. Vegni, “Scattering cancellation by metamaterial cylindrical multilayers,” J. Eur. Opt. Soc. 4, 09021 (2009).
[Crossref]

Botten, L. C.

Chan, C. T.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref] [PubMed]

Chen, H.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref] [PubMed]

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99(6), 063903 (2007).
[Crossref] [PubMed]

Cohoon, D. K.

D. K. Cohoon, “An exact solution of Mie type for scattering by a multilayer anisotropic sphere,” J. Electromag. Wave. 3(5), 421–448 (1989).
[Crossref]

Engheta, N.

M. G. Silveirinha, A. Alù, and N. Engheta, “Parallel-plate metamaterials for cloaking structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(3), 036603 (2007).
[Crossref] [PubMed]

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016623 (2005).
[Crossref] [PubMed]

Feng, Y.

C. W. Qiu, L. Hu, X. Xu, and Y. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4), 047602 (2009).
[Crossref] [PubMed]

Fung, T. H.

L. Gao, T. H. Fung, K. W. Yu, and C. W. Qiu, “Electromagnetic transparency by coated spheres with radial anisotropy,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(4), 046609 (2008).
[Crossref] [PubMed]

Gao, L.

Y. Ni, L. Gao, and C.-W. Qiu, “Achieving invisibility of homogeneous cylindrically anisotropic cylinders,” Plasmonics 5(3), 251–258 (2010).
[Crossref]

L. Gao, T. H. Fung, K. W. Yu, and C. W. Qiu, “Electromagnetic transparency by coated spheres with radial anisotropy,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(4), 046609 (2008).
[Crossref] [PubMed]

He, S.

Hu, L.

C. W. Qiu, L. Hu, X. Xu, and Y. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4), 047602 (2009).
[Crossref] [PubMed]

Jin, Y.

Kettunen, H.

H. Wallén, H. Kettunen, and A. Sihvola, “Anomalous absorption, plasmonic resonances, and invisibility of radially anisotropic spheres,” Radio Sci. 50(1), 18–28 (2015).
[Crossref]

H. Kettunen, H. Wallén, and A. Sihvola, “Cloaking and magnifying using radial anisotropy,” J. Appl. Phys. 114(4), 044110 (2013).
[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(6), 063903 (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]

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref] [PubMed]

Ma, H.

C.-W. Qiu, A. Novitsky, H. Ma, and S. Qu, “Electromagnetic interaction of arbitrary radial-dependent anisotropic spheres and improved invisibility for nonlinear-transformation-based cloaks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(1), 016604 (2009).
[Crossref] [PubMed]

McPhedran, R. C.

Milton, G. W.

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(10), 6314–6323 (2007).
[Crossref] [PubMed]

G. W. Milton and N.-A. P. Nicorovici, “On the cloaking effects associated with anomalous localized resonance,” Proc. R. Soc. Lond. A 462(2074), 3027–3059 (2006).
[Crossref]

Ni, Y.

Y. Ni, L. Gao, and C.-W. Qiu, “Achieving invisibility of homogeneous cylindrically anisotropic cylinders,” Plasmonics 5(3), 251–258 (2010).
[Crossref]

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(10), 6314–6323 (2007).
[Crossref] [PubMed]

G. W. Milton and N.-A. P. Nicorovici, “On the cloaking effects associated with anomalous localized resonance,” Proc. R. Soc. Lond. A 462(2074), 3027–3059 (2006).
[Crossref]

Novitsky, A.

C.-W. Qiu, A. Novitsky, H. Ma, and S. Qu, “Electromagnetic interaction of arbitrary radial-dependent anisotropic spheres and improved invisibility for nonlinear-transformation-based cloaks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(1), 016604 (2009).
[Crossref] [PubMed]

Pendry, J. B.

Philbin, T. G.

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

Qiu, C. W.

C. W. Qiu, L. Hu, X. Xu, and Y. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4), 047602 (2009).
[Crossref] [PubMed]

L. Gao, T. H. Fung, K. W. Yu, and C. W. Qiu, “Electromagnetic transparency by coated spheres with radial anisotropy,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(4), 046609 (2008).
[Crossref] [PubMed]

Qiu, C.-W.

Y. Ni, L. Gao, and C.-W. Qiu, “Achieving invisibility of homogeneous cylindrically anisotropic cylinders,” Plasmonics 5(3), 251–258 (2010).
[Crossref]

C.-W. Qiu, A. Novitsky, H. Ma, and S. Qu, “Electromagnetic interaction of arbitrary radial-dependent anisotropic spheres and improved invisibility for nonlinear-transformation-based cloaks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(1), 016604 (2009).
[Crossref] [PubMed]

Qu, S.

C.-W. Qiu, A. Novitsky, H. Ma, and S. Qu, “Electromagnetic interaction of arbitrary radial-dependent anisotropic spheres and improved invisibility for nonlinear-transformation-based cloaks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(1), 016604 (2009).
[Crossref] [PubMed]

Schurig, D.

Shalaev, V. M.

V. M. Shalaev, “Physics. Transforming light,” Science 322(5900), 384–386 (2008).
[Crossref] [PubMed]

Sheng, P.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref] [PubMed]

Sihvola, A.

H. Wallén, H. Kettunen, and A. Sihvola, “Anomalous absorption, plasmonic resonances, and invisibility of radially anisotropic spheres,” Radio Sci. 50(1), 18–28 (2015).
[Crossref]

H. Kettunen, H. Wallén, and A. Sihvola, “Cloaking and magnifying using radial anisotropy,” J. Appl. Phys. 114(4), 044110 (2013).
[Crossref]

A. Sihvola, “Particular properties of the dielectric response of negative-permittivity scatterers,” PIERS Online 3(3), 246–247 (2007).
[Crossref]

Silveirinha, M. G.

M. G. Silveirinha, A. Alù, and N. Engheta, “Parallel-plate metamaterials for cloaking structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(3), 036603 (2007).
[Crossref] [PubMed]

Smith, D. R.

Tricarico, S.

S. Tricarico, F. Bilotti, and L. Vegni, “Scattering cancellation by metamaterial cylindrical multilayers,” J. Eur. Opt. Soc. 4, 09021 (2009).
[Crossref]

Vegni, L.

S. Tricarico, F. Bilotti, and L. Vegni, “Scattering cancellation by metamaterial cylindrical multilayers,” J. Eur. Opt. Soc. 4, 09021 (2009).
[Crossref]

Wallén, H.

H. Wallén, H. Kettunen, and A. Sihvola, “Anomalous absorption, plasmonic resonances, and invisibility of radially anisotropic spheres,” Radio Sci. 50(1), 18–28 (2015).
[Crossref]

H. Kettunen, H. Wallén, and A. Sihvola, “Cloaking and magnifying using radial anisotropy,” J. Appl. Phys. 114(4), 044110 (2013).
[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(6), 063903 (2007).
[Crossref] [PubMed]

Xu, X.

C. W. Qiu, L. Hu, X. Xu, and Y. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4), 047602 (2009).
[Crossref] [PubMed]

Yu, K. W.

L. Gao, T. H. Fung, K. W. Yu, and C. W. Qiu, “Electromagnetic transparency by coated spheres with radial anisotropy,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(4), 046609 (2008).
[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(6), 063903 (2007).
[Crossref] [PubMed]

Zhang, P.

J. Appl. Phys. (1)

H. Kettunen, H. Wallén, and A. Sihvola, “Cloaking and magnifying using radial anisotropy,” J. Appl. Phys. 114(4), 044110 (2013).
[Crossref]

J. Electromag. Wave. (1)

D. K. Cohoon, “An exact solution of Mie type for scattering by a multilayer anisotropic sphere,” J. Electromag. Wave. 3(5), 421–448 (1989).
[Crossref]

J. Eur. Opt. Soc. (1)

S. Tricarico, F. Bilotti, and L. Vegni, “Scattering cancellation by metamaterial cylindrical multilayers,” J. Eur. Opt. Soc. 4, 09021 (2009).
[Crossref]

Nat. Mater. (1)

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref] [PubMed]

Opt. Express (4)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (5)

C. W. Qiu, L. Hu, X. Xu, and Y. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4), 047602 (2009).
[Crossref] [PubMed]

C.-W. Qiu, A. Novitsky, H. Ma, and S. Qu, “Electromagnetic interaction of arbitrary radial-dependent anisotropic spheres and improved invisibility for nonlinear-transformation-based cloaks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(1), 016604 (2009).
[Crossref] [PubMed]

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016623 (2005).
[Crossref] [PubMed]

M. G. Silveirinha, A. Alù, and N. Engheta, “Parallel-plate metamaterials for cloaking structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(3), 036603 (2007).
[Crossref] [PubMed]

L. Gao, T. H. Fung, K. W. Yu, and C. W. Qiu, “Electromagnetic transparency by coated spheres with radial anisotropy,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(4), 046609 (2008).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99(6), 063903 (2007).
[Crossref] [PubMed]

PIERS Online (1)

A. Sihvola, “Particular properties of the dielectric response of negative-permittivity scatterers,” PIERS Online 3(3), 246–247 (2007).
[Crossref]

Plasmonics (1)

Y. Ni, L. Gao, and C.-W. Qiu, “Achieving invisibility of homogeneous cylindrically anisotropic cylinders,” Plasmonics 5(3), 251–258 (2010).
[Crossref]

Proc. R. Soc. Lond. A (1)

G. W. Milton and N.-A. P. Nicorovici, “On the cloaking effects associated with anomalous localized resonance,” Proc. R. Soc. Lond. A 462(2074), 3027–3059 (2006).
[Crossref]

Prog. Opt. (1)

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

Radio Sci. (1)

H. Wallén, H. Kettunen, and A. Sihvola, “Anomalous absorption, plasmonic resonances, and invisibility of radially anisotropic spheres,” Radio Sci. 50(1), 18–28 (2015).
[Crossref]

Science (3)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

V. M. Shalaev, “Physics. Transforming light,” Science 322(5900), 384–386 (2008).
[Crossref] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1 Cross-section of an annular spherical shell with radially inhomogeneous anisotropic permittivity ε r,t (r) , surrounding a dielectric inclusion with permittivity ε c , and embedded in a medium with permittivity ε m .The outer and inner shell radii areaand b, respectively. Radial and tangential components of the permittivity are ε r and ε t , respectively. E 0 is external static electric field.
Fig. 2
Fig. 2 Tangential component of the permittivity ε t0 versus radial component ε r0 of the spherical shell as a function of power law m associated with radial dependence of the permittivity of the shell. The numbers near the curves indicate the value of power law index m. The external permittivity ε m =1 .
Fig. 3
Fig. 3 Plot of effective contrast Δ ε ef as a function of the ratio ε t0 / ε r0 , for homogeneous and radially inhomogeneous permittivities within the spherical shell, for different values of inclusion permittivity ε c . In each case, the ratio of outer to inner shell radius a/b=3 , while m=0 (homogeneous), m=0.5,m=0.5 correspond respectively to solid, dashed and dot-dashed lines. (a) ε c =1.5 ; (b) ε c =3 .
Fig. 4
Fig. 4 Permittivity contrast Δ ε ef as a function of inhomogeneity index m. Both figures: fixed ratio ε t0 / ε r0 =10 , external permittivity ε m =1 , inclusion permittivities ε c =1.5,3,6 (corresponding respectively to solid, dashed and dot-dashed lines). Individual figures: (a) Ratio of shell radii a/b=3 ; (b) Ratio of shell radii a/b=10 .
Fig. 5
Fig. 5 Spatial distribution of electric potential within cross-section of the spherical shell. Solid lines are equipotential lines. Lines of force of the applied electric field are perpendicular to the equipotential lines shown in Fig. 5. (a) Δ ε ef 0, ε r0 =20, ε c =10, ε m =1,a=2b,m=2 ;(b) Δ ε ef =0, ε r0 =1, ε c =1, ε m =3,a=3b,m=1 .
Fig. 6
Fig. 6 Comparison of efficiency of cloaking by spherical and cylindrical shells with radially inhomogeneous permittivity. In all curves: permittivity of inclusion ε c =2 ; permittivity of external medium ε m =1 ; ratio of outer to inner radius a/b=3 ; numbers near the curves show value of m;spherical geometry - solid lines, cylindrical geometry – dashed lines.

Equations (18)

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ϕ( r,θ )=Arcosθ,rb, ϕ( r,θ )=( B r t 1 +C r t 2 )cosθ,bra, ϕ( r,θ )=( F r 2 E 0 r )cosθ,ra,
t 1 , 2 = 1 2 [ ( m + 1 ) ± ( m + 1 ) 2 + 8 ε t 0 ε r 0 ] .
Ab=B b t 1 +C b t 2 , B a t 1 +C a t 2 =F/ a 2 E 0 a, ε c A= ε r0 b m1 ( B t 1 b t 1 +C t 2 b t 2 ), ε r0 a m1 ( B t 1 a t 1 +C t 2 a t 2 )= ε m ( 2F/ a 3 E 0 ).
α s = 3 ε e f ε m ε e f + 2 ε m .
ε ef = ε r0 t 2 [ ε r0 ε c t 1 ( b a ) m 1 ] ( b a ) ξ t 1 [ ε r0 ε c t 2 ( b a ) m 1 ] [ ε r0 ε c t 1 ( b a ) m 1 ] ( b a ) ξ [ ε r0 ε c t 2 ( b a ) m 1 ] ,
ε r0 t 1 = ε m .
ε t0 = ε m 2 ( ε m ε r0 +m+1 ),
ε e f = ε m + Δ ε e f , Δ ε e f = 2 ξ ε m m + 1 ξ [ ε m ε c ( b a ) m 1 ] ( b a ) ξ 1 m + 1 + ξ m + 1 ξ ε m ε c ( b a ) m + [ ε m ε c ( b a ) m 1 ] ( b a ) ξ .
( b a ) m = ε c ε m .
ϕ( ρ,φ )=Aρcosφ,ρb, ϕ( ρ,φ )=( B ρ t 1 +C ρ t 2 )cosφ,bρa, ϕ( ρ,φ )=( D ρ 1 E 0 ρ )cosφ,ρa,
t 1,2 = 1 2 [ m± m 2 +4 ε t0 ε ρ0 ].
A b = B b t 1 + C b t 2 , B a t 1 + C a t 2 = F / a 2 E 0 a , ε c A = ε ρ 0 b m 1 ( B t 1 b t 1 + C t 2 b t 2 ) , ε ρ 0 a m 1 ( B t 1 a t 1 + C t 2 a t 2 ) = ε m ( 2 F / a 3 E 0 ) .
ξ= m 2 +4 ε t0 ε ρ0 .
ε t0 = ε m ( ε m ε ρ0 +m ),
A= 3ξ ε m ε c ( b a ) ξ+m3 2 E 0 [ ε r0 ε c t 1 ( b a ) m 1 ]( 2 ε m ε r0 + t 2 ) ( b a ) ξ [ ε r0 ε c t 2 ( b a ) m 1 ]( 2 ε m ε r0 + t 1 ) ,
B= 3 ε m ε r0 [ ε r0 ε c t 2 ( b a ) m 1 ] a ξ+m+3 2 E 0 [ ε r0 ε c t 1 ( b a ) m 1 ]( 2 ε m ε r0 + t 2 ) ( b a ) ξ [ ε r0 ε c t 2 ( b a ) m 1 ]( 2 ε m ε r0 + t 1 ) ,
C= 3 ε m ε r0 a ξ+m+3 2 ( b a ) ξ [ ε r0 ε c t 1 ( b a ) m 1 ] E 0 [ ε r0 ε c t 1 ( b a ) m 1 ]( 2 ε m ε r0 + t 2 ) ( b a ) ξ [ ε r0 ε c t 2 ( b a ) m 1 ]( 2 ε m ε r0 + t 1 ) ,
F= ( ε m ε r0 t 2 )[ ε r0 ε c t 1 ( b a ) m 1 ] ( b a ) ξ ( ε m ε r0 t 1 )[ ε r0 ε c t 2 ( b a ) m 1 ] [ ε r0 ε c t 1 ( b a ) m 1 ]( 2 ε m ε r0 + t 2 ) ( b a ) ξ [ ε r0 ε c t 2 ( b a ) m 1 ]( 2 ε m ε r0 + t 1 ) a 3 E 0 ,

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