Abstract

We analyze cloaking of transverse electric (TE) fields through homogenization of radially symmetric metallic structures. The two-dimensional circular cloak consists of concentric layers cut into a large number of small infinitely conducting sectors which is equivalent to a highly anisotropic permittivity. We find that a wave radiated by a magnetic line current source located a couple of wavelengths away from the cloak is almost unperturbed in magnitude but not in phase. Our structured cloak is shown to work for different wavelengths provided they are ten times larger than the outermost sectors.

© 2008 Optical Society of America

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References

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  1. J.B. Pendry, D. Shurig, and D.R. Smith, “Controlling electromagnetic fields,” Science 3121780–1782 (2006).
    [Crossref] [PubMed]
  2. U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys.  8, 247 (2006).
    [Crossref]
  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 314977–980 (2006).
    [Crossref] [PubMed]
  4. U. Leonhardt, “Optical conformal mapping,” Science 3121777–1780 (2006).
    [Crossref] [PubMed]
  5. 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]
  6. R.C. McPhedran, N.A. Nicorovici, and G.W. Milton,“Optical and dielectric properties of partially resonant composites,” Phys. Rev. B 49, 8479–8482 (1994).
    [Crossref]
  7. J.B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [Crossref] [PubMed]
  8. J.B. Pendry and S.A. Ramakrishna, “Focussing light using negative refraction,” J. Phys. Cond. Matter 15, 6345–6364 (2003).
    [Crossref]
  9. D. Maystre and S. Enoch, “Perfect lenses with left-handed material: Alice’s mirror?,” J. Opt. Soc. Am. A 21, 122 (2004).
    [Crossref]
  10. S.A. Ramakrishna, “Physics of negative refractive index materials,” Rep. Prog. Phys. 68, 449–521 (2005).
    [Crossref]
  11. G.W. Milton and N.A. Nicorovici, “On the cloaking effects associated with anomalous localised resonance,” Proc. Roy. Lond. A 462, 3027–3059 (2006).
    [Crossref]
  12. 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 (2007).
    [Crossref] [PubMed]
  13. W. Cai, U.K. Chettiar, A.V. Kildiev, and V.M. Shalaev, “Optical Cloaking with metamaterials,” Nature 1, 224–227 (2007).
  14. 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]
  15. S. Guenneau and F. Zolla, “Homogenization of three-dimensional finite photonic crystals,” JEWA14, 529–530 (2000) & Progress In Electromagnetics Research 27, 91–127 (2000).
  16. D.P. Gaillot, C. Croenne, and D. Lippens, “An all-dielectric route for terahertz cloaking,” Opt. Express 16, 3986–3992 (2008).
    [Crossref] [PubMed]

2008 (1)

2007 (4)

2006 (5)

J.B. Pendry, D. Shurig, and D.R. Smith, “Controlling electromagnetic fields,” Science 3121780–1782 (2006).
[Crossref] [PubMed]

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys.  8, 247 (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 314977–980 (2006).
[Crossref] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science 3121777–1780 (2006).
[Crossref] [PubMed]

G.W. Milton and N.A. Nicorovici, “On the cloaking effects associated with anomalous localised resonance,” Proc. Roy. Lond. A 462, 3027–3059 (2006).
[Crossref]

2005 (1)

S.A. Ramakrishna, “Physics of negative refractive index materials,” Rep. Prog. Phys. 68, 449–521 (2005).
[Crossref]

2004 (1)

2003 (1)

J.B. Pendry and S.A. Ramakrishna, “Focussing light using negative refraction,” J. Phys. Cond. Matter 15, 6345–6364 (2003).
[Crossref]

2000 (1)

J.B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

1994 (1)

R.C. McPhedran, N.A. Nicorovici, and G.W. Milton,“Optical and dielectric properties of partially resonant composites,” Phys. Rev. B 49, 8479–8482 (1994).
[Crossref]

Botten, L.C.

Cai, W.

W. Cai, U.K. Chettiar, A.V. Kildiev, and V.M. Shalaev, “Optical Cloaking with metamaterials,” Nature 1, 224–227 (2007).

Chettiar, U.K.

W. Cai, U.K. Chettiar, A.V. Kildiev, and V.M. Shalaev, “Optical Cloaking with metamaterials,” Nature 1, 224–227 (2007).

Croenne, C.

Cummer, S.A.

D. Schurig, J.J. Mock, B.J. Justice, S.A. Cummer, J.B. Pendry, A.F. Starr, and D.R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314977–980 (2006).
[Crossref] [PubMed]

Enoch, S.

Gaillot, D.P.

Greenleaf, A.

Guenneau, S.

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]

S. Guenneau and F. Zolla, “Homogenization of three-dimensional finite photonic crystals,” JEWA14, 529–530 (2000) & Progress In Electromagnetics Research 27, 91–127 (2000).

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 314977–980 (2006).
[Crossref] [PubMed]

Kildiev, A.V.

W. Cai, U.K. Chettiar, A.V. Kildiev, and V.M. Shalaev, “Optical Cloaking with metamaterials,” Nature 1, 224–227 (2007).

Kurylev, Y.

Lassas, M.

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 3121777–1780 (2006).
[Crossref] [PubMed]

Lippens, D.

Maystre, D.

McPhedran, R.C.

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 (2007).
[Crossref] [PubMed]

R.C. McPhedran, N.A. Nicorovici, and G.W. Milton,“Optical and dielectric properties of partially resonant composites,” Phys. Rev. B 49, 8479–8482 (1994).
[Crossref]

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

G.W. Milton and N.A. Nicorovici, “On the cloaking effects associated with anomalous localised resonance,” Proc. Roy. Lond. A 462, 3027–3059 (2006).
[Crossref]

R.C. McPhedran, N.A. Nicorovici, and G.W. Milton,“Optical and dielectric properties of partially resonant composites,” Phys. Rev. B 49, 8479–8482 (1994).
[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 314977–980 (2006).
[Crossref] [PubMed]

Nicolet, A.

Nicorovici, N.A.

G.W. Milton and N.A. Nicorovici, “On the cloaking effects associated with anomalous localised resonance,” Proc. Roy. Lond. A 462, 3027–3059 (2006).
[Crossref]

R.C. McPhedran, N.A. Nicorovici, and G.W. Milton,“Optical and dielectric properties of partially resonant composites,” Phys. Rev. B 49, 8479–8482 (1994).
[Crossref]

Nicorovici, N.A.P.

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]

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 314977–980 (2006).
[Crossref] [PubMed]

J.B. Pendry, D. Shurig, and D.R. Smith, “Controlling electromagnetic fields,” Science 3121780–1782 (2006).
[Crossref] [PubMed]

J.B. Pendry and S.A. Ramakrishna, “Focussing light using negative refraction,” J. Phys. Cond. Matter 15, 6345–6364 (2003).
[Crossref]

J.B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

Philbin, T. G.

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

Ramakrishna, S.A.

S.A. Ramakrishna, “Physics of negative refractive index materials,” Rep. Prog. Phys. 68, 449–521 (2005).
[Crossref]

J.B. Pendry and S.A. Ramakrishna, “Focussing light using negative refraction,” J. Phys. Cond. Matter 15, 6345–6364 (2003).
[Crossref]

Schurig, D.

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 314977–980 (2006).
[Crossref] [PubMed]

Shalaev, V.M.

W. Cai, U.K. Chettiar, A.V. Kildiev, and V.M. Shalaev, “Optical Cloaking with metamaterials,” Nature 1, 224–227 (2007).

Shurig, D.

J.B. Pendry, D. Shurig, and D.R. Smith, “Controlling electromagnetic fields,” Science 3121780–1782 (2006).
[Crossref] [PubMed]

Smith, D.R.

J.B. Pendry, D. Shurig, and D.R. Smith, “Controlling electromagnetic fields,” Science 3121780–1782 (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 314977–980 (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 314977–980 (2006).
[Crossref] [PubMed]

Uhlmann, G.

Zolla, F.

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]

S. Guenneau and F. Zolla, “Homogenization of three-dimensional finite photonic crystals,” JEWA14, 529–530 (2000) & Progress In Electromagnetics Research 27, 91–127 (2000).

J. Opt. Soc. Am. A (1)

J. Phys. Cond. Matter (1)

J.B. Pendry and S.A. Ramakrishna, “Focussing light using negative refraction,” J. Phys. Cond. Matter 15, 6345–6364 (2003).
[Crossref]

Nature (1)

W. Cai, U.K. Chettiar, A.V. Kildiev, and V.M. Shalaev, “Optical Cloaking with metamaterials,” Nature 1, 224–227 (2007).

New J. Phys (1)

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

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. B (1)

R.C. McPhedran, N.A. Nicorovici, and G.W. Milton,“Optical and dielectric properties of partially resonant composites,” Phys. Rev. B 49, 8479–8482 (1994).
[Crossref]

Phys. Rev. Lett. (1)

J.B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

Proc. Roy. Lond. A (1)

G.W. Milton and N.A. Nicorovici, “On the cloaking effects associated with anomalous localised resonance,” Proc. Roy. Lond. A 462, 3027–3059 (2006).
[Crossref]

Rep. Prog. Phys. (1)

S.A. Ramakrishna, “Physics of negative refractive index materials,” Rep. Prog. Phys. 68, 449–521 (2005).
[Crossref]

Science (3)

J.B. Pendry, D. Shurig, and D.R. Smith, “Controlling electromagnetic fields,” Science 3121780–1782 (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 314977–980 (2006).
[Crossref] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science 3121777–1780 (2006).
[Crossref] [PubMed]

Other (1)

S. Guenneau and F. Zolla, “Homogenization of three-dimensional finite photonic crystals,” JEWA14, 529–530 (2000) & Progress In Electromagnetics Research 27, 91–127 (2000).

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Figures (3)

Fig. 1.
Fig. 1.

Left: Geometry of the structured infinitely conducting cloak. The structure consists of 256 angular sectors. Right: Diffraction of the field radiated by a magnetic wire source by an infinitely conducting F-shaped obstacle surrounded by a homogeneous dielectric anisotropic coating with effective permittivity ε h o m ¯ ¯ = diag ( 1.7 , 8.2 , ) and effective transmission conditions n ( ε h o m ¯ ¯ 1 ( + i γ ) H hom ) | r = n ( + i γ ) H hom | r + on its inner and outer boundaries (r=R 1=0.144 and r=R 2=0.4). The frequency ν is equal to 3.5.

Fig. 2.
Fig. 2.

Real part ℜe(H 3) of the longitudinal component H 3 of the magnetic field along the x 2-axis. The origin of the x 2 axis is taken at point (4,4) of Fig. 3 and it ends at point (0,0). A magnetic line source of wavelength λ=c/ν=c/3.5 is located at point (2.3,2.3). The vertical thick bold lines represent the outer boundary of the cloak.

Fig. 3.
Fig. 3.

2D plot of the real part ℜe(H 3) of the longitudinal component H 3 of the magnetic field radiated by a harmonic line current source of wavelength λ=c/ν. Left panel: Diffraction by an infinitely conducting F-shaped obstacle; Right panel: Diffraction by an infinitely conducting F-shaped obstacle surrounded by the structured cloak. When the frequency ν increases, the diffraction worsens and cloaking becomes less effective.

Equations (8)

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r = R 1 + r ( R 2 R 1 ) R 2 , 0 r R 2 ,
θ = θ , 0 < θ 2 π ,
x 3 = x 3 , x 3 I R ,
ε r = μ r = r R 1 r , ε θ = μ θ = r r R 1 , ε 3 = μ 3 = ( R 2 R 2 R 1 ) 2 r R 1 r .
ε r = ( R 2 R 2 R 1 ) 2 ( r R 1 r ) 2 , ε θ = ( R 2 R 2 R 1 ) 2 , μ 3 = 1 .
ε h o m ¯ ¯ = 1 area ( Y * ) ( area ( Y * ) 0 0 0 area ( Y * ) 0 0 0 ) ( ϕ rr ϕ 0 ϕ θr ϕ θθ 0 0 0 0 ) ,
i , j { r , θ } , ϕ ij = < V j y i > Y * = < V i y j > Y * = < V i · V j > Y * ,
𝒦 j : Δ V j = 0 , in Y * = Y B , and V j n = n j , on B ,

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