Abstract

We present a semiclassical description of non-magnetic cloaking. The semiclassical result is confirmed by numerical simulations of a gaussian beam scattering from the cloak. Further analysis reveals that certain beams penetrate the non-magnetic cloak thereby degrading the performance.

© 2008 Optical Society of America

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References

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  1. A. Greenleaf, M. Lassas, and G. Uhlmann, "On nonuniqueness for Calderons inverse problem," Math. Res. Let. 10, 685-693 (2003).
  2. J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 17801782 (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 314, 977980 (2006).
  4. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nature Photon. 1, 224-227 (2007).
    [CrossRef]
  5. G. W. Milton and N. Nicorovici, "On the cloaking effects associated with anomalous localised resonance," Proc. R. Soc. A 462, 30273059 (2006).
    [CrossRef]
  6. A. Alu and N. Engheta, "Achieving transparency with plasmonic and metamaterial coatings," Phys. Rev. E. 72, 016623 (2005).
    [CrossRef]
  7. S. A. Cummer, B. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E. 74, 036621 (2006).
    [CrossRef]
  8. D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794 (2006).
    [CrossRef] [PubMed]
  9. W. Cai, U. K. Chettiar, A. K. Kildishev, G. W. Milton, and V. M. Shalaev, "Non-magnetic cloak without reflection," arXiv:0707.3641v1.
  10. U. Leonhardt, "Optical conformal mapping," Science 31217771780 (2006).
    [CrossRef]
  11. Z. Jacob, L. V. Alekseyev, and E. Narimanov, "Semiclassical theory of the hyperlens," J. Opt. Soc. Am. A 24, A52-A59 (2007).
    [CrossRef]

2007

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

Z. Jacob, L. V. Alekseyev, and E. Narimanov, "Semiclassical theory of the hyperlens," J. Opt. Soc. Am. A 24, A52-A59 (2007).
[CrossRef]

2006

S. A. Cummer, B. 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, "Optical conformal mapping," Science 31217771780 (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 (2006).
[CrossRef] [PubMed]

G. W. Milton and N. Nicorovici, "On the cloaking effects associated with anomalous localised resonance," Proc. R. Soc. A 462, 30273059 (2006).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 17801782 (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, 977980 (2006).

2005

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

2003

A. Greenleaf, M. Lassas, and G. Uhlmann, "On nonuniqueness for Calderons inverse problem," Math. Res. Let. 10, 685-693 (2003).

Alekseyev, L. V.

Alu, A.

A. Alu 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," Nature Photon. 1, 224-227 (2007).
[CrossRef]

Chettiar, U. K.

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

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 314, 977980 (2006).

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

Engheta, N.

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

Greenleaf, A.

A. Greenleaf, M. Lassas, and G. Uhlmann, "On nonuniqueness for Calderons inverse problem," Math. Res. Let. 10, 685-693 (2003).

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, 977980 (2006).

Kildishev, A. V.

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

Lassas, M.

A. Greenleaf, M. Lassas, and G. Uhlmann, "On nonuniqueness for Calderons inverse problem," Math. Res. Let. 10, 685-693 (2003).

Leonhardt, U.

U. Leonhardt, "Optical conformal mapping," Science 31217771780 (2006).
[CrossRef]

Milton, G. W.

G. W. Milton and N. Nicorovici, "On the cloaking effects associated with anomalous localised resonance," Proc. R. Soc. A 462, 30273059 (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, 977980 (2006).

Narimanov, E.

Nicorovici, N.

G. W. Milton and N. Nicorovici, "On the cloaking effects associated with anomalous localised resonance," Proc. R. Soc. A 462, 30273059 (2006).
[CrossRef]

Pendry, J. B.

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, 977980 (2006).

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 17801782 (2006).
[CrossRef]

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

Popa, B.

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

Schurig, D.

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

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 17801782 (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, 977980 (2006).

Shalaev, V. M.

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

Smith, D. R.

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, 977980 (2006).

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 17801782 (2006).
[CrossRef]

S. A. Cummer, B. 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. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794 (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, 977980 (2006).

Uhlmann, G.

A. Greenleaf, M. Lassas, and G. Uhlmann, "On nonuniqueness for Calderons inverse problem," Math. Res. Let. 10, 685-693 (2003).

J. Opt. Soc. Am. A

Math. Res. Let.

A. Greenleaf, M. Lassas, and G. Uhlmann, "On nonuniqueness for Calderons inverse problem," Math. Res. Let. 10, 685-693 (2003).

Nature Photon.

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

Opt. Express

Phys. Rev. E.

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

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

Proc. R. Soc. A

G. W. Milton and N. Nicorovici, "On the cloaking effects associated with anomalous localised resonance," Proc. R. Soc. A 462, 30273059 (2006).
[CrossRef]

Science

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 17801782 (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, 977980 (2006).

U. Leonhardt, "Optical conformal mapping," Science 31217771780 (2006).
[CrossRef]

Other

W. Cai, U. K. Chettiar, A. K. Kildishev, G. W. Milton, and V. M. Shalaev, "Non-magnetic cloak without reflection," arXiv:0707.3641v1.

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Figures (4)

Fig. 1.
Fig. 1.

(a) Cylindrical cloak, gaussian beam incident on the cloak (inset). (b) Calculated ray trajectories. Shown in the inset are ray trajectories in a cloaking medium (blue), ray trajectory in vacuum (red), cloaked region of radius a

Fig. 2.
Fig. 2.

(Intensity in false color) (a) gaussian beam in vacuum (position of cloak is also shown for comparison) (b) gaussian beam incident on the cloak showing the smooth bending and some reflections. Superimposed ray trajectory in black evaluated analytically corresponds well to the center of the beam.

Fig. 3.
Fig. 3.

(a) Intensity in false color of a gaussian beam incident on the cloak showing compression within the device (b) Ray calculations exhibiting the same compression

Fig. 4.
Fig. 4.

(a) On-axis gaussian beam shows the isotropic scattering as well as penetration within the cloak (b) Real part of the on axis gaussian beam (c) Intensity in false color of a slightly off axis gaussian beam. The cloaking performance degrades if the impact parameter is not large compared to the beam width.

Equations (25)

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H = c p r 2 ε θ + p θ 2 r 2 ε r
r sin ( θ ) = ρ
( r a ) sin ( θ ) = ρ
H vacuum = c p r 2 + p θ 2 r 2
H cloak = c p r 2 + p θ 2 ( r a ) 2
ε r ( r a ) 2 r 2 ε θ = 1
ε r = c 1 ( r a ) 2 r 2 ε θ = c 2
H cloak = c p r 2 c 2 + p θ 2 ( r a ) 2 c 1
r ( θ ) = a + b sin ( θ i ) c 1 sin [ c 2 c 1 ( θ θ 0 ) ]
θ 0 = θ i c 2 c 1 arcsin [ b sin ( θ i ) ( b a ) c 1 ]
θ 0 = 0 c 1 = c 2
c 1 = b 2 ( b a ) 2
ε r = η ( r a ) 2 r 2 ε θ = η
B z = R 1 ( r ) exp ( im θ )
E θ = R 2 ( r ) exp ( im θ )
r 2 d 2 R 1 d r + r d R 1 d r + [ ε θ k 0 2 r 2 m 2 ε θ ε r ] R 1 = 0
d 2 R 1 d r + 1 r d R 1 d r + [ η k 0 2 m 2 ( r a ) 2 ] R 1 = 0
R 2 ( r ) = 1 ik 0 ε θ R 1 ( r ) r
R 1 ( r ) = H m ( k 0 r ) + r m + H m + ( k 0 r )
R 2 ( r ) = 1 i ( D H m ( k 0 r ) + r m + D H m + ( k 0 r ) )
R 1 ( r ) = t m H m ( k 0 r ) + t m + H m + ( k 0 r )
R 2 ( r ) = 1 i ( t m D H m ( k 0 r ) + t m + D H m + ( k 0 r ) )
( R 1 ( a ) R 2 ( a ) ) = T m ( R 1 ( b ) R 2 ( b ) )
det ( T m ) = r max r in
t m + = t m

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