Abstract

We extend the design of radially symmetric invisibility cloaks through transformation optics as proposed by Pendry et al. [Science 312, 1780 (2006)] to coated cylinders of an arbitrary cross section. The validity of our Fourier-based approach is confirmed by both analytical and numerical results for a cloak displaying a nonconvex cross section of varying thickness. In the former case, we evaluate the Green’s function of a line source in the transformed coordinates. In the latter case, we implement a full-wave finite-element model for a cylindrical antenna radiating a p-polarized electric field in the presence of a F-shaped lossy object surrounded by the cloak.

© 2008 Optical Society of America

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  1. J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
    [CrossRef] [PubMed]
  2. G. W. Milton, N. A. P. Nicorovici, R. C. McPhedran, and V. A. Podolskiy, Proc. R. Soc. London Ser. A 461, 3999 (2005).
    [CrossRef]
  3. S. Guenneau, B. Gralak, and J. B. Pendry, Opt. Lett. 30, 1204 (2005).
    [CrossRef] [PubMed]
  4. J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
    [CrossRef] [PubMed]
  5. U. Leonhardt, Science 312, 1777 (2006).
    [CrossRef] [PubMed]
  6. A. Alu and N. Engheta, Phys. Rev. E 95, 016623 (2005).
    [CrossRef]
  7. G. W. Milton and N. A. Nicorovici, Proc. R. Soc. London Ser. A 462, 3027 (2006).
    [CrossRef]
  8. F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, Opt. Lett. 32, 1069 (2007).
    [CrossRef] [PubMed]
  9. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
    [CrossRef] [PubMed]
  10. W. Cai, U. K. Chettiar, A. V. Kildiev, and V. M. Shalaev, Nat. Photonics 1, 224 (2007).
    [CrossRef]
  11. D. Kwon and D. H. Werner, Appl. Phys. Lett. 92, 013501 (2008).
    [CrossRef]
  12. A. Nicolet, F. Zolla, and S. Guenneau, IEEE Trans. Magn. 44, 1150 (2008).
    [CrossRef]
  13. M. Rham, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
    [CrossRef]
  14. A. Nicolet, J. F. Remacle, B. Meys, A. Genon, and W. Legros, Appl. Phys. 75, 6036 (1994).
    [CrossRef]
  15. P. Dular, C. Geuzaine, F. Henrotte, and W. Legros, IEEE Trans. Magn. 34, 3395 (1998) (see also http://geuz.org/getdp/).
    [CrossRef]

2008 (3)

D. Kwon and D. H. Werner, Appl. Phys. Lett. 92, 013501 (2008).
[CrossRef]

A. Nicolet, F. Zolla, and S. Guenneau, IEEE Trans. Magn. 44, 1150 (2008).
[CrossRef]

M. Rham, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

2007 (2)

W. Cai, U. K. Chettiar, A. V. Kildiev, and V. M. Shalaev, Nat. Photonics 1, 224 (2007).
[CrossRef]

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, Opt. Lett. 32, 1069 (2007).
[CrossRef] [PubMed]

2006 (4)

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

G. W. Milton and N. A. Nicorovici, Proc. R. Soc. London Ser. A 462, 3027 (2006).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

U. Leonhardt, Science 312, 1777 (2006).
[CrossRef] [PubMed]

2005 (3)

A. Alu and N. Engheta, Phys. Rev. E 95, 016623 (2005).
[CrossRef]

G. W. Milton, N. A. P. Nicorovici, R. C. McPhedran, and V. A. Podolskiy, Proc. R. Soc. London Ser. A 461, 3999 (2005).
[CrossRef]

S. Guenneau, B. Gralak, and J. B. Pendry, Opt. Lett. 30, 1204 (2005).
[CrossRef] [PubMed]

2000 (1)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

1998 (1)

P. Dular, C. Geuzaine, F. Henrotte, and W. Legros, IEEE Trans. Magn. 34, 3395 (1998) (see also http://geuz.org/getdp/).
[CrossRef]

1994 (1)

A. Nicolet, J. F. Remacle, B. Meys, A. Genon, and W. Legros, Appl. Phys. 75, 6036 (1994).
[CrossRef]

Alu, A.

A. Alu and N. Engheta, Phys. Rev. E 95, 016623 (2005).
[CrossRef]

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildiev, and V. M. Shalaev, Nat. Photonics 1, 224 (2007).
[CrossRef]

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildiev, and V. M. Shalaev, Nat. Photonics 1, 224 (2007).
[CrossRef]

Cummer, S. A.

M. Rham, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

Dular, P.

P. Dular, C. Geuzaine, F. Henrotte, and W. Legros, IEEE Trans. Magn. 34, 3395 (1998) (see also http://geuz.org/getdp/).
[CrossRef]

Engheta, N.

A. Alu and N. Engheta, Phys. Rev. E 95, 016623 (2005).
[CrossRef]

Genon, A.

A. Nicolet, J. F. Remacle, B. Meys, A. Genon, and W. Legros, Appl. Phys. 75, 6036 (1994).
[CrossRef]

Geuzaine, C.

P. Dular, C. Geuzaine, F. Henrotte, and W. Legros, IEEE Trans. Magn. 34, 3395 (1998) (see also http://geuz.org/getdp/).
[CrossRef]

Gralak, B.

Guenneau, S.

Henrotte, F.

P. Dular, C. Geuzaine, F. Henrotte, and W. Legros, IEEE Trans. Magn. 34, 3395 (1998) (see also http://geuz.org/getdp/).
[CrossRef]

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

Kildiev, A. V.

W. Cai, U. K. Chettiar, A. V. Kildiev, and V. M. Shalaev, Nat. Photonics 1, 224 (2007).
[CrossRef]

Kwon, D.

D. Kwon and D. H. Werner, Appl. Phys. Lett. 92, 013501 (2008).
[CrossRef]

Legros, W.

P. Dular, C. Geuzaine, F. Henrotte, and W. Legros, IEEE Trans. Magn. 34, 3395 (1998) (see also http://geuz.org/getdp/).
[CrossRef]

A. Nicolet, J. F. Remacle, B. Meys, A. Genon, and W. Legros, Appl. Phys. 75, 6036 (1994).
[CrossRef]

Leonhardt, U.

U. Leonhardt, Science 312, 1777 (2006).
[CrossRef] [PubMed]

McPhedran, R. C.

G. W. Milton, N. A. P. Nicorovici, R. C. McPhedran, and V. A. Podolskiy, Proc. R. Soc. London Ser. A 461, 3999 (2005).
[CrossRef]

Meys, B.

A. Nicolet, J. F. Remacle, B. Meys, A. Genon, and W. Legros, Appl. Phys. 75, 6036 (1994).
[CrossRef]

Milton, G. W.

G. W. Milton and N. A. Nicorovici, Proc. R. Soc. London Ser. A 462, 3027 (2006).
[CrossRef]

G. W. Milton, N. A. P. Nicorovici, R. C. McPhedran, and V. A. Podolskiy, Proc. R. Soc. London Ser. A 461, 3999 (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, Science 314, 977 (2006).
[CrossRef] [PubMed]

Nicolet, A.

A. Nicolet, F. Zolla, and S. Guenneau, IEEE Trans. Magn. 44, 1150 (2008).
[CrossRef]

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, Opt. Lett. 32, 1069 (2007).
[CrossRef] [PubMed]

A. Nicolet, J. F. Remacle, B. Meys, A. Genon, and W. Legros, Appl. Phys. 75, 6036 (1994).
[CrossRef]

Nicorovici, N. A.

G. W. Milton and N. A. Nicorovici, Proc. R. Soc. London Ser. A 462, 3027 (2006).
[CrossRef]

Nicorovici, N. A. P.

G. W. Milton, N. A. P. Nicorovici, R. C. McPhedran, and V. A. Podolskiy, Proc. R. Soc. London Ser. A 461, 3999 (2005).
[CrossRef]

Pendry, J. B.

M. Rham, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, Opt. Lett. 32, 1069 (2007).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

S. Guenneau, B. Gralak, and J. B. Pendry, Opt. Lett. 30, 1204 (2005).
[CrossRef] [PubMed]

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Podolskiy, V. A.

G. W. Milton, N. A. P. Nicorovici, R. C. McPhedran, and V. A. Podolskiy, Proc. R. Soc. London Ser. A 461, 3999 (2005).
[CrossRef]

Remacle, J. F.

A. Nicolet, J. F. Remacle, B. Meys, A. Genon, and W. Legros, Appl. Phys. 75, 6036 (1994).
[CrossRef]

Rham, M.

M. Rham, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

Roberts, D. A.

M. Rham, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

Schurig, D.

M. Rham, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

Shalaev, V. M.

W. Cai, U. K. Chettiar, A. V. Kildiev, and V. M. Shalaev, Nat. Photonics 1, 224 (2007).
[CrossRef]

Smith, D. R.

M. Rham, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (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, Science 314, 977 (2006).
[CrossRef] [PubMed]

Werner, D. H.

D. Kwon and D. H. Werner, Appl. Phys. Lett. 92, 013501 (2008).
[CrossRef]

Zolla, F.

A. Nicolet, F. Zolla, and S. Guenneau, IEEE Trans. Magn. 44, 1150 (2008).
[CrossRef]

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, Opt. Lett. 32, 1069 (2007).
[CrossRef] [PubMed]

Appl. Phys. (1)

A. Nicolet, J. F. Remacle, B. Meys, A. Genon, and W. Legros, Appl. Phys. 75, 6036 (1994).
[CrossRef]

Appl. Phys. Lett. (1)

D. Kwon and D. H. Werner, Appl. Phys. Lett. 92, 013501 (2008).
[CrossRef]

IEEE Trans. Magn. (2)

A. Nicolet, F. Zolla, and S. Guenneau, IEEE Trans. Magn. 44, 1150 (2008).
[CrossRef]

P. Dular, C. Geuzaine, F. Henrotte, and W. Legros, IEEE Trans. Magn. 34, 3395 (1998) (see also http://geuz.org/getdp/).
[CrossRef]

Nat. Photonics (1)

W. Cai, U. K. Chettiar, A. V. Kildiev, and V. M. Shalaev, Nat. Photonics 1, 224 (2007).
[CrossRef]

Opt. Lett. (2)

Photonics Nanostruct. Fundam. Appl. (1)

M. Rham, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

Phys. Rev. E (1)

A. Alu and N. Engheta, Phys. Rev. E 95, 016623 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Proc. R. Soc. London Ser. A (2)

G. W. Milton, N. A. P. Nicorovici, R. C. McPhedran, and V. A. Podolskiy, Proc. R. Soc. London Ser. A 461, 3999 (2005).
[CrossRef]

G. W. Milton and N. A. Nicorovici, Proc. R. Soc. London Ser. A 462, 3027 (2006).
[CrossRef]

Science (3)

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

U. Leonhardt, Science 312, 1777 (2006).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Variation of entries ( T 1 ) r r , ( T 1 ) r θ = ( T 1 ) θ r , and ( T 1 ) θ θ = ( T 1 ) z z = c 11 of the inverse metric tensor T 1 on the outer boundary R 2 ( θ ) of the cloak with respect to the angle θ in radians [c.f. Eqs. (4, 6)].

Fig. 2
Fig. 2

Real part of the longitudinal electric field E z radiated by a wire source antenna centered at point (2.5,2) in presence of the arbitrary cloak with boundaries defined by Eq. (9). The central computational domain is a disk centered at point (0,0) of radius 4. It is surrounded by an annulus of perfectly matched layers ( 4 ρ 5 ) .

Fig. 3
Fig. 3

Zoom on the central region of Fig. 2.

Fig. 4
Fig. 4

Green’s function in transformed coordinates and associated ray picture. Boundaries of the corresponding cloak are drawn for comparison with Figs. 2, 3.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

{ ρ ( ρ , θ ) = R 1 ( θ ) + ρ R 2 ( θ ) R 1 ( θ ) R 2 ( θ ) θ = θ , 0 < θ 2 π z = z , z R } ,
J ( ρ , θ ) = ( ρ ( ρ , θ ) , θ , z ) ( ρ , θ , z ) .
ϵ ͇ = ϵ T 1 , μ ͇ = μ T 1 ,
T 1 = ( c 12 2 + f ρ 2 c 11 f ρ ρ c 12 f ρ 0 c 12 f ρ c 11 ρ f ρ 0 0 0 c 11 f ρ ρ ) ,
c 12 ( ρ , θ ) = [ ρ R 2 ( θ ) ] R 2 ( θ ) d R 1 ( θ ) d θ [ ρ R 1 ( θ ) ] R 1 ( θ ) [ R 2 ( θ ) R 1 ( θ ) ] 2 d R 2 ( θ ) d θ ,
f ρ ( ρ , θ ) = [ ρ R 1 ( θ ) ] R 2 ( θ ) R 2 ( θ ) R 1 ( θ ) .
( μ T ͇ 1 E z ) + μ 0 ϵ 0 ω 2 ϵ z z E z = i ω I s μ 0 δ r s ,
ρ ( θ ) = a 0 + k = 1 n [ a k cos ( k θ ) + b k sin ( k θ ) ] ,
R 1 ( θ ) = 1 + 0.1 sin ( θ ) 0.15 cos ( 2 θ ) + 0.2 sin ( 3 θ ) + 0.1 cos ( 4 θ ) ,
R 2 ( θ ) = 2 0.1 cos ( 2 θ ) 0.15 cos ( 3 θ ) + 0.3 sin ( 3 θ ) + 0.2 cos ( 4 θ ) .

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