Abstract

In this Letter, we propose an engineered design of optical cloaks based on the scattering cancellation technique and intended to reduce the observability of cylindrical objects. The cover, consisting of a periodic arrangement of core–shell nanospheres, is designed in such a way to exhibit near-zero values of the real part of the homogenized effective permittivity at optical frequencies. Full-wave numerical simulations, considering the measured data of the dielectric function of the plasmonic material composing the shell, show that the cloak is able to reduce by about 6dB the scattering cross section of a finite-length cylinder at around 740THz with a 3dB fractional bandwidth of about 7%. We show also that this result is not significantly affected by the perturbation of the periodic alignment of the core–shell nanospheres, due to possible fabrication issues or to an amorphous arrangement.

© 2011 Optical Society of America

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  1. J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  5. A. Alù and N. Engheta, Phys. Rev. E 72, 016623 (2005).
    [CrossRef]
  6. M. G. Silveirinha, A. Alù, and N. Engheta, Phys. Rev. E 75, 036603 (2007).
    [CrossRef]
  7. F. Bilotti, S. Tricarico, and L. Vegni, New J. Phys. 10, 115035(2008).
    [CrossRef]
  8. F. Bilotti, S. Tricarico, and L. Vegni, IEEE Trans. Nanotechnol. 9, 55 (2010).
    [CrossRef]
  9. S. Tricarico, F. Bilotti, A. Alù, and L. Vegni, Phys. Rev. E 81, 026602 (2010).
    [CrossRef]
  10. S. Tricarico, F. Bilotti, and L. Vegni, Phys. Rev. B 82, 045109 (2010).
    [CrossRef]
  11. F. Bilotti, S. Tricarico, F. Pierini, and L. Vegni, Opt. Lett. 36, 211 (2011).
    [CrossRef] [PubMed]
  12. S. Mühlig, M. Farhat, C. Rockstuhl, and F. Lederer, Phys. Rev. B 83, 195116 (2011).
    [CrossRef]
  13. A. Sihvola, Subsurf. Sens. Technol. Appl. 1, 393 (2000).
    [CrossRef]
  14. A. Sihvola, Prog. Electromagn. Res. 66, 191 (2006).
    [CrossRef]
  15. P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370(1972).
    [CrossRef]
  16. T. G. Mackay, J. Nanophoton. 2, 029503 (2008).
    [CrossRef]
  17. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, Science 302, 419 (2003).
    [CrossRef] [PubMed]
  18. Computer Simulation Technology, CST Studio Suite 2011, http://www.cst.com.

2011 (2)

F. Bilotti, S. Tricarico, F. Pierini, and L. Vegni, Opt. Lett. 36, 211 (2011).
[CrossRef] [PubMed]

S. Mühlig, M. Farhat, C. Rockstuhl, and F. Lederer, Phys. Rev. B 83, 195116 (2011).
[CrossRef]

2010 (3)

F. Bilotti, S. Tricarico, and L. Vegni, IEEE Trans. Nanotechnol. 9, 55 (2010).
[CrossRef]

S. Tricarico, F. Bilotti, A. Alù, and L. Vegni, Phys. Rev. E 81, 026602 (2010).
[CrossRef]

S. Tricarico, F. Bilotti, and L. Vegni, Phys. Rev. B 82, 045109 (2010).
[CrossRef]

2008 (2)

F. Bilotti, S. Tricarico, and L. Vegni, New J. Phys. 10, 115035(2008).
[CrossRef]

T. G. Mackay, J. Nanophoton. 2, 029503 (2008).
[CrossRef]

2007 (2)

M. G. Silveirinha, A. Alù, and N. Engheta, Phys. Rev. E 75, 036603 (2007).
[CrossRef]

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

2006 (4)

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

U. Leonhardt, Science 312, 1777 (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]

A. Sihvola, Prog. Electromagn. Res. 66, 191 (2006).
[CrossRef]

2005 (1)

A. Alù and N. Engheta, Phys. Rev. E 72, 016623 (2005).
[CrossRef]

2003 (1)

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, Science 302, 419 (2003).
[CrossRef] [PubMed]

2000 (1)

A. Sihvola, Subsurf. Sens. Technol. Appl. 1, 393 (2000).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370(1972).
[CrossRef]

Alù, A.

S. Tricarico, F. Bilotti, A. Alù, and L. Vegni, Phys. Rev. E 81, 026602 (2010).
[CrossRef]

M. G. Silveirinha, A. Alù, and N. Engheta, Phys. Rev. E 75, 036603 (2007).
[CrossRef]

A. Alù and N. Engheta, Phys. Rev. E 72, 016623 (2005).
[CrossRef]

Bilotti, F.

F. Bilotti, S. Tricarico, F. Pierini, and L. Vegni, Opt. Lett. 36, 211 (2011).
[CrossRef] [PubMed]

F. Bilotti, S. Tricarico, and L. Vegni, IEEE Trans. Nanotechnol. 9, 55 (2010).
[CrossRef]

S. Tricarico, F. Bilotti, A. Alù, and L. Vegni, Phys. Rev. E 81, 026602 (2010).
[CrossRef]

S. Tricarico, F. Bilotti, and L. Vegni, Phys. Rev. B 82, 045109 (2010).
[CrossRef]

F. Bilotti, S. Tricarico, and L. Vegni, New J. Phys. 10, 115035(2008).
[CrossRef]

Cai, W.

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

Chettiar, U. K.

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

Christy, R. W.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370(1972).
[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, Science 314, 977(2006).
[CrossRef] [PubMed]

Engheta, N.

M. G. Silveirinha, A. Alù, and N. Engheta, Phys. Rev. E 75, 036603 (2007).
[CrossRef]

A. Alù and N. Engheta, Phys. Rev. E 72, 016623 (2005).
[CrossRef]

Farhat, M.

S. Mühlig, M. Farhat, C. Rockstuhl, and F. Lederer, Phys. Rev. B 83, 195116 (2011).
[CrossRef]

Halas, N. J.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, Science 302, 419 (2003).
[CrossRef] [PubMed]

Johnson, P. B.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370(1972).
[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]

Kildishev, A. V.

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

Lederer, F.

S. Mühlig, M. Farhat, C. Rockstuhl, and F. Lederer, Phys. Rev. B 83, 195116 (2011).
[CrossRef]

Leonhardt, U.

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

Mackay, T. G.

T. G. Mackay, J. Nanophoton. 2, 029503 (2008).
[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]

Mühlig, S.

S. Mühlig, M. Farhat, C. Rockstuhl, and F. Lederer, Phys. Rev. B 83, 195116 (2011).
[CrossRef]

Nordlander, P.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, Science 302, 419 (2003).
[CrossRef] [PubMed]

Pendry, J. B.

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]

Pierini, F.

Prodan, E.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, Science 302, 419 (2003).
[CrossRef] [PubMed]

Radloff, C.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, Science 302, 419 (2003).
[CrossRef] [PubMed]

Rockstuhl, C.

S. Mühlig, M. Farhat, C. Rockstuhl, and F. Lederer, Phys. Rev. B 83, 195116 (2011).
[CrossRef]

Schurig, D.

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]

Shalaev, V. M.

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

Sihvola, A.

A. Sihvola, Prog. Electromagn. Res. 66, 191 (2006).
[CrossRef]

A. Sihvola, Subsurf. Sens. Technol. Appl. 1, 393 (2000).
[CrossRef]

Silveirinha, M. G.

M. G. Silveirinha, A. Alù, and N. Engheta, Phys. Rev. E 75, 036603 (2007).
[CrossRef]

Smith, D. R.

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]

Tricarico, S.

F. Bilotti, S. Tricarico, F. Pierini, and L. Vegni, Opt. Lett. 36, 211 (2011).
[CrossRef] [PubMed]

S. Tricarico, F. Bilotti, A. Alù, and L. Vegni, Phys. Rev. E 81, 026602 (2010).
[CrossRef]

F. Bilotti, S. Tricarico, and L. Vegni, IEEE Trans. Nanotechnol. 9, 55 (2010).
[CrossRef]

S. Tricarico, F. Bilotti, and L. Vegni, Phys. Rev. B 82, 045109 (2010).
[CrossRef]

F. Bilotti, S. Tricarico, and L. Vegni, New J. Phys. 10, 115035(2008).
[CrossRef]

Vegni, L.

F. Bilotti, S. Tricarico, F. Pierini, and L. Vegni, Opt. Lett. 36, 211 (2011).
[CrossRef] [PubMed]

F. Bilotti, S. Tricarico, and L. Vegni, IEEE Trans. Nanotechnol. 9, 55 (2010).
[CrossRef]

S. Tricarico, F. Bilotti, A. Alù, and L. Vegni, Phys. Rev. E 81, 026602 (2010).
[CrossRef]

S. Tricarico, F. Bilotti, and L. Vegni, Phys. Rev. B 82, 045109 (2010).
[CrossRef]

F. Bilotti, S. Tricarico, and L. Vegni, New J. Phys. 10, 115035(2008).
[CrossRef]

IEEE Trans. Nanotechnol. (1)

F. Bilotti, S. Tricarico, and L. Vegni, IEEE Trans. Nanotechnol. 9, 55 (2010).
[CrossRef]

J. Nanophoton. (1)

T. G. Mackay, J. Nanophoton. 2, 029503 (2008).
[CrossRef]

Nat. Photon. (1)

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

New J. Phys. (1)

F. Bilotti, S. Tricarico, and L. Vegni, New J. Phys. 10, 115035(2008).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (3)

S. Mühlig, M. Farhat, C. Rockstuhl, and F. Lederer, Phys. Rev. B 83, 195116 (2011).
[CrossRef]

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370(1972).
[CrossRef]

S. Tricarico, F. Bilotti, and L. Vegni, Phys. Rev. B 82, 045109 (2010).
[CrossRef]

Phys. Rev. E (3)

S. Tricarico, F. Bilotti, A. Alù, and L. Vegni, Phys. Rev. E 81, 026602 (2010).
[CrossRef]

A. Alù and N. Engheta, Phys. Rev. E 72, 016623 (2005).
[CrossRef]

M. G. Silveirinha, A. Alù, and N. Engheta, Phys. Rev. E 75, 036603 (2007).
[CrossRef]

Prog. Electromagn. Res. (1)

A. Sihvola, Prog. Electromagn. Res. 66, 191 (2006).
[CrossRef]

Science (4)

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, Science 302, 419 (2003).
[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]

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]

Subsurf. Sens. Technol. Appl. (1)

A. Sihvola, Subsurf. Sens. Technol. Appl. 1, 393 (2000).
[CrossRef]

Other (1)

Computer Simulation Technology, CST Studio Suite 2011, http://www.cst.com.

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Figures (6)

Fig. 1
Fig. 1

(a) Finite-length dielectric cylinder covered by a homogenous cloak and (b) cloak made by core–shell nanospheres. ε d = 2 , a = 50 nm , L = 484 nm .

Fig. 2
Fig. 2

Real part (solid line) and imaginary part (dashed line) of the effective permittivity of the core–shell nanosphere arrangement with f = 0.28 .

Fig. 3
Fig. 3

Total SCS for the bare dielectric cylinder (solid line), for the cylinder covered by a cloak consisting of 117 core–shell nanospheres (dashed line), and for the cylinder with a homogenous cover (dotted–dashed line).

Fig. 4
Fig. 4

3D SCS patterns of the (a) bare and the (b) covered cylinder at the cloak frequency of 740 THz . Please note that, at this frequency, the maximum value of the SCS is reduced by 3.4 dB , while the total SCS is reduced by about 6 dB (see Fig. 3).

Fig. 5
Fig. 5

Plots of the electric field amplitudes and phases at the cloak frequency ( 740 THz ) on the y = 0 plane for the (a) bare and (b) covered cylinder.

Fig. 6
Fig. 6

Total SCS of the covered cylinder for different values of Δ.

Equations (2)

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

ε e = ε m + n α 1 n α / ( 3 ε m ) ,
α = 3 ε m V ( ε 1 ε m ) ( ε 2 + 2 ε 1 ) + β ( 2 ε 1 + ε m ) ( ε 2 ε 1 ) ( ε 1 + 2 ε m ) ( ε 2 + 2 ε 1 ) + 2 β ( ε 1 ε m ) ( ε 2 ε 1 ) ,

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