Abstract

We propose multilayer cylindrical invisibility cloaks that are optimized for oblique incidences through a combination of analytic formalism of scattering and genetic optimization. We show that by using only four layers of homogeneous and anisotropic metamaterials without large values of constitutive parameters, the scattering for oblique incidences can be reduced by 2 orders. Although the optimization is done at a single incident angle, the cloak provides reduced scattering over a large range of incident angles.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2009

B. Zhang and B.-I. Wu, Phys. Rev. Lett. 103, 243901 (2009).
[CrossRef]

S. Xi, H. Chen, B. Zhang, B.-I. Wu, and J. A. Kong, Phys. Rev. B 79, 155122 (2009).
[CrossRef]

B.-I. Popa and S. A. Cummer, Phys. Rev. A 79, 023806 (2009).
[CrossRef]

2008

2007

M. Yan, Z. Ruan, and M. Qiu, Phys. Rev. Lett. 99, 233901 (2007).
[CrossRef]

H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef] [PubMed]

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, Phys. Rev. B 76, 121101(R) (2007).

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

Y. Huang, Y. Feng, and T. Jiang, Opt. Express 15, 11133 (2007).
[CrossRef] [PubMed]

2006

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]

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, Phys. Rev. E 74, 036621 (2006).
[CrossRef]

Cai, W.

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

Chen, H.

S. Xi, H. Chen, B. Zhang, B.-I. Wu, and J. A. Kong, Phys. Rev. B 79, 155122 (2009).
[CrossRef]

B. Zhang, H. Chen, and B.-I. Wu, Opt. Express 16, 14655 (2008).
[CrossRef] [PubMed]

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, Phys. Rev. B 76, 121101(R) (2007).

H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

Chettiar, U. K.

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

Chew, W. C.

W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE, 1995).

Cummer, S. A.

B.-I. Popa and S. A. Cummer, Phys. Rev. A 79, 023806 (2009).
[CrossRef]

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, Phys. Rev. E 74, 036621 (2006).
[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]

Feng, Y.

Huang, Y.

Jiang, T.

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. Photonics 1, 224 (2007).
[CrossRef]

Kong, J. A.

S. Xi, H. Chen, B. Zhang, B.-I. Wu, and J. A. Kong, Phys. Rev. B 79, 155122 (2009).
[CrossRef]

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, Phys. Rev. B 76, 121101(R) (2007).

H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

Leonhardt, U.

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

Luo, Y.

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, Phys. Rev. B 76, 121101(R) (2007).

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]

Neff, C. W.

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, Phys. Rev. Lett. 99, 113903 (2007).
[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]

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, Phys. Rev. E 74, 036621 (2006).
[CrossRef]

Popa, B. I.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, Phys. Rev. E 74, 036621 (2006).
[CrossRef]

Popa, B.-I.

B.-I. Popa and S. A. Cummer, Phys. Rev. A 79, 023806 (2009).
[CrossRef]

Qiu, M.

M. Yan, Z. Ruan, and M. Qiu, Phys. Rev. Lett. 99, 233901 (2007).
[CrossRef]

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef] [PubMed]

Ran, L.

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, Phys. Rev. B 76, 121101(R) (2007).

Ruan, Z.

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef] [PubMed]

M. Yan, Z. Ruan, and M. Qiu, Phys. Rev. Lett. 99, 233901 (2007).
[CrossRef]

Schurig, D.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, Phys. Rev. E 74, 036621 (2006).
[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]

Shalaev, V. M.

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

Smith, D. R.

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

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, Phys. Rev. E 74, 036621 (2006).
[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]

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]

Wu, B. I.

H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

Wu, B.-I.

S. Xi, H. Chen, B. Zhang, B.-I. Wu, and J. A. Kong, Phys. Rev. B 79, 155122 (2009).
[CrossRef]

B. Zhang and B.-I. Wu, Phys. Rev. Lett. 103, 243901 (2009).
[CrossRef]

B. Zhang, H. Chen, and B.-I. Wu, Opt. Express 16, 14655 (2008).
[CrossRef] [PubMed]

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, Phys. Rev. B 76, 121101(R) (2007).

Xi, S.

S. Xi, H. Chen, B. Zhang, B.-I. Wu, and J. A. Kong, Phys. Rev. B 79, 155122 (2009).
[CrossRef]

Yan, M.

M. Yan, Z. Ruan, and M. Qiu, Phys. Rev. Lett. 99, 233901 (2007).
[CrossRef]

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef] [PubMed]

Zhang, B.

B. Zhang and B.-I. Wu, Phys. Rev. Lett. 103, 243901 (2009).
[CrossRef]

S. Xi, H. Chen, B. Zhang, B.-I. Wu, and J. A. Kong, Phys. Rev. B 79, 155122 (2009).
[CrossRef]

B. Zhang, H. Chen, and B.-I. Wu, Opt. Express 16, 14655 (2008).
[CrossRef] [PubMed]

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, Phys. Rev. B 76, 121101(R) (2007).

H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

Nat. Photonics

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

Opt. Express

Phys. Rev. A

B.-I. Popa and S. A. Cummer, Phys. Rev. A 79, 023806 (2009).
[CrossRef]

Phys. Rev. B

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, Phys. Rev. B 76, 121101(R) (2007).

S. Xi, H. Chen, B. Zhang, B.-I. Wu, and J. A. Kong, Phys. Rev. B 79, 155122 (2009).
[CrossRef]

Phys. Rev. E

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, Phys. Rev. E 74, 036621 (2006).
[CrossRef]

Phys. Rev. Lett.

H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef] [PubMed]

B. Zhang and B.-I. Wu, Phys. Rev. Lett. 103, 243901 (2009).
[CrossRef]

M. Yan, Z. Ruan, and M. Qiu, Phys. Rev. Lett. 99, 233901 (2007).
[CrossRef]

Science

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]

Other

W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE, 1995).

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Figures (3)

Fig. 1
Fig. 1

Configuration of a four-layer cloak when a vertically polarized plane wave is obliquely incident with the incident angle of α.

Fig. 2
Fig. 2

E z field distribution in x y plane due to scattering from a (a) bare PEC cylinder, (b) four-layer cloak with three parameters ( ϵ z , μ ρ , and μ ϕ ) optimized, and (c) four-layer cloak with all six parameters optimized, when a vertically polarized plane wave is obliquely incident from left to right with the incident angle of 30 ° . From (a) to (c), the scattering efficiency Q sca is 1.175, 0.498, and 0.013, respectively.

Fig. 3
Fig. 3

Dependence of scattering efficiency Q sca on the incident angle for the four-layer cloak achieved by optimizing all six parameters in each layer within the cloak. The dotted curves correspond to the scattering efficiencies from the cloak with loss tangents 0.05 and 0.1 and from the bare PEC core without the cloak, respectively.

Tables (1)

Tables Icon

Table 1 Relative Constitutive Parameters for Optimized Four-Layer Cloak by (I) Optimizing Three Parameters in Each Layer and (II) Optimizing Six Parameters in Each Layer

Equations (1)

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V ¯ ( R M + 1 ) = [ j = ( M 1 ) N + 1 M N ( I ¯ ¯ + Δ ρ T ¯ ¯ ( ρ j ) ) ] · [ j = ( M 2 ) N + 1 ( M 1 ) N ( I ¯ ¯ + Δ ρ T ¯ ¯ ( ρ j ) ) ] · [ j = 1 N ( I ¯ ¯ + Δ ρ T ¯ ¯ ( ρ j ) ) ] · V ¯ ( R 1 ) ,

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