Abstract

We propose a novel kind of trapeziform cloak requiring only homogeneous anisotropic materials. Large-scale flat cloaks can be degenerated from the general trapeziform cloak with PEC inner boundary, and be realized by isotropic nonmagnetic materials for optical frequencies with controlled index profiles and improved invisibility. With the support of PEC inner boundary, large vehicles and objects of arbitrary shape can be concealed between the PEC and ground, and PEC can be firm by adding pillars in the cloaking space. Full-wave simulations validate the proposed cloaking concept, which is not only based on simple isotropic nonmagnetic materials but also realizable in practice.

© 2010 OSA

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References

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  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
    [CrossRef] [PubMed]
  2. W. X. Jiang, T. J. Cui, X. M. Yang, Q. Cheng, R. P. Liu, and D. R. Smith, “Invisibility cloak without singularity,” Appl. Phys. Lett. 93(19), 194102 (2008).
    [CrossRef]
  3. M. Schmiele, C. Rockstuhl, and F. Lederer, “Strategy for cloaking of twisted domains,” Phys. Rev. A 79(5), 053854 (2009), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-9-332 .
    [CrossRef]
  4. T. C. Han, X. H. Tang, and F. Xiao, “The petal-shape cloak,” J. Electromagn. Waves Appl. 23(14), 2055–2062 (2009).
    [CrossRef]
  5. Y. You, G. W. Kattawar, and P. Yang, “Invisibility cloaks for toroids,” Opt. Express 17(8), 6591–6599 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-8-6591 .
    [CrossRef] [PubMed]
  6. J. Hu, X. Zhou, and G. Hu, “Design method for electromagnetic cloak with arbitrary shapes based on Laplace’s equation,” Opt. Express 17(3), 1308–1320 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-15-13070 .
    [CrossRef] [PubMed]
  7. H. S. Chen, B. I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99(6), 063903 (2007).
    [CrossRef] [PubMed]
  8. C.-W. Qiu, A. Novitsky, H. Ma, and S. Qu, “Electromagnetic interaction of arbitrary radial-dependent anisotropic spheres and improved invisibility for nonlinear-transformation-based cloaks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(1), 016604 (2009).
    [CrossRef] [PubMed]
  9. A. Novitsky, C.-W. Qiu, and S. Zouhdi, “Transformation-based spherical cloaks designed by an implicit transformation-independent method: Theory and optimization,” N. J. Phys. 11(11), 113001 (2009).
    [CrossRef]
  10. M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
    [CrossRef] [PubMed]
  11. H. Y. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered systems using the transformation media concept,” Phys. Rev. B 78(5), 054204 (2008).
    [CrossRef]
  12. Y. Luo, J. Zhang, H. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “A rigorous analysis of plane-transformed invisibility cloaks,” IEEE Trans. Antenn. Propag. 57(12), 3926–3933 (2009).
    [CrossRef]
  13. J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
    [CrossRef] [PubMed]
  14. R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
    [CrossRef] [PubMed]
  15. C.-W. Qiu, L. Hu, X. Xu, and Y. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4), 047602 (2009).
    [CrossRef] [PubMed]
  16. C.-W. Qiu, L. Hu, B. Zhang, B. I. Wu, S. G. Johnson, and J. D. Joannopoulos, “Spherical cloaking using nonlinear transformations for improved segmentation into concentric isotropic coatings,” Opt. Express 17(16), 13467–13478 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-16-13467 .
    [CrossRef] [PubMed]

2009 (10)

M. Schmiele, C. Rockstuhl, and F. Lederer, “Strategy for cloaking of twisted domains,” Phys. Rev. A 79(5), 053854 (2009), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-9-332 .
[CrossRef]

T. C. Han, X. H. Tang, and F. Xiao, “The petal-shape cloak,” J. Electromagn. Waves Appl. 23(14), 2055–2062 (2009).
[CrossRef]

Y. You, G. W. Kattawar, and P. Yang, “Invisibility cloaks for toroids,” Opt. Express 17(8), 6591–6599 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-8-6591 .
[CrossRef] [PubMed]

J. Hu, X. Zhou, and G. Hu, “Design method for electromagnetic cloak with arbitrary shapes based on Laplace’s equation,” Opt. Express 17(3), 1308–1320 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-15-13070 .
[CrossRef] [PubMed]

C.-W. Qiu, A. Novitsky, H. Ma, and S. Qu, “Electromagnetic interaction of arbitrary radial-dependent anisotropic spheres and improved invisibility for nonlinear-transformation-based cloaks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(1), 016604 (2009).
[CrossRef] [PubMed]

A. Novitsky, C.-W. Qiu, and S. Zouhdi, “Transformation-based spherical cloaks designed by an implicit transformation-independent method: Theory and optimization,” N. J. Phys. 11(11), 113001 (2009).
[CrossRef]

Y. Luo, J. Zhang, H. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “A rigorous analysis of plane-transformed invisibility cloaks,” IEEE Trans. Antenn. Propag. 57(12), 3926–3933 (2009).
[CrossRef]

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

C.-W. Qiu, L. Hu, X. Xu, and Y. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4), 047602 (2009).
[CrossRef] [PubMed]

C.-W. Qiu, L. Hu, B. Zhang, B. I. Wu, S. G. Johnson, and J. D. Joannopoulos, “Spherical cloaking using nonlinear transformations for improved segmentation into concentric isotropic coatings,” Opt. Express 17(16), 13467–13478 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-16-13467 .
[CrossRef] [PubMed]

2008 (4)

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[CrossRef] [PubMed]

W. X. Jiang, T. J. Cui, X. M. Yang, Q. Cheng, R. P. Liu, and D. R. Smith, “Invisibility cloak without singularity,” Appl. Phys. Lett. 93(19), 194102 (2008).
[CrossRef]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
[CrossRef] [PubMed]

H. Y. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered systems using the transformation media concept,” Phys. Rev. B 78(5), 054204 (2008).
[CrossRef]

2007 (1)

H. S. Chen, B. I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99(6), 063903 (2007).
[CrossRef] [PubMed]

2006 (1)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Chan, C. T.

H. Y. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered systems using the transformation media concept,” Phys. Rev. B 78(5), 054204 (2008).
[CrossRef]

Chen, H.

Y. Luo, J. Zhang, H. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “A rigorous analysis of plane-transformed invisibility cloaks,” IEEE Trans. Antenn. Propag. 57(12), 3926–3933 (2009).
[CrossRef]

Chen, H. S.

H. S. Chen, B. I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99(6), 063903 (2007).
[CrossRef] [PubMed]

Chen, H. Y.

H. Y. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered systems using the transformation media concept,” Phys. Rev. B 78(5), 054204 (2008).
[CrossRef]

Cheng, Q.

W. X. Jiang, T. J. Cui, X. M. Yang, Q. Cheng, R. P. Liu, and D. R. Smith, “Invisibility cloak without singularity,” Appl. Phys. Lett. 93(19), 194102 (2008).
[CrossRef]

Chin, J. Y.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

Cui, T. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

W. X. Jiang, T. J. Cui, X. M. Yang, Q. Cheng, R. P. Liu, and D. R. Smith, “Invisibility cloak without singularity,” Appl. Phys. Lett. 93(19), 194102 (2008).
[CrossRef]

Cummer, S. A.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
[CrossRef] [PubMed]

Feng, Y.

C.-W. Qiu, L. Hu, X. Xu, and Y. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4), 047602 (2009).
[CrossRef] [PubMed]

Han, T. C.

T. C. Han, X. H. Tang, and F. Xiao, “The petal-shape cloak,” J. Electromagn. Waves Appl. 23(14), 2055–2062 (2009).
[CrossRef]

Hu, G.

Hu, J.

Hu, L.

Ji, C.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

Jiang, W. X.

W. X. Jiang, T. J. Cui, X. M. Yang, Q. Cheng, R. P. Liu, and D. R. Smith, “Invisibility cloak without singularity,” Appl. Phys. Lett. 93(19), 194102 (2008).
[CrossRef]

Joannopoulos, J. D.

Johnson, S. G.

Kattawar, G. W.

Kong, J. A.

Y. Luo, J. Zhang, H. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “A rigorous analysis of plane-transformed invisibility cloaks,” IEEE Trans. Antenn. Propag. 57(12), 3926–3933 (2009).
[CrossRef]

H. S. Chen, B. I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99(6), 063903 (2007).
[CrossRef] [PubMed]

Lederer, F.

M. Schmiele, C. Rockstuhl, and F. Lederer, “Strategy for cloaking of twisted domains,” Phys. Rev. A 79(5), 053854 (2009), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-9-332 .
[CrossRef]

Li, J.

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[CrossRef] [PubMed]

Liu, R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

Liu, R. P.

W. X. Jiang, T. J. Cui, X. M. Yang, Q. Cheng, R. P. Liu, and D. R. Smith, “Invisibility cloak without singularity,” Appl. Phys. Lett. 93(19), 194102 (2008).
[CrossRef]

Luo, Y.

Y. Luo, J. Zhang, H. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “A rigorous analysis of plane-transformed invisibility cloaks,” IEEE Trans. Antenn. Propag. 57(12), 3926–3933 (2009).
[CrossRef]

Ma, H.

C.-W. Qiu, A. Novitsky, H. Ma, and S. Qu, “Electromagnetic interaction of arbitrary radial-dependent anisotropic spheres and improved invisibility for nonlinear-transformation-based cloaks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(1), 016604 (2009).
[CrossRef] [PubMed]

Mock, J. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

Novitsky, A.

A. Novitsky, C.-W. Qiu, and S. Zouhdi, “Transformation-based spherical cloaks designed by an implicit transformation-independent method: Theory and optimization,” N. J. Phys. 11(11), 113001 (2009).
[CrossRef]

C.-W. Qiu, A. Novitsky, H. Ma, and S. Qu, “Electromagnetic interaction of arbitrary radial-dependent anisotropic spheres and improved invisibility for nonlinear-transformation-based cloaks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(1), 016604 (2009).
[CrossRef] [PubMed]

Pendry, J. B.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
[CrossRef] [PubMed]

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Qiu, C.-W.

A. Novitsky, C.-W. Qiu, and S. Zouhdi, “Transformation-based spherical cloaks designed by an implicit transformation-independent method: Theory and optimization,” N. J. Phys. 11(11), 113001 (2009).
[CrossRef]

C.-W. Qiu, A. Novitsky, H. Ma, and S. Qu, “Electromagnetic interaction of arbitrary radial-dependent anisotropic spheres and improved invisibility for nonlinear-transformation-based cloaks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(1), 016604 (2009).
[CrossRef] [PubMed]

C.-W. Qiu, L. Hu, X. Xu, and Y. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4), 047602 (2009).
[CrossRef] [PubMed]

C.-W. Qiu, L. Hu, B. Zhang, B. I. Wu, S. G. Johnson, and J. D. Joannopoulos, “Spherical cloaking using nonlinear transformations for improved segmentation into concentric isotropic coatings,” Opt. Express 17(16), 13467–13478 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-16-13467 .
[CrossRef] [PubMed]

Qu, S.

C.-W. Qiu, A. Novitsky, H. Ma, and S. Qu, “Electromagnetic interaction of arbitrary radial-dependent anisotropic spheres and improved invisibility for nonlinear-transformation-based cloaks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(1), 016604 (2009).
[CrossRef] [PubMed]

Rahm, M.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
[CrossRef] [PubMed]

Ran, L.

Y. Luo, J. Zhang, H. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “A rigorous analysis of plane-transformed invisibility cloaks,” IEEE Trans. Antenn. Propag. 57(12), 3926–3933 (2009).
[CrossRef]

Rockstuhl, C.

M. Schmiele, C. Rockstuhl, and F. Lederer, “Strategy for cloaking of twisted domains,” Phys. Rev. A 79(5), 053854 (2009), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-9-332 .
[CrossRef]

Schmiele, M.

M. Schmiele, C. Rockstuhl, and F. Lederer, “Strategy for cloaking of twisted domains,” Phys. Rev. A 79(5), 053854 (2009), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-9-332 .
[CrossRef]

Schurig, D.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Smith, D. R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

W. X. Jiang, T. J. Cui, X. M. Yang, Q. Cheng, R. P. Liu, and D. R. Smith, “Invisibility cloak without singularity,” Appl. Phys. Lett. 93(19), 194102 (2008).
[CrossRef]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Tang, X. H.

T. C. Han, X. H. Tang, and F. Xiao, “The petal-shape cloak,” J. Electromagn. Waves Appl. 23(14), 2055–2062 (2009).
[CrossRef]

Wu, B. I.

Wu, B.-I.

Y. Luo, J. Zhang, H. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “A rigorous analysis of plane-transformed invisibility cloaks,” IEEE Trans. Antenn. Propag. 57(12), 3926–3933 (2009).
[CrossRef]

Xiao, F.

T. C. Han, X. H. Tang, and F. Xiao, “The petal-shape cloak,” J. Electromagn. Waves Appl. 23(14), 2055–2062 (2009).
[CrossRef]

Xu, X.

C.-W. Qiu, L. Hu, X. Xu, and Y. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4), 047602 (2009).
[CrossRef] [PubMed]

Yang, P.

Yang, X. M.

W. X. Jiang, T. J. Cui, X. M. Yang, Q. Cheng, R. P. Liu, and D. R. Smith, “Invisibility cloak without singularity,” Appl. Phys. Lett. 93(19), 194102 (2008).
[CrossRef]

You, Y.

Zhang, B.

Zhang, J.

Y. Luo, J. Zhang, H. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “A rigorous analysis of plane-transformed invisibility cloaks,” IEEE Trans. Antenn. Propag. 57(12), 3926–3933 (2009).
[CrossRef]

Zhou, X.

Zouhdi, S.

A. Novitsky, C.-W. Qiu, and S. Zouhdi, “Transformation-based spherical cloaks designed by an implicit transformation-independent method: Theory and optimization,” N. J. Phys. 11(11), 113001 (2009).
[CrossRef]

Appl. Phys. Lett. (1)

W. X. Jiang, T. J. Cui, X. M. Yang, Q. Cheng, R. P. Liu, and D. R. Smith, “Invisibility cloak without singularity,” Appl. Phys. Lett. 93(19), 194102 (2008).
[CrossRef]

IEEE Trans. Antenn. Propag. (1)

Y. Luo, J. Zhang, H. Chen, L. Ran, B.-I. Wu, and J. A. Kong, “A rigorous analysis of plane-transformed invisibility cloaks,” IEEE Trans. Antenn. Propag. 57(12), 3926–3933 (2009).
[CrossRef]

J. Electromagn. Waves Appl. (1)

T. C. Han, X. H. Tang, and F. Xiao, “The petal-shape cloak,” J. Electromagn. Waves Appl. 23(14), 2055–2062 (2009).
[CrossRef]

N. J. Phys. (1)

A. Novitsky, C.-W. Qiu, and S. Zouhdi, “Transformation-based spherical cloaks designed by an implicit transformation-independent method: Theory and optimization,” N. J. Phys. 11(11), 113001 (2009).
[CrossRef]

Opt. Express (3)

Phys. Rev. A (1)

M. Schmiele, C. Rockstuhl, and F. Lederer, “Strategy for cloaking of twisted domains,” Phys. Rev. A 79(5), 053854 (2009), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-9-332 .
[CrossRef]

Phys. Rev. B (1)

H. Y. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered systems using the transformation media concept,” Phys. Rev. B 78(5), 054204 (2008).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

C.-W. Qiu, L. Hu, X. Xu, and Y. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4), 047602 (2009).
[CrossRef] [PubMed]

C.-W. Qiu, A. Novitsky, H. Ma, and S. Qu, “Electromagnetic interaction of arbitrary radial-dependent anisotropic spheres and improved invisibility for nonlinear-transformation-based cloaks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(1), 016604 (2009).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

H. S. Chen, B. I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99(6), 063903 (2007).
[CrossRef] [PubMed]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
[CrossRef] [PubMed]

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[CrossRef] [PubMed]

Science (2)

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

The scheme of coordinate transformation from the virtual space (a) to physical space (b). k 1 represents the slope of the inner PEC boundary in Region I (identical to that in Region II).

Fig. 2
Fig. 2

Snapshot of the electric field for a Gaussian beam incident from the right at an oblique direction of 45 . (a) A perfectly reflective flat boundary. (b) A trapeziform cloak with inner PEC boundaries as in Fig. 1(b). (c) The triangular cloak degenerated from a trapeziform cloak when Region III vanishes. (d) The degenerate flat cloak when b = h .

Fig. 3
Fig. 3

Electric field distributions of the flat cloak with M-layered isotropic materials based on two sets of effective medium theories. (a-c) correspond to the old set [Eq. (8)] while (d-f) correspond to the new set [Eq. (9)]. (a, d) M = 20. (b, e) M = 40. (c, f) M = 60. The dashed semi-circle is the observation radius for measuring the average power flow for the reflective beam.

Fig. 4
Fig. 4

Comparison of the average power flow of the isotropic flat cloak in Fig. 3(c) and Fig. 3(f), mimicked by old [Eq. (8)] and new [Eq. (9)] effective medium theories. (a) M = 40, (b) M = 60. The same incidence is used as Fig. 2.

Fig. 5
Fig. 5

The relative index profiles of the isotropic flat cloak in Fig. 2(d) mimicked by old [Eq. (8)] and new [Eq. (9)] effective medium theories with M = 5.

Fig. 6
Fig. 6

(Color online) Magnetic field distributions for a Gaussian beam incident from the right at 45 on (a) a perfectly reflective flat boundary, (b) a bumped reflective boundary, (c) a nonmagnetic flat cloak placed above the bumped boundary, (d) an isotropic nonmagnetic flat cloak placed above the bumped boundary with M = 40.

Equations (9)

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

ε = μ = A A T / det ( A )  
x = x ' ,    y = k 1 ( x + d ) + k r y + h ,    z = z '
ε I = μ I = 1 k r [ 1         k 1     0 k 1 k 1 2 + k r 2           0 0         0       1 ]
x = x ,    y = k 1 ( d x ) + k r y + h ,    z = z '
ε II = μ II = 1 k r [ 1         k 1       0 k 1 k 1 2 + k r 2 0 0           0       1 ]
x = x ' ,    y = k r y + h ,    z = z '
ε III = μ III = diag [ b + h b , b b + h ,     b + h b ]
ε A = μ A = ε x + ε x 2 ε x ε y ;    ε B = μ B = ε x ε x 2 ε x ε y
ε A = μ B = ε x + ε x 2 ε x ε y ;    ε B = μ A = ε x ε x 2 ε x ε y

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