Nonmagnetic electromagnetic transparent wall realized by a metal-dielectric multilayer structure

Zhong Lei Mei; Yan Li Xu; Jing Bai; Tie Jun Cui

doi:10.1364/OE.20.016955

Nonmagnetic electromagnetic transparent wall realized by a metal-dielectric multilayer structure

Zhong Lei Mei, Yan Li Xu, Jing Bai, and Tie Jun Cui

Optics Express
Vol. 20,
Issue 15,
pp. 16955-16967
(2012)
•https://doi.org/10.1364/OE.20.016955

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Zhong Lei Mei, Yan Li Xu, Jing Bai, and Tie Jun Cui, "Nonmagnetic electromagnetic transparent wall realized by a metal-dielectric multilayer structure," Opt. Express 20, 16955-16967 (2012)

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Related Topics
Table of Contents Category
- Metamaterials
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Metamaterials (160.3918)
- Multilayers (230.4170)
- Electromagnetic optics (260.2110)

About this Article
History
- Original Manuscript: May 1, 2012
- Revised Manuscript: July 6, 2012
- Manuscript Accepted: July 6, 2012
- Published: July 11, 2012

Accessible

Open Access

Abstract

We present a nonmagnetic electromagnetic transparent wall (EMTW) using the principle of total transmission and phase compensation. The device consists of two or more nonmagnetic stacked anisotropic slabs. With proper design of the constitutive tensors and relative thicknesses of each slab, EMTW is achieved which is independent of the incident angle of striking EM waves. The realization of the anisotropic slabs and furthermore EMTW in the optical range is mimicked using a metal-dielectric nano-structured system with alternating Na₃AlF₆-Ag layers. Compared to the magnetic version, the new design makes a major step forward and provides a practical path to experimental demonstration of EMTW. The proposed structure has potential applications in the antireflection coatings, microwave absorbing materials, and high-performance radomes.

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References

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|
Author
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Publication

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref] [PubMed]
G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
[Crossref] [PubMed]
V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[Crossref]
J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[Crossref] [PubMed]
J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[Crossref]
B. J. Arritt, D. R. Smith, and T. Khraishi, “Equivalent circuit analysis of metamaterial strain-dependent effective medium parameters,” J. Appl. Phys. 109(7), 073512 (2011).
[Crossref]
V. D. Lam, J. B. Kim, S. J. Lee, and Y. P. Lee, “Left-handed behavior of combined and fishnet structures,” J. Appl. Phys. 103(3), 033107 (2008).
[Crossref]
A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[Crossref] [PubMed]
B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
[Crossref]
Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).
[Crossref] [PubMed]
Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]
X. F. Xu, Y. J. Feng, Y. Hao, J. M. Zhao, and T. Jiang, “Infrared carpet cloak designed with uniform silicon grating structure,” Appl. Phys. Lett. 95(18), 184102 (2009).
[Crossref]
H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express 15(24), 15886–15891 (2007).
[Crossref] [PubMed]
H. Y. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[Crossref]
S. Xi, H. S. Chen, B. Wu, and J. A. Kong, “One-directional perfect cloak created with homogeneous material,” IEEE Microw. Wireless Compon. Lett. 19(3), 131–133 (2009).
[Crossref]
D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[Crossref] [PubMed]
Y. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev. 40(5), 2494–2507 (2011).
[Crossref] [PubMed]
C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5, 523–530 (2011).
Z. L. Mei, T. M. Niu, J. Bai, and T. J. Cui, “Design of a one-dimensional electromagnetic transparent wall,” J. Opt. Soc. Am. A 27(10), 2237–2243 (2010).
[Crossref] [PubMed]
Y. Zhang, B. Fluegel, and A. Mascarenhas, “Total negative refraction in real crystals for ballistic electrons and light,” Phys. Rev. Lett. 91(15), 157404 (2003).
[Crossref] [PubMed]
Z. Liu, Z. Lin, and S. T. Chui, “Negative refraction and omnidirectional total transmission at a planar interface associated with a uniaxial medium,” Phys. Rev. B 69(11), 115402 (2004).
[Crossref]
Y. Huang, Y. Feng, and T. Jiang, “Electromagnetic cloaking by layered structure of homogeneous isotropic materials,” Opt. Express 15(18), 11133–11141 (2007).
[Crossref] [PubMed]
H. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered systems using the transformation media concept,” Phys. Rev. B 78(5), 054204 (2008).
[Crossref]
M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).
P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]
J. Y. Chin, M. Lu, and T. J. Cui, “Metamaterial polarizers by electric-field-coupled resonators,” Appl. Phys. Lett. 93(25), 251903 (2008).
[Crossref]

2011 (3)

B. J. Arritt, D. R. Smith, and T. Khraishi, “Equivalent circuit analysis of metamaterial strain-dependent effective medium parameters,” J. Appl. Phys. 109(7), 073512 (2011).
[Crossref]

Y. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev. 40(5), 2494–2507 (2011).
[Crossref] [PubMed]

C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5, 523–530 (2011).

2010 (1)

Z. L. Mei, T. M. Niu, J. Bai, and T. J. Cui, “Design of a one-dimensional electromagnetic transparent wall,” J. Opt. Soc. Am. A 27(10), 2237–2243 (2010).
[Crossref] [PubMed]

2009 (2)

X. F. Xu, Y. J. Feng, Y. Hao, J. M. Zhao, and T. Jiang, “Infrared carpet cloak designed with uniform silicon grating structure,” Appl. Phys. Lett. 95(18), 184102 (2009).
[Crossref]

S. Xi, H. S. Chen, B. Wu, and J. A. Kong, “One-directional perfect cloak created with homogeneous material,” IEEE Microw. Wireless Compon. Lett. 19(3), 131–133 (2009).
[Crossref]

2008 (4)

V. D. Lam, J. B. Kim, S. J. Lee, and Y. P. Lee, “Left-handed behavior of combined and fishnet structures,” J. Appl. Phys. 103(3), 033107 (2008).
[Crossref]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[Crossref] [PubMed]

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

J. Y. Chin, M. Lu, and T. J. Cui, “Metamaterial polarizers by electric-field-coupled resonators,” Appl. Phys. Lett. 93(25), 251903 (2008).
[Crossref]

2007 (6)

Y. Huang, Y. Feng, and T. Jiang, “Electromagnetic cloaking by layered structure of homogeneous isotropic materials,” Opt. Express 15(18), 11133–11141 (2007).
[Crossref] [PubMed]

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express 15(24), 15886–15891 (2007).
[Crossref] [PubMed]

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[Crossref] [PubMed]

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[Crossref]

H. Y. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[Crossref]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

2006 (3)

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
[Crossref]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
[Crossref] [PubMed]

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).
[Crossref] [PubMed]

2004 (2)

Z. Liu, Z. Lin, and S. T. Chui, “Negative refraction and omnidirectional total transmission at a planar interface associated with a uniaxial medium,” Phys. Rev. B 69(11), 115402 (2004).
[Crossref]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[Crossref] [PubMed]

2003 (1)

Y. Zhang, B. Fluegel, and A. Mascarenhas, “Total negative refraction in real crystals for ballistic electrons and light,” Phys. Rev. Lett. 91(15), 157404 (2003).
[Crossref] [PubMed]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref] [PubMed]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Alekseyev, L.

Alekseyev, L. V.

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).
[Crossref] [PubMed]

Arritt, B. J.

B. J. Arritt, D. R. Smith, and T. Khraishi, “Equivalent circuit analysis of metamaterial strain-dependent effective medium parameters,” J. Appl. Phys. 109(7), 073512 (2011).
[Crossref]

Bai, J.

Z. L. Mei, T. M. Niu, J. Bai, and T. J. Cui, “Design of a one-dimensional electromagnetic transparent wall,” J. Opt. Soc. Am. A 27(10), 2237–2243 (2010).
[Crossref] [PubMed]

Bartal, G.

Chan, C. T.

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

H. Y. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[Crossref]

Chen, H.

H. 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. S.

S. Xi, H. S. Chen, B. Wu, and J. A. Kong, “One-directional perfect cloak created with homogeneous material,” IEEE Microw. Wireless Compon. Lett. 19(3), 131–133 (2009).
[Crossref]

Chen, H. Y.

H. Y. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[Crossref]

Chin, J. Y.

J. Y. Chin, M. Lu, and T. J. Cui, “Metamaterial polarizers by electric-field-coupled resonators,” Appl. Phys. Lett. 93(25), 251903 (2008).
[Crossref]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Chui, S. T.

Cui, T. J.

Z. L. Mei, T. M. Niu, J. Bai, and T. J. Cui, “Design of a one-dimensional electromagnetic transparent wall,” J. Opt. Soc. Am. A 27(10), 2237–2243 (2010).
[Crossref] [PubMed]

J. Y. Chin, M. Lu, and T. J. Cui, “Metamaterial polarizers by electric-field-coupled resonators,” Appl. Phys. Lett. 93(25), 251903 (2008).
[Crossref]

Dolling, G.

Enkrich, C.

Feng, Y.

Y. Huang, Y. Feng, and T. Jiang, “Electromagnetic cloaking by layered structure of homogeneous isotropic materials,” Opt. Express 15(18), 11133–11141 (2007).
[Crossref] [PubMed]

Feng, Y. J.

X. F. Xu, Y. J. Feng, Y. Hao, J. M. Zhao, and T. Jiang, “Infrared carpet cloak designed with uniform silicon grating structure,” Appl. Phys. Lett. 95(18), 184102 (2009).
[Crossref]

Fluegel, B.

Y. Zhang, B. Fluegel, and A. Mascarenhas, “Total negative refraction in real crystals for ballistic electrons and light,” Phys. Rev. Lett. 91(15), 157404 (2003).
[Crossref] [PubMed]

Franz, K. J.

Genov, D. A.

Gmachl, C.

Hao, Y.

X. F. Xu, Y. J. Feng, Y. Hao, J. M. Zhao, and T. Jiang, “Infrared carpet cloak designed with uniform silicon grating structure,” Appl. Phys. Lett. 95(18), 184102 (2009).
[Crossref]

Hoffman, A. J.

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[Crossref]

Howard, S. S.

Huang, Y.

Y. Huang, Y. Feng, and T. Jiang, “Electromagnetic cloaking by layered structure of homogeneous isotropic materials,” Opt. Express 15(18), 11133–11141 (2007).
[Crossref] [PubMed]

Jacob, Z.

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).
[Crossref] [PubMed]

Jiang, T.

X. F. Xu, Y. J. Feng, Y. Hao, J. M. Zhao, and T. Jiang, “Infrared carpet cloak designed with uniform silicon grating structure,” Appl. Phys. Lett. 95(18), 184102 (2009).
[Crossref]

Y. Huang, Y. Feng, and T. Jiang, “Electromagnetic cloaking by layered structure of homogeneous isotropic materials,” Opt. Express 15(18), 11133–11141 (2007).
[Crossref] [PubMed]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Khraishi, T.

B. J. Arritt, D. R. Smith, and T. Khraishi, “Equivalent circuit analysis of metamaterial strain-dependent effective medium parameters,” J. Appl. Phys. 109(7), 073512 (2011).
[Crossref]

Kim, J. B.

V. D. Lam, J. B. Kim, S. J. Lee, and Y. P. Lee, “Left-handed behavior of combined and fishnet structures,” J. Appl. Phys. 103(3), 033107 (2008).
[Crossref]

Kong, J. A.

S. Xi, H. S. Chen, B. Wu, and J. A. Kong, “One-directional perfect cloak created with homogeneous material,” IEEE Microw. Wireless Compon. Lett. 19(3), 131–133 (2009).
[Crossref]

Lam, V. D.

V. D. Lam, J. B. Kim, S. J. Lee, and Y. P. Lee, “Left-handed behavior of combined and fishnet structures,” J. Appl. Phys. 103(3), 033107 (2008).
[Crossref]

Lee, H.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express 15(24), 15886–15891 (2007).
[Crossref] [PubMed]

Lee, S. J.

V. D. Lam, J. B. Kim, S. J. Lee, and Y. P. Lee, “Left-handed behavior of combined and fishnet structures,” J. Appl. Phys. 103(3), 033107 (2008).
[Crossref]

Lee, Y. P.

V. D. Lam, J. B. Kim, S. J. Lee, and Y. P. Lee, “Left-handed behavior of combined and fishnet structures,” J. Appl. Phys. 103(3), 033107 (2008).
[Crossref]

Lin, Z.

Linden, S.

Liu, Y.

Y. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev. 40(5), 2494–2507 (2011).
[Crossref] [PubMed]

Liu, Z.

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express 15(24), 15886–15891 (2007).
[Crossref] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Lu, M.

J. Y. Chin, M. Lu, and T. J. Cui, “Metamaterial polarizers by electric-field-coupled resonators,” Appl. Phys. Lett. 93(25), 251903 (2008).
[Crossref]

Mascarenhas, A.

Y. Zhang, B. Fluegel, and A. Mascarenhas, “Total negative refraction in real crystals for ballistic electrons and light,” Phys. Rev. Lett. 91(15), 157404 (2003).
[Crossref] [PubMed]

Mei, Z. L.

Z. L. Mei, T. M. Niu, J. Bai, and T. J. Cui, “Design of a one-dimensional electromagnetic transparent wall,” J. Opt. Soc. Am. A 27(10), 2237–2243 (2010).
[Crossref] [PubMed]

Narimanov, E.

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).
[Crossref] [PubMed]

Narimanov, E. E.

Niu, T. M.

Z. L. Mei, T. M. Niu, J. Bai, and T. J. Cui, “Design of a one-dimensional electromagnetic transparent wall,” J. Opt. Soc. Am. A 27(10), 2237–2243 (2010).
[Crossref] [PubMed]

Pendry, J. B.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
[Crossref]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[Crossref] [PubMed]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[Crossref]

Podolskiy, V. A.

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[Crossref]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref] [PubMed]

Shalaev, V. M.

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[Crossref]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref] [PubMed]

Sivco, D. L.

Smith, D. R.

B. J. Arritt, D. R. Smith, and T. Khraishi, “Equivalent circuit analysis of metamaterial strain-dependent effective medium parameters,” J. Appl. Phys. 109(7), 073512 (2011).
[Crossref]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[Crossref] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref] [PubMed]

Soukoulis, C. M.

C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5, 523–530 (2011).

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[Crossref]

Sun, C.

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express 15(24), 15886–15891 (2007).
[Crossref] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Tsai, D. P.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
[Crossref]

Ulin-Avila, E.

Valentine, J.

Wasserman, D.

Wegener, M.

C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5, 523–530 (2011).

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[Crossref] [PubMed]

Wood, B.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
[Crossref]

Wu, B.

S. Xi, H. S. Chen, B. Wu, and J. A. Kong, “One-directional perfect cloak created with homogeneous material,” IEEE Microw. Wireless Compon. Lett. 19(3), 131–133 (2009).
[Crossref]

Xi, S.

S. Xi, H. S. Chen, B. Wu, and J. A. Kong, “One-directional perfect cloak created with homogeneous material,” IEEE Microw. Wireless Compon. Lett. 19(3), 131–133 (2009).
[Crossref]

Xiong, Y.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express 15(24), 15886–15891 (2007).
[Crossref] [PubMed]

Xu, X. F.

X. F. Xu, Y. J. Feng, Y. Hao, J. M. Zhao, and T. Jiang, “Infrared carpet cloak designed with uniform silicon grating structure,” Appl. Phys. Lett. 95(18), 184102 (2009).
[Crossref]

Zentgraf, T.

Zhang, S.

Zhang, X.

Y. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev. 40(5), 2494–2507 (2011).
[Crossref] [PubMed]

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express 15(24), 15886–15891 (2007).
[Crossref] [PubMed]

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Fig. 1 TM waves passing through an anisotropic slab and the slab’s configuration. (a) TM waves passing through an anisotropic slab, (b) adjustment of the optical axes.

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Fig. 2 EMTW realized with stacked anisotropic materials

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Fig. 3 Calculated parameters when type I is utilized in the design. (a)

η

; (b)

K

; (c)

θ

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Fig. 4 A simple bilayer configuration for the realization of EMTW

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Fig. 5 Magnetic field distributions when a Gaussian beam propagate in free space (a), through an ideal EMTW (b), through a layered EMTW without loss (c) and with losses (d,e). For the layered structure,

ε_{1} = - 2.4012

ε_{2} = 1.8225

θ = {67.5098}^{°}

for the left slab, and

ε_{1} = - 2.4012

ε_{2} = 1.8225

θ = - {67.5098}^{°}

for the right one. The thicknesses of the constitutive isotropic material layers are t₁ = 6.418 nm and t₂ = 10 nm, respectively in the simulation. The loss tangents for material 1 in cases (d) and (e) are 0.01 and 0.1036, respectively. (f-h) Similar to (c) but with a different incident angle (

α \approx - {21.25}^{°}

α \approx {35.37}^{°}

and

α \approx - {32.87}^{°}

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Fig. 6 Normalized magnetic field distributions along the cross-section line for different cases. Black solid line: vacuum; red circles: ideal anisotropic materials; the blue curve with plus sign: layered structure without loss; green dotted line and pink stars represent the layered structures with loss tangents of 0.01 and 0.1036, respectively.

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Fig. 7 Magnetic field distributions when a Gaussian beam with an incidence angle of

α \approx - {32.87}^{°}

propagates in different environments. Note that the figure is very similar to Fig. 5 but with a different incident angle for the Gaussian beam.

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Fig. 8 Normalized magnetic field distributions along the cross-section line for different cases. Black solid line: vacuum; red circles: ideal anisotropic materials; the blue curve with plus sign: layered structure without loss; green dotted line and pink stars represent the layered structures with loss tangents of 0.01 and 0.1036, respectively. Note the figure is similar to Fig. 6 in the paper but with a different incident angle for the Gaussian beam.

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Tables (1)

Table 1 Requirements on the Material Parameters

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Equations (24)

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\bar{\bar{ε}} = (\begin{matrix} ε_{11} & ε_{12} & 0 \\ ε_{21} & ε_{22} & 0 \\ 0 & 0 & ε_{33} \end{matrix}), μ = μ_{33},

ε_{11} k_{x}^{2} + ε_{21} k_{x} k_{y} + ε_{12} k_{x} k_{y} + ε_{22} k_{y}^{2} = Δ k_{0}^{2} μ_{33},

(\begin{matrix} ε_{11} & ε_{12} & ε_{13} \\ ε_{21} & ε_{22} & ε_{23} \\ ε_{31} & ε_{32} & ε_{33} \end{matrix}) = (\begin{matrix} \cos^{2} θ ε_{u} + \sin^{2} θ ε_{v} & \cos θ \sin θ (ε_{u} - ε_{v}) & 0 \\ \cos θ \sin θ (ε_{u} - ε_{v}) & \sin^{2} θ ε_{u} + \cos^{2} θ ε_{v} & 0 \\ 0 & 0 & ε_{w} \end{matrix}) .

ε_{u} {(\cos θ k_{x} + \sin θ k_{y})}^{2} + ε_{v} {(- \sin θ k_{x} + \cos θ k_{y})}^{2} = Δ k_{0}^{2} μ_{33},

H_{z}^{1} = H_{0} e^{- j (k_{x 1} x + k_{y 1} y)} + D e^{- j (- k_{x 1} x + k_{y 1} y)}, (x \leq 0),

H_{z}^{2} = A e^{- j (k_{x 2} x + k_{y 2} y)} + B e^{- j (- k_{x 2} x + k_{y 2} y)}, (0 \leq x \leq d),

H_{z}^{3} = C e^{- j [k_{x 1} (x - d) + k_{y 1} y]}, (x \geq d),

{\begin{cases} H_{0} + D = A + B \\ N A + \bar{N} B = H_{0} - D \\ A' + B' = C \\ N A' + \bar{N} B' = C \end{cases},

r = \frac{D}{H_{0}} = \frac{R - S}{R + S},

t = \frac{C}{H_{0}} = \frac{2}{R + S},

S = ((\bar{N} - 1) / (\bar{N} - N)) N e^{j k_{x 2} d} + ((1 - N) / (\bar{N} - N)) \bar{N} e^{- j k_{x 2} d} .

ε_{u} ε_{v} = 1; ε_{11} μ_{33} = 1

\sin^{2} θ = ((1 / μ_{33}) - ε_{u}) / (ε_{v} - ε_{u}) .

\sin θ = \sqrt{\frac{K}{1 + K}}, \cos θ = \sqrt{\frac{1}{1 + K}},

δ φ = \sum_{i = 1}^{N} k_{x i} d_{i} = \sum_{i = 1}^{N} (- ((K_{i} - 1) / \sqrt{K_{i}}) k_{0} \sin α + k_{0} \cos α) d_{i} .

δ φ' = \sum_{i = 1}^{N} k_{x i} d_{i} = k_{0} \cos α \sum_{i = 1}^{N} d_{i} .

\sum_{i = 1}^{N} (- ((K_{i} - 1) / \sqrt{K_{i}}) d_{i}) = 0,

\frac{d_{1}}{d_{2}} = - \sqrt{\frac{K_{1}}{K_{2}}} \frac{K_{2} - 1}{K_{1} - 1} .

ε_{x} = ε_{u} = \frac{(1 + η) ε_{1} ε_{2}}{η ε_{1} + ε_{2}},

ε_{y} = ε_{v} = \frac{(ε_{1} + η ε_{2})}{(1 + η)},

η = \frac{ε_{2} (1 - ε_{1}^{2})}{ε_{1} (ε_{2}^{2} - 1)} > 0,

K = ε_{u} = \frac{ε_{1} ε_{2} + 1}{ε_{1} + ε_{2}} > 0.

ε_{u 1} = 5.8341, ε_{v 1} = 0.1714, η_{1} = 1.5581, θ_{1} = {67.5098}^{°},

ε_{u 2} = 0.1714, ε_{v 2} = 5.8341, η_{2} = 1.5581, θ_{2} = - {67.5098}^{°} .

	I	II	III	IV	V	VI
$ε_{1}$	$(1, \infty)$	$(1, \infty)$	$(0, 1)$	$(- \infty, - ε_{2})$	$(0, 1)$	$(- ε_{2}, 0)$
$ε_{2}$	$(- \infty, - ε_{1})$	$(0, 1)$	$(- ε_{1}, 0)$	$(1, \infty)$	$(1, \infty)$	$(0, 1)$