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.

© 2012 OSA

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  4. 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,” Nature455(7211), 376–379 (2008).
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  6. 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).
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  7. 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).
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    [CrossRef]
  22. Y. Huang, Y. Feng, and T. Jiang, “Electromagnetic cloaking by layered structure of homogeneous isotropic materials,” Opt. Express15(18), 11133–11141 (2007).
    [CrossRef] [PubMed]
  23. H. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered systems using the transformation media concept,” Phys. Rev. B78(5), 054204 (2008).
    [CrossRef]
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    [CrossRef]

2011

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. Photonics5, 523–530 (2011).

2010

2009

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

H. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered systems using the transformation media concept,” Phys. Rev. B78(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]

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,” Nature455(7211), 376–379 (2008).
[CrossRef] [PubMed]

2007

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]

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express15(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]

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics1(1), 41–48 (2007).
[CrossRef]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science315(5819), 1686 (2007).
[CrossRef] [PubMed]

Y. Huang, Y. Feng, and T. Jiang, “Electromagnetic cloaking by layered structure of homogeneous isotropic materials,” Opt. Express15(18), 11133–11141 (2007).
[CrossRef] [PubMed]

2006

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B74(11), 115116 (2006).
[CrossRef]

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express14(18), 8247–8256 (2006).
[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,” Science312(5775), 892–894 (2006).
[CrossRef] [PubMed]

2004

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. B69(11), 115402 (2004).
[CrossRef]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science305(5685), 788–792 (2004).
[CrossRef] [PubMed]

2003

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

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science292(5514), 77–79 (2001).
[CrossRef] [PubMed]

1999

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

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Alekseyev, L.

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]

Alekseyev, L. V.

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.

Bartal, G.

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,” Nature455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Chan, C. T.

H. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered systems using the transformation media concept,” Phys. Rev. B78(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. B78(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. B6(12), 4370–4379 (1972).
[CrossRef]

Chui, S. T.

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. B69(11), 115402 (2004).
[CrossRef]

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. A27(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.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science312(5775), 892–894 (2006).
[CrossRef] [PubMed]

Enkrich, C.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science312(5775), 892–894 (2006).
[CrossRef] [PubMed]

Feng, Y.

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.

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]

Genov, D. A.

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,” Nature455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Gmachl, C.

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]

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.

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]

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.

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]

Huang, Y.

Jacob, Z.

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. Express15(18), 11133–11141 (2007).
[CrossRef] [PubMed]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(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.

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express15(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,” Science315(5819), 1686 (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.

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. B69(11), 115402 (2004).
[CrossRef]

Linden, S.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science312(5775), 892–894 (2006).
[CrossRef] [PubMed]

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. Express15(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,” Science315(5819), 1686 (2007).
[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. B69(11), 115402 (2004).
[CrossRef]

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.

Narimanov, E.

Narimanov, E. E.

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]

Niu, T. M.

Pendry, J. B.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B74(11), 115116 (2006).
[CrossRef]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science305(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.

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]

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,” Science292(5514), 77–79 (2001).
[CrossRef] [PubMed]

Shalaev, V. M.

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics1(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,” Science292(5514), 77–79 (2001).
[CrossRef] [PubMed]

Sivco, D. L.

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]

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,” Science305(5685), 788–792 (2004).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science292(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. Photonics5, 523–530 (2011).

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science312(5775), 892–894 (2006).
[CrossRef] [PubMed]

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. Express15(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,” Science315(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. B74(11), 115116 (2006).
[CrossRef]

Ulin-Avila, E.

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,” Nature455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Valentine, J.

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,” Nature455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Wasserman, D.

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]

Wegener, M.

C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics5, 523–530 (2011).

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Figures (8)

Fig. 1
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.

Fig. 2
Fig. 2

EMTW realized with stacked anisotropic materials

Fig. 3
Fig. 3

Calculated parameters when type I is utilized in the design. (a) η ; (b) K ; (c) θ .

Fig. 4
Fig. 4

A simple bilayer configuration for the realization of EMTW

Fig. 5
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 21.25 ° , α 35.37 ° and α 32.87 ° ).

Fig. 6
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.

Fig. 7
Fig. 7

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

Fig. 8
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.

Tables (1)

Tables Icon

Table 1 Requirements on the Material Parameters

Equations (24)

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ε ¯ ¯ =( ε 11 ε 12 0 ε 21 ε 22 0 0 0 ε 33 ),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 ,
( ε 11 ε 12 ε 13 ε 21 ε 22 ε 23 ε 31 ε 32 ε 33 )=( cos 2 θ ε u + sin 2 θ ε v cosθsinθ( ε u ε v ) 0 cosθsinθ( ε u ε v ) sin 2 θ ε u + cos 2 θ ε v 0 0 0 ε w ).
ε u (cosθ k x +sinθ k y ) 2 + ε v (sinθ k x +cosθ k y ) 2 =Δ k 0 2 μ 33 ,
H z 1 = H 0 e j( k x1 x+ k y1 y) +D e j( k x1 x+ k y1 y) , (x0),
H z 2 =A e j( k x2 x+ k y2 y) +B e j( k x2 x+ k y2 y) , (0xd),
H z 3 =C e j[ k x1 (xd)+ k y1 y] , (xd),
{ H 0 +D=A+B NA+ N ¯ B= H 0 D A'+B'=C NA'+ N ¯ B'=C ,
r= D H 0 = RS R+S ,
t= C H 0 = 2 R+S ,
S=( ( N ¯ 1) / ( N ¯ N) )N e j k x2 d +( (1N) / ( N ¯ N) ) N ¯ e j k x2 d .
ε u ε v =1; ε 11 μ 33 =1
sin 2 θ= ((1/ μ 33 ) ε u ) / ( ε v ε u ) .
sinθ= K 1+K ,cosθ= 1 1+K ,
δφ= i=1 N k xi d i = i=1 N (( ( K i 1) / K i ) k 0 sinα+ k 0 cosα) d i .
δφ'= i=1 N k xi d i = k 0 cosα i=1 N d i .
i=1 N (( ( K i 1) / K i ) d i )=0,
d 1 d 2 = K 1 K 2 K 2 1 K 1 1 .
ε x = ε u = (1+η) ε 1 ε 2 η ε 1 + ε 2 ,
ε y = ε v = ( ε 1 +η ε 2 ) (1+η) ,
η= ε 2 (1 ε 1 2 ) ε 1 ( ε 2 2 1) >0,
K= ε u = ε 1 ε 2 +1 ε 1 + ε 2 >0.
ε u1 =5.8341, ε v1 =0.1714, η 1 =1.5581, θ 1 = 67.5098 ° ,
ε u2 =0.1714, ε v2 =5.8341, η 2 =1.5581, θ 2 = 67.5098 ° .

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