Abstract

Based on analytical derivations and numerical simulations, we show that both reflection and transmission can be canceled at the surface of a metamaterial (MM) with a metal–dielectric stratified structure. Strong anisotropic absorption and the surface direction are found to play important roles in this phenomenon. For the angle between the surface and the layers of MMs above a critical value, only reflection is eliminated and transmission is permitted. Since they are not related to resonance, the phenomena can occur in a broad frequency range.

© 2009 Optical Society of America

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References

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  1. For a recent review, see D. R. Smith, J. B. Pendry, and M. Wiltshire, Science 305, 788 (2004).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  6. P. A. Belov and Y. Hao, Phys. Rev. B 73, 113110 (2006).
    [CrossRef]
  7. X. Li, Z. Liang, X. Liu, X. Jiang, and J. Zi, Appl. Phys. Lett. 93, 171111 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  10. R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  12. U. Leonhardt, Science 312, 1777 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  18. L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
    [CrossRef] [PubMed]
  19. Handbook of Optical Constants of Solids, E.D.Palik, ed. (Academic, 1985).
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    [CrossRef]
  21. V. Yannopapas, Phys. Rev. B 73, 113108 (2006).
    [CrossRef]
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    [CrossRef] [PubMed]
  23. J. Ng, H. Chen, and C. T. Chan, Opt. Lett. 34, 644 (2009).
    [CrossRef] [PubMed]

2009 (3)

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

J. Yang, X. Hu, X. Li, Z. Liu, Z. Liang, X. Jiang, and J. Zi, Phys. Rev. B 80, 125103 (2009).
[CrossRef]

J. Ng, H. Chen, and C. T. Chan, Opt. Lett. 34, 644 (2009).
[CrossRef] [PubMed]

2008 (2)

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, Phys. Rev. Lett. 100, 207402 (2008).
[CrossRef] [PubMed]

X. Li, Z. Liang, X. Liu, X. Jiang, and J. Zi, Appl. Phys. Lett. 93, 171111 (2008).
[CrossRef]

2006 (6)

P. A. Belov and Y. Hao, Phys. Rev. B 73, 113110 (2006).
[CrossRef]

X. Hu, C. T. Chan, J. Zi, M. Li, and K. M. Ho, Phys. Rev. Lett. 96, 223901 (2006).
[CrossRef] [PubMed]

V. Yannopapas, Phys. Rev. B 73, 113108 (2006).
[CrossRef]

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

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]

2005 (1)

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef] [PubMed]

2004 (1)

For a recent review, see D. R. Smith, J. B. Pendry, and M. Wiltshire, Science 305, 788 (2004).
[CrossRef] [PubMed]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

2000 (1)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

1999 (2)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

P. Halevi, A. A. Krokhin, and J. Arriaga, Phys. Rev. Lett. 82, 719 (1999).
[CrossRef]

1998 (1)

J. Zi, J. Wan, and C. Zhang, Appl. Phys. Lett. 73, 2084 (1998).
[CrossRef]

1978 (1)

D. Bergman, Phys. Rep. 43, 377 (1978).
[CrossRef]

1968 (1)

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Arriaga, J.

P. Halevi, A. A. Krokhin, and J. Arriaga, Phys. Rev. Lett. 82, 719 (1999).
[CrossRef]

Belov, P. A.

P. A. Belov and Y. Hao, Phys. Rev. B 73, 113110 (2006).
[CrossRef]

Bergman, D.

D. Bergman, Phys. Rep. 43, 377 (1978).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Catrysse, P. B.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

Chan, C. T.

J. Ng, H. Chen, and C. T. Chan, Opt. Lett. 34, 644 (2009).
[CrossRef] [PubMed]

X. Hu, C. T. Chan, J. Zi, M. Li, and K. M. Ho, Phys. Rev. Lett. 96, 223901 (2006).
[CrossRef] [PubMed]

Chen, H.

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]

Fan, S.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef] [PubMed]

Halevi, P.

P. Halevi, A. A. Krokhin, and J. Arriaga, Phys. Rev. Lett. 82, 719 (1999).
[CrossRef]

Hao, Y.

P. A. Belov and Y. Hao, Phys. Rev. B 73, 113110 (2006).
[CrossRef]

Ho, K. M.

X. Hu, C. T. Chan, J. Zi, M. Li, and K. M. Ho, Phys. Rev. Lett. 96, 223901 (2006).
[CrossRef] [PubMed]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Hu, X.

J. Yang, X. Hu, X. Li, Z. Liu, Z. Liang, X. Jiang, and J. Zi, Phys. Rev. B 80, 125103 (2009).
[CrossRef]

X. Hu, C. T. Chan, J. Zi, M. Li, and K. M. Ho, Phys. Rev. Lett. 96, 223901 (2006).
[CrossRef] [PubMed]

Jiang, X.

J. Yang, X. Hu, X. Li, Z. Liu, Z. Liang, X. Jiang, and J. Zi, Phys. Rev. B 80, 125103 (2009).
[CrossRef]

X. Li, Z. Liang, X. Liu, X. Jiang, and J. Zi, Appl. Phys. Lett. 93, 171111 (2008).
[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]

Krokhin, A. A.

P. Halevi, A. A. Krokhin, and J. Arriaga, Phys. Rev. Lett. 82, 719 (1999).
[CrossRef]

Landy, N. I.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, Phys. Rev. Lett. 100, 207402 (2008).
[CrossRef] [PubMed]

Lee, H.

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef] [PubMed]

Leonhardt, U.

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

Li, M.

X. Hu, C. T. Chan, J. Zi, M. Li, and K. M. Ho, Phys. Rev. Lett. 96, 223901 (2006).
[CrossRef] [PubMed]

Li, X.

J. Yang, X. Hu, X. Li, Z. Liu, Z. Liang, X. Jiang, and J. Zi, Phys. Rev. B 80, 125103 (2009).
[CrossRef]

X. Li, Z. Liang, X. Liu, X. Jiang, and J. Zi, Appl. Phys. Lett. 93, 171111 (2008).
[CrossRef]

Liang, Z.

J. Yang, X. Hu, X. Li, Z. Liu, Z. Liang, X. Jiang, and J. Zi, Phys. Rev. B 80, 125103 (2009).
[CrossRef]

X. Li, Z. Liang, X. Liu, X. Jiang, and J. Zi, Appl. Phys. Lett. 93, 171111 (2008).
[CrossRef]

Liu, X.

X. Li, Z. Liang, X. Liu, X. Jiang, and J. Zi, Appl. Phys. Lett. 93, 171111 (2008).
[CrossRef]

Liu, Z.

J. Yang, X. Hu, X. Li, Z. Liu, Z. Liang, X. Jiang, and J. Zi, Phys. Rev. B 80, 125103 (2009).
[CrossRef]

Mock, J. J.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, Phys. Rev. Lett. 100, 207402 (2008).
[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]

Ng, J.

Padilla, W. J.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, Phys. Rev. Lett. 100, 207402 (2008).
[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]

For a recent review, see D. R. Smith, J. B. Pendry, and M. Wiltshire, Science 305, 788 (2004).
[CrossRef] [PubMed]

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Sajuyigbe, S.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, Phys. Rev. Lett. 100, 207402 (2008).
[CrossRef] [PubMed]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Schurig, D.

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]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Smith, D. R.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, Phys. Rev. Lett. 100, 207402 (2008).
[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]

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

For a recent review, see D. R. Smith, J. B. Pendry, and M. Wiltshire, Science 305, 788 (2004).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[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]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Sun, C.

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef] [PubMed]

Verslegers, L.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

Veselago, V. G.

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Wan, J.

J. Zi, J. Wan, and C. Zhang, Appl. Phys. Lett. 73, 2084 (1998).
[CrossRef]

Wiltshire, M.

For a recent review, see D. R. Smith, J. B. Pendry, and M. Wiltshire, Science 305, 788 (2004).
[CrossRef] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Yang, J.

J. Yang, X. Hu, X. Li, Z. Liu, Z. Liang, X. Jiang, and J. Zi, Phys. Rev. B 80, 125103 (2009).
[CrossRef]

Yannopapas, V.

V. Yannopapas, Phys. Rev. B 73, 113108 (2006).
[CrossRef]

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

Yu, Z.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

Zhang, C.

J. Zi, J. Wan, and C. Zhang, Appl. Phys. Lett. 73, 2084 (1998).
[CrossRef]

Zhang, X.

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef] [PubMed]

Zi, J.

J. Yang, X. Hu, X. Li, Z. Liu, Z. Liang, X. Jiang, and J. Zi, Phys. Rev. B 80, 125103 (2009).
[CrossRef]

X. Li, Z. Liang, X. Liu, X. Jiang, and J. Zi, Appl. Phys. Lett. 93, 171111 (2008).
[CrossRef]

X. Hu, C. T. Chan, J. Zi, M. Li, and K. M. Ho, Phys. Rev. Lett. 96, 223901 (2006).
[CrossRef] [PubMed]

J. Zi, J. Wan, and C. Zhang, Appl. Phys. Lett. 73, 2084 (1998).
[CrossRef]

Appl. Phys. Lett. (2)

X. Li, Z. Liang, X. Liu, X. Jiang, and J. Zi, Appl. Phys. Lett. 93, 171111 (2008).
[CrossRef]

J. Zi, J. Wan, and C. Zhang, Appl. Phys. Lett. 73, 2084 (1998).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Opt. Lett. (1)

Phys. Rep. (1)

D. Bergman, Phys. Rep. 43, 377 (1978).
[CrossRef]

Phys. Rev. B (3)

P. A. Belov and Y. Hao, Phys. Rev. B 73, 113110 (2006).
[CrossRef]

J. Yang, X. Hu, X. Li, Z. Liu, Z. Liang, X. Jiang, and J. Zi, Phys. Rev. B 80, 125103 (2009).
[CrossRef]

V. Yannopapas, Phys. Rev. B 73, 113108 (2006).
[CrossRef]

Phys. Rev. Lett. (5)

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, Phys. Rev. Lett. 100, 207402 (2008).
[CrossRef] [PubMed]

P. Halevi, A. A. Krokhin, and J. Arriaga, Phys. Rev. Lett. 82, 719 (1999).
[CrossRef]

X. Hu, C. T. Chan, J. Zi, M. Li, and K. M. Ho, Phys. Rev. Lett. 96, 223901 (2006).
[CrossRef] [PubMed]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef] [PubMed]

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Science (6)

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef] [PubMed]

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

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]

For a recent review, see D. R. Smith, J. B. Pendry, and M. Wiltshire, Science 305, 788 (2004).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Other (3)

Handbook of Optical Constants of Solids, E.D.Palik, ed. (Academic, 1985).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

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Figures (4)

Fig. 1
Fig. 1

(a) Re ( k z ) and (b) Im ( k z ) as functions of k x for p-polarized EM waves with wavelength of 1 μ m in a periodic Au-dielectric stratified structure. The thicknesses of Au and dielectric layers are d 1 = 20 nm and d 2 = 80 nm , respectively. The dielectric constant of the dielectric layers is ϵ 2 = 2.34 . The solid and dashed curves are the results for the real structure [by Eq. (1)] and corresponding effective medium [by Eq. (2)], respectively. The circle in (a) is the equifrequency curve of EM waves in air.

Fig. 2
Fig. 2

Impinging of a p-polarized plane wave with k x = 0 upon air from the effective medium studied in Fig. 1. (a) Transmission as a function of the angle between the exit facet and z axis θ for wavelength of 1 μ m . (b) θ c and θ b as functions of wavelength.

Fig. 3
Fig. 3

Im ( k r k 0 ) of the reflected wave in the stratified structure (SS) or corresponding effective medium (Eff) for the case studied in Fig. 2. (a) Im ( k r k 0 ) as a function of θ at wavelength of 1 μ m . (b) Im ( k r k 0 ) as a function of wavelength when θ = 45 ° . The dotted curves are Im ( k i k 0 ) of the incident wave.

Fig. 4
Fig. 4

Finite-element simulation of impinging of a p-polarized Gaussian beam upon air from the periodic Au-dielectric stratified structure (SS) studied in Fig. 2. (a)–(c) λ = 0.7 , 1, and 3 μ m for θ = 45 ° . (d)–(e) λ = 0.7 , 1, and 3 μ m for θ = 60 ° . Black (blue online) and gray (red online) colors represent positive and negative values of magnetic field, respectively.

Equations (4)

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

cos ( k x d ) = cos ( q 1 x d 1 ) cos ( q 2 x d 2 ) 1 2 ( η + η 1 ) sin ( q 1 x d 1 ) sin ( q 2 x d 2 ) .
k x 2 ϵ z + k z 2 ϵ x = k 0 2 ,
T = Re ( A t ) Re ( A i ) | A i A r A t A r | 2 ,
θ c = arccos ϵ x 1 , θ b = arccos ( 1 + ϵ x ) 1 .

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