Abstract

Effective optical constants of stratified metal–dielectric metameterial are presented. The effective constants are determined by the two-complex reflectivity method (TCRM). The TCRM reveals the full components of the effective permittivity and permeability tensors and indicates the remarkable anisotropy of metallic and dielectric components below the effective plasma frequency. On the other hand, above the plasma frequency, one of the effective refractive indices takes a positive value less than unity and is associated with small loss. The photonic states are confirmed by the distribution of electromagnetic fields.

© 2007 Optical Society of America

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2006 (1)

2004 (4)

J. B. Pendry and D. R. Smith, Phys. Today 57(6), 37 (2004).
[CrossRef]

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, Phys. Rev. E 70, 048603 (2004).
[CrossRef]

R. A. Depine and A. Lakhtakia, Phys. Rev. E 70, 048601 (2004).
[CrossRef]

A. L. Efros, Phys. Rev. E 70, 048602 (2004).
[CrossRef]

2003 (1)

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, Phys. Rev. E 68, 065602(R) (2003).
[CrossRef]

2002 (2)

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195401 (2002).
[CrossRef]

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, Phys. Rev. B 66, 045102 (2002).
[CrossRef]

1998 (1)

M. Scalora, M. J. Blemer, A. S. Manka, S. D. Pethel, J. P. Dowling, and C. M. Bowden, J. Appl. Phys. 83, 2377 (1998).
[CrossRef]

1996 (1)

1980 (1)

1979 (1)

1972 (1)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Azzam, R. M. A.

Blemer, M. J.

M. Scalora, M. J. Blemer, A. S. Manka, S. D. Pethel, J. P. Dowling, and C. M. Bowden, J. Appl. Phys. 83, 2377 (1998).
[CrossRef]

Bowden, C. M.

M. Scalora, M. J. Blemer, A. S. Manka, S. D. Pethel, J. P. Dowling, and C. M. Bowden, J. Appl. Phys. 83, 2377 (1998).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Depine, R. A.

R. A. Depine and A. Lakhtakia, Phys. Rev. E 70, 048601 (2004).
[CrossRef]

Dolling, G.

Dowling, J. P.

M. Scalora, M. J. Blemer, A. S. Manka, S. D. Pethel, J. P. Dowling, and C. M. Bowden, J. Appl. Phys. 83, 2377 (1998).
[CrossRef]

Efros, A. L.

A. L. Efros, Phys. Rev. E 70, 048602 (2004).
[CrossRef]

Enkrich, C.

Gippius, N. A.

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, Phys. Rev. B 66, 045102 (2002).
[CrossRef]

Ishihara, T.

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, Phys. Rev. B 66, 045102 (2002).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Koschny, T.

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, Phys. Rev. E 70, 048603 (2004).
[CrossRef]

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, Phys. Rev. E 68, 065602(R) (2003).
[CrossRef]

Lakhtakia, A.

R. A. Depine and A. Lakhtakia, Phys. Rev. E 70, 048601 (2004).
[CrossRef]

Li, L.

Linden, S.

Manka, A. S.

M. Scalora, M. J. Blemer, A. S. Manka, S. D. Pethel, J. P. Dowling, and C. M. Bowden, J. Appl. Phys. 83, 2377 (1998).
[CrossRef]

Markos, P.

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, Phys. Rev. E 70, 048603 (2004).
[CrossRef]

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, Phys. Rev. E 68, 065602(R) (2003).
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195401 (2002).
[CrossRef]

Muljarov, E. A.

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, Phys. Rev. B 66, 045102 (2002).
[CrossRef]

Pendry, J. B.

J. B. Pendry and D. R. Smith, Phys. Today 57(6), 37 (2004).
[CrossRef]

Pethel, S. D.

M. Scalora, M. J. Blemer, A. S. Manka, S. D. Pethel, J. P. Dowling, and C. M. Bowden, J. Appl. Phys. 83, 2377 (1998).
[CrossRef]

Scalora, M.

M. Scalora, M. J. Blemer, A. S. Manka, S. D. Pethel, J. P. Dowling, and C. M. Bowden, J. Appl. Phys. 83, 2377 (1998).
[CrossRef]

Schultz, S.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195401 (2002).
[CrossRef]

Smith, D. R.

J. B. Pendry and D. R. Smith, Phys. Today 57(6), 37 (2004).
[CrossRef]

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, Phys. Rev. E 70, 048603 (2004).
[CrossRef]

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, Phys. Rev. E 68, 065602(R) (2003).
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195401 (2002).
[CrossRef]

Soukoulis, C. M.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, Opt. Lett. 31, 1800 (2006).
[CrossRef] [PubMed]

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, Phys. Rev. E 70, 048603 (2004).
[CrossRef]

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, Phys. Rev. E 68, 065602(R) (2003).
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195401 (2002).
[CrossRef]

Tikhodeev, S. G.

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, Phys. Rev. B 66, 045102 (2002).
[CrossRef]

Wegener, M.

Yablonskii, A. L.

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, Phys. Rev. B 66, 045102 (2002).
[CrossRef]

Appl. Opt. (1)

J. Appl. Phys. (1)

M. Scalora, M. J. Blemer, A. S. Manka, S. D. Pethel, J. P. Dowling, and C. M. Bowden, J. Appl. Phys. 83, 2377 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Lett. (1)

Phys. Rev. B (3)

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, Phys. Rev. B 66, 045102 (2002).
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195401 (2002).
[CrossRef]

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Phys. Rev. E (4)

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, Phys. Rev. E 68, 065602(R) (2003).
[CrossRef]

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, Phys. Rev. E 70, 048603 (2004).
[CrossRef]

R. A. Depine and A. Lakhtakia, Phys. Rev. E 70, 048601 (2004).
[CrossRef]

A. L. Efros, Phys. Rev. E 70, 048602 (2004).
[CrossRef]

Phys. Today (1)

J. B. Pendry and D. R. Smith, Phys. Today 57(6), 37 (2004).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic drawing of SMDM and the coordinate configuration. Gray indicates metal (silver) layers, and white is dielectric ( Mg F 2 ) layers. (b) Optical configuration of the TCRM. Incident light is s polarization, that is, E in y .

Fig. 2
Fig. 2

(a) Reflectance spectra. Solid line, under normal incidence on the x y plane; dotted line, under nornal incidence with E in z on the y z plane. (b) x component of effective ϵ and μ. Upper solid line, Re ( ϵ x ) ; dotted line, Im ( ϵ x ) ; lower solid line, Re ( μ x ) ; dashed line, Im ( μ x ) . (c) z component of effective ϵ and μ. The notations are similar to (b): replace x in (b) with z. (d) Refractive indices. Upper solid line, Re ( n z ) ; dotted line, Im ( n z ) ; lower solid line, Re ( n x ) ; dashed line, Im ( n x ) .

Fig. 3
Fig. 3

(a) Effect of refractive index n z at 3.0 eV . Solid line, electric field E y ( z ) of the incident light ( E in y , normal incidence on the x y plane) in vacuum and the refracted component in SMDM; dashed line, E y ( z ) evaluated by using n z ; Fig. 2d shows n z = 0.67 + 0.04 i at 3.0 eV .

Fig. 4
Fig. 4

Profile of electric field E y at 3.74 eV (solid line) under normal incidence on the x y plane. Dashed line, profile calculated from the effective refractive index n z at 3.74 eV in Fig. 2d. Weak reflection is not included in vacuum for simplicity.

Equations (2)

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k ̂ z ( θ ) μ x = n 1 cos θ μ 1 1 r s ( θ ) 1 + r s ( θ ) .
ϵ y = k ̂ z ( θ ) 2 μ x + k ̂ x ( θ ) 2 μ z ,

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