Abstract

We analyze the transmission and reflection of electromagnetic waves calculated from transfer matrix simulations of periodic arrangements of thin metallic wires. The effective permittivity and the absorption of the arrangements of wires are determined. Their dependence on the wire thickness and the conductance of the metallic wires is studied. The cutoff frequency, or effective plasma frequency, is obtained and compared with analytical predictions. It is shown that the periodic arrangement of wires exhibits a frequency region in which the real part of the permittivity is negative while its imaginary part is very small. This behavior is seen for wires with thickness as small as 17 µm with a lattice constant of 3.33 mm.

© 2003 Optical Society of America

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  1. P. Markoš and C. M. Soukoulis, “Left-handed materials,” December6, 2002, e-print cond-mat/0212136, http://arxiv.org .
  2. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
    [CrossRef] [PubMed]
  3. M. M. Sigalas, C. T. Chan, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 52, 11744 (1995).
    [CrossRef]
  4. A. K. Sarychev and V. M. Shalaev, “Comment on paper ‘Extremely low frequency plasmons in metallic microstructures’,” March6, 2001, e-print cond-mat/0103145, http://arxiv.org .
  5. S. I. Maslovski, S. A. Tretyakov, and P. A. Belov, Microwave Opt. Technol. Lett. 35, 47 (2002).
    [CrossRef]
  6. J. Brown, Progr. Dielectrics 2, 195 (1960).
  7. W. Rotman, IRE Trans. Antennas Propag. AP 10, 82 (1962).
    [CrossRef]
  8. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Shultz, Phys. Rev. Lett. 84, 4184 (2000).
    [CrossRef] [PubMed]
  9. R. A. Shelby, D. R. Smith, and S. Shultz, Science 292, 77 (2001).
    [CrossRef] [PubMed]
  10. K. Li, S. J. McLean, R. B. Gregor, C. G. Parazzoli, and M. H. Tanielian, “Free-space focused-beam characterization of left handed materials,” Appl. Phys. Lett. (to be published).
  11. E. V. Ponizovskaya, M. Nieto-Vesperinas, and N. Garcia, Appl. Phys. Lett. 81, 4470 (2002).
    [CrossRef]
  12. E. Ozbay, K. Aydin, E. Cubukcu, and M. Bayindir, “Transmission and reflection properties of composite double negative metamaterials in free-space,” Composite Metamaterials (to be published).
  13. P. Markoš and C. M. Soukoulis, Phys. Rev. E 65, 036622 (2002).
    [CrossRef]
  14. D. Smith, S. Shultz, P. Markoš, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
    [CrossRef]
  15. J. D. Jackson, Classical Electrodynamics, 3rd. ed. (Wiley, New York, 1999).
  16. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, J. Phys. Condens. Matter. 10, 4785 (1998).
    [CrossRef]

2002 (4)

S. I. Maslovski, S. A. Tretyakov, and P. A. Belov, Microwave Opt. Technol. Lett. 35, 47 (2002).
[CrossRef]

E. V. Ponizovskaya, M. Nieto-Vesperinas, and N. Garcia, Appl. Phys. Lett. 81, 4470 (2002).
[CrossRef]

P. Markoš and C. M. Soukoulis, Phys. Rev. E 65, 036622 (2002).
[CrossRef]

D. Smith, S. Shultz, P. Markoš, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

2001 (1)

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

2000 (1)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Shultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

1998 (1)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, J. Phys. Condens. Matter. 10, 4785 (1998).
[CrossRef]

1996 (1)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

1995 (1)

M. M. Sigalas, C. T. Chan, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 52, 11744 (1995).
[CrossRef]

1962 (1)

W. Rotman, IRE Trans. Antennas Propag. AP 10, 82 (1962).
[CrossRef]

1960 (1)

J. Brown, Progr. Dielectrics 2, 195 (1960).

Aydin, K.

E. Ozbay, K. Aydin, E. Cubukcu, and M. Bayindir, “Transmission and reflection properties of composite double negative metamaterials in free-space,” Composite Metamaterials (to be published).

Bayindir, M.

E. Ozbay, K. Aydin, E. Cubukcu, and M. Bayindir, “Transmission and reflection properties of composite double negative metamaterials in free-space,” Composite Metamaterials (to be published).

Belov, P. A.

S. I. Maslovski, S. A. Tretyakov, and P. A. Belov, Microwave Opt. Technol. Lett. 35, 47 (2002).
[CrossRef]

Brown, J.

J. Brown, Progr. Dielectrics 2, 195 (1960).

Chan, C. T.

M. M. Sigalas, C. T. Chan, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 52, 11744 (1995).
[CrossRef]

Cubukcu, E.

E. Ozbay, K. Aydin, E. Cubukcu, and M. Bayindir, “Transmission and reflection properties of composite double negative metamaterials in free-space,” Composite Metamaterials (to be published).

Garcia, N.

E. V. Ponizovskaya, M. Nieto-Vesperinas, and N. Garcia, Appl. Phys. Lett. 81, 4470 (2002).
[CrossRef]

Gregor, R. B.

K. Li, S. J. McLean, R. B. Gregor, C. G. Parazzoli, and M. H. Tanielian, “Free-space focused-beam characterization of left handed materials,” Appl. Phys. Lett. (to be published).

Ho, K. M.

M. M. Sigalas, C. T. Chan, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 52, 11744 (1995).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, J. Phys. Condens. Matter. 10, 4785 (1998).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd. ed. (Wiley, New York, 1999).

Li, K.

K. Li, S. J. McLean, R. B. Gregor, C. G. Parazzoli, and M. H. Tanielian, “Free-space focused-beam characterization of left handed materials,” Appl. Phys. Lett. (to be published).

Markoš, P.

D. Smith, S. Shultz, P. Markoš, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

P. Markoš and C. M. Soukoulis, Phys. Rev. E 65, 036622 (2002).
[CrossRef]

P. Markoš and C. M. Soukoulis, “Left-handed materials,” December6, 2002, e-print cond-mat/0212136, http://arxiv.org .

Maslovski, S. I.

S. I. Maslovski, S. A. Tretyakov, and P. A. Belov, Microwave Opt. Technol. Lett. 35, 47 (2002).
[CrossRef]

McLean, S. J.

K. Li, S. J. McLean, R. B. Gregor, C. G. Parazzoli, and M. H. Tanielian, “Free-space focused-beam characterization of left handed materials,” Appl. Phys. Lett. (to be published).

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Shultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

Nieto-Vesperinas, M.

E. V. Ponizovskaya, M. Nieto-Vesperinas, and N. Garcia, Appl. Phys. Lett. 81, 4470 (2002).
[CrossRef]

Ozbay, E.

E. Ozbay, K. Aydin, E. Cubukcu, and M. Bayindir, “Transmission and reflection properties of composite double negative metamaterials in free-space,” Composite Metamaterials (to be published).

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Shultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

Parazzoli, C. G.

K. Li, S. J. McLean, R. B. Gregor, C. G. Parazzoli, and M. H. Tanielian, “Free-space focused-beam characterization of left handed materials,” Appl. Phys. Lett. (to be published).

Pendry, J. B.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, J. Phys. Condens. Matter. 10, 4785 (1998).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

Ponizovskaya, E. V.

E. V. Ponizovskaya, M. Nieto-Vesperinas, and N. Garcia, Appl. Phys. Lett. 81, 4470 (2002).
[CrossRef]

Rotman, W.

W. Rotman, IRE Trans. Antennas Propag. AP 10, 82 (1962).
[CrossRef]

Sarychev, A. K.

A. K. Sarychev and V. M. Shalaev, “Comment on paper ‘Extremely low frequency plasmons in metallic microstructures’,” March6, 2001, e-print cond-mat/0103145, http://arxiv.org .

Shalaev, V. M.

A. K. Sarychev and V. M. Shalaev, “Comment on paper ‘Extremely low frequency plasmons in metallic microstructures’,” March6, 2001, e-print cond-mat/0103145, http://arxiv.org .

Shelby, R. A.

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

Shultz, S.

D. Smith, S. Shultz, P. Markoš, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

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

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Shultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

Sigalas, M. M.

M. M. Sigalas, C. T. Chan, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 52, 11744 (1995).
[CrossRef]

Smith, D.

D. Smith, S. Shultz, P. Markoš, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Smith, D. R.

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

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Shultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

Soukoulis, C. M.

P. Markoš and C. M. Soukoulis, Phys. Rev. E 65, 036622 (2002).
[CrossRef]

D. Smith, S. Shultz, P. Markoš, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

M. M. Sigalas, C. T. Chan, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 52, 11744 (1995).
[CrossRef]

P. Markoš and C. M. Soukoulis, “Left-handed materials,” December6, 2002, e-print cond-mat/0212136, http://arxiv.org .

Stewart, W. J.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, J. Phys. Condens. Matter. 10, 4785 (1998).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

Tanielian, M. H.

K. Li, S. J. McLean, R. B. Gregor, C. G. Parazzoli, and M. H. Tanielian, “Free-space focused-beam characterization of left handed materials,” Appl. Phys. Lett. (to be published).

Tretyakov, S. A.

S. I. Maslovski, S. A. Tretyakov, and P. A. Belov, Microwave Opt. Technol. Lett. 35, 47 (2002).
[CrossRef]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Shultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

Youngs, I.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, J. Phys. Condens. Matter. 10, 4785 (1998).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

E. V. Ponizovskaya, M. Nieto-Vesperinas, and N. Garcia, Appl. Phys. Lett. 81, 4470 (2002).
[CrossRef]

IRE Trans. Antennas Propag. AP (1)

W. Rotman, IRE Trans. Antennas Propag. AP 10, 82 (1962).
[CrossRef]

J. Phys. Condens. Matter. (1)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, J. Phys. Condens. Matter. 10, 4785 (1998).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

S. I. Maslovski, S. A. Tretyakov, and P. A. Belov, Microwave Opt. Technol. Lett. 35, 47 (2002).
[CrossRef]

Phys. Rev. B (2)

D. Smith, S. Shultz, P. Markoš, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

M. M. Sigalas, C. T. Chan, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 52, 11744 (1995).
[CrossRef]

Phys. Rev. E (1)

P. Markoš and C. M. Soukoulis, Phys. Rev. E 65, 036622 (2002).
[CrossRef]

Phys. Rev. Lett. (2)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Shultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

Progr. Dielectrics (1)

J. Brown, Progr. Dielectrics 2, 195 (1960).

Science (1)

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

Other (5)

K. Li, S. J. McLean, R. B. Gregor, C. G. Parazzoli, and M. H. Tanielian, “Free-space focused-beam characterization of left handed materials,” Appl. Phys. Lett. (to be published).

P. Markoš and C. M. Soukoulis, “Left-handed materials,” December6, 2002, e-print cond-mat/0212136, http://arxiv.org .

A. K. Sarychev and V. M. Shalaev, “Comment on paper ‘Extremely low frequency plasmons in metallic microstructures’,” March6, 2001, e-print cond-mat/0103145, http://arxiv.org .

E. Ozbay, K. Aydin, E. Cubukcu, and M. Bayindir, “Transmission and reflection properties of composite double negative metamaterials in free-space,” Composite Metamaterials (to be published).

J. D. Jackson, Classical Electrodynamics, 3rd. ed. (Wiley, New York, 1999).

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Figures (4)

Fig. 1
Fig. 1

Effective permittivity as a function of frequency for various shapes of the metallic wires. The lattice period in all cases is a=3.33 mm. We used metallic permittivity m=-3+588i×103.

Fig. 2
Fig. 2

Plasma frequency as a function of the wire radius. The lattice constant is a=5 mm. The solid, dashed, and dotted–dashed curves are the results from Pendry et al.,2 Sarychev and Shalaev,4 and Maslovski et al.,5 respectively. The dotted curve is a fit of our data to the function fp=a0/lna1/r with parameters a0=20.9 and a1=0.84.

Fig. 3
Fig. 3

Ratio κ=eff/eff for a lattice of wires with radius 50 µm. The metallic permittivity is (open circles) m=-3+588i×103 and (full circles) m=-3+5 880i×103. The dashed (solid) curve is absorption for the corresponding system obtained numerically by the TMM. These numerical results confirm that losses are smaller for higher metallic permittivity and that the value of the plasma frequency, estimated approximately from the position of the maximum of κ, does not depend on the value of the metallic permittivity.

Fig. 4
Fig. 4

Effective permittivity for a lattice of thin metallic wires. The wire radius is r=15 µm, and the lattice constant is a=5 mm. The metallic permittivity is m=-2000+106 i. Two different discretizations are used with mesh sizes of (open symbols) 30 µm and (filled symbols) 15 µm. The solid and dashed curves are fitted to Eq. (1) with fp=11.1 GHz and γ=1.2 GHz. The length of the system was (open symbols) up to 60 unit lengths and (filled symbols) 10 unit lengths. The inset shows the numerically calculated absorption as a function of frequency.

Equations (5)

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

eff=1-fp2f2+2iγf.
fp2=clight22πa2 lna/r,
fp2=clight22πa2lna/2r+π/2-3,
fp2=clight22πa2ln a2/4ra-r.
cosnkL=12t1-r2+t2.

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