Abstract

We show that equivalent circuits offer a qualitative and even quantitative simple explanation for the behavior of various types of left-handed (or negative-index) metamaterials. This allows us to optimize design features and parameters while avoiding trial and error simulations or fabrications. In particular, we apply this unifying circuit approach in accounting for the features and in optimizing the structure employing parallel metallic bars on the two sides of a dielectric film.

© 2006 Optical Society of America

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  1. V. Veselago, Sov. Phys. Usp. 10, 509 (1968).
    [Crossref]
  2. J. Pendry, A. Holden, W. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
    [Crossref] [PubMed]
  3. J. Pendry, A. Holden, D. Robbins, and W. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
    [Crossref]
  4. J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
    [Crossref] [PubMed]
  5. J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, Phys. Rev. B 73, 041101 (2006).
    [Crossref]
  6. V. M. Shalaev, W. S. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, Opt. Lett. 30, 3356 (2005).
    [Crossref]
  7. D. Smith, W. Padilla, D. Vier, S. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
    [Crossref] [PubMed]
  8. D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
    [Crossref]
  9. J. Zhou, T. Koschny, L. Zhang, G. Tuttle, and C. M. Soukoulis, Appl. Phys. Lett. 88, 221103 (2006).
    [Crossref]
  10. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, Science 312, 892 (2006).
    [Crossref] [PubMed]
  11. S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, Phys. Rev. Lett. 94, 037402 (2005).
    [Crossref] [PubMed]
  12. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, Phys. Rev. Lett. 95, 137404 (2005).
    [Crossref] [PubMed]

2006 (3)

J. Zhou, T. Koschny, L. Zhang, G. Tuttle, and C. M. Soukoulis, Appl. Phys. Lett. 88, 221103 (2006).
[Crossref]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, Science 312, 892 (2006).
[Crossref] [PubMed]

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, Phys. Rev. B 73, 041101 (2006).
[Crossref]

2005 (4)

V. M. Shalaev, W. S. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, Opt. Lett. 30, 3356 (2005).
[Crossref]

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, Phys. Rev. Lett. 94, 037402 (2005).
[Crossref] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, Phys. Rev. Lett. 95, 137404 (2005).
[Crossref] [PubMed]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[Crossref] [PubMed]

2002 (1)

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[Crossref]

2000 (1)

D. Smith, W. Padilla, D. Vier, S. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[Crossref] [PubMed]

1999 (1)

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

1996 (1)

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

1968 (1)

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

Brueck, S. R. J.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, Phys. Rev. Lett. 95, 137404 (2005).
[Crossref] [PubMed]

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, Phys. Rev. Lett. 94, 037402 (2005).
[Crossref] [PubMed]

Cai, W. S.

Chettiar, U. K.

Dolling, G.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, Science 312, 892 (2006).
[Crossref] [PubMed]

Drachev, V. P.

Economou, E. N.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[Crossref] [PubMed]

Enkrich, C.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, Science 312, 892 (2006).
[Crossref] [PubMed]

Fan, W.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, Phys. Rev. Lett. 95, 137404 (2005).
[Crossref] [PubMed]

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, Phys. Rev. Lett. 94, 037402 (2005).
[Crossref] [PubMed]

Frauenglass, A.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, Phys. Rev. Lett. 94, 037402 (2005).
[Crossref] [PubMed]

Holden, A.

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

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

Kafesaki, M.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[Crossref] [PubMed]

Kildishev, A. V.

Koschny, T.

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, Phys. Rev. B 73, 041101 (2006).
[Crossref]

J. Zhou, T. Koschny, L. Zhang, G. Tuttle, and C. M. Soukoulis, Appl. Phys. Lett. 88, 221103 (2006).
[Crossref]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[Crossref] [PubMed]

Linden, S.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, Science 312, 892 (2006).
[Crossref] [PubMed]

Malloy, K. J.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, Phys. Rev. Lett. 95, 137404 (2005).
[Crossref] [PubMed]

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, Phys. Rev. Lett. 94, 037402 (2005).
[Crossref] [PubMed]

Markos, P.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[Crossref]

Minhas, B. K.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, Phys. Rev. Lett. 94, 037402 (2005).
[Crossref] [PubMed]

Nemat-Nasser, S.

D. Smith, W. Padilla, D. Vier, S. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[Crossref] [PubMed]

Osgood, R. M.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, Phys. Rev. Lett. 95, 137404 (2005).
[Crossref] [PubMed]

Padilla, W.

D. Smith, W. Padilla, D. Vier, S. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[Crossref] [PubMed]

Panoiu, N. C.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, Phys. Rev. Lett. 95, 137404 (2005).
[Crossref] [PubMed]

Pendry, J.

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

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

Pendry, J. B.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[Crossref] [PubMed]

Robbins, D.

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

Sarychev, A. K.

Schultz, S.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[Crossref]

D. Smith, W. Padilla, D. Vier, S. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[Crossref] [PubMed]

Shalaev, V. M.

Smith, D.

D. Smith, W. Padilla, D. Vier, S. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[Crossref] [PubMed]

Smith, D. R.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[Crossref]

Soukoulis, C. M.

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, Phys. Rev. B 73, 041101 (2006).
[Crossref]

J. Zhou, T. Koschny, L. Zhang, G. Tuttle, and C. M. Soukoulis, Appl. Phys. Lett. 88, 221103 (2006).
[Crossref]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, Science 312, 892 (2006).
[Crossref] [PubMed]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[Crossref] [PubMed]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[Crossref]

Stewart, W.

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

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

Tuttle, G.

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, Phys. Rev. B 73, 041101 (2006).
[Crossref]

J. Zhou, T. Koschny, L. Zhang, G. Tuttle, and C. M. Soukoulis, Appl. Phys. Lett. 88, 221103 (2006).
[Crossref]

Veselago, V.

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

Vier, D.

D. Smith, W. Padilla, D. Vier, S. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[Crossref] [PubMed]

Wegener, M.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, Science 312, 892 (2006).
[Crossref] [PubMed]

Youngs, I.

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

Yuan, H. K.

Zhang, L.

J. Zhou, T. Koschny, L. Zhang, G. Tuttle, and C. M. Soukoulis, Appl. Phys. Lett. 88, 221103 (2006).
[Crossref]

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, Phys. Rev. B 73, 041101 (2006).
[Crossref]

Zhang, S.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, Phys. Rev. Lett. 94, 037402 (2005).
[Crossref] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, Phys. Rev. Lett. 95, 137404 (2005).
[Crossref] [PubMed]

Zhou, J.

J. Zhou, T. Koschny, L. Zhang, G. Tuttle, and C. M. Soukoulis, Appl. Phys. Lett. 88, 221103 (2006).
[Crossref]

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, Phys. Rev. B 73, 041101 (2006).
[Crossref]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

J. Zhou, T. Koschny, L. Zhang, G. Tuttle, and C. M. Soukoulis, Appl. Phys. Lett. 88, 221103 (2006).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

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

Opt. Lett. (1)

Phys. Rev. B (2)

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, Phys. Rev. B 73, 041101 (2006).
[Crossref]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[Crossref]

Phys. Rev. Lett. (5)

D. Smith, W. Padilla, D. Vier, S. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[Crossref] [PubMed]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[Crossref] [PubMed]

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

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, Phys. Rev. Lett. 94, 037402 (2005).
[Crossref] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, Phys. Rev. Lett. 95, 137404 (2005).
[Crossref] [PubMed]

Science (1)

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, Science 312, 892 (2006).
[Crossref] [PubMed]

Sov. Phys. Usp. (1)

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

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Figures (5)

Fig. 1
Fig. 1

The two-cut single metallic SRR (a) can be transformed to a pair of parallel metallic bars separated by a dielectric; (b) view in ( E , k ) plane; (c) view in ( E , H ) plane. Adding continuous wires results in design (d) [view in ( E , H ) plane], which can be modified to (e) a fully connected one on both sides of the thin dielectric board. The dashed squares define unit cells with dimensions a x (parallel to H ), a y (parallel to E ), and a z (parallel to k ).

Fig. 2
Fig. 2

At magnetic resonance the currents (a) [in the ( E , k ) plane, view in the H direction], the magnetic field (b) [in the ( H , k ) plane] and the electric field (c) [in the ( E , k ) plane] are shown. Sizes of the cones show the intensity of (b) magnetic field H and (c) electric field E on a logarithmic scale.

Fig. 3
Fig. 3

Current distribution of the design with two parallel metallic bars (a) [view in plane, one parallel plate is behind the other] can be accounted for by (b) the equivalent circuit, which, since points 1 and 2 are equivalent because of the periodicity, reduces to circuits (c) and (d) for the magnetic and electric resonances, respectively.

Fig. 4
Fig. 4

Magnetic resonant frequency f m crossover with electrical resonant f e as a y l = 1 + b l varies between 7.1 mm and 7.3 mm ; a x = 20 mm .

Fig. 5
Fig. 5

Retrieved ϵ eff (solid curves) and μ eff (dotted curves) for two cut wires. (a) and (b) correspond to points a ( a y = 7.3 mm , a x = 20 mm ) and b ( a y = 7.1 mm , a x = 20 mm ) in Fig. 4. Notice that both responses are Lorentz-like.

Equations (2)

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f m = ω m 2 π = 1 2 π l ϵ μ c 1 2 = 1 2 π c 1 ϵ r 2 c l ,
( f e f m ) 2 = L m L e ( 1 + C m C e ) < 1 .

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