Abstract

We study the optical properties of metamaterials made from cut-wire pairs or plate pairs. We obtain a more pronounced optical response for arrays of plate pairs, a geometry that also eliminates the undesirable polarization anisotropy of the cut-wire pairs. The measured optical spectra agree with simulations, revealing negative magnetic permeability in the range of telecommunications wavelengths. Thus nanoscopic plate pairs might serve as an alternative to the established split-ring resonator design.

© 2005 Optical Society of America

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  1. R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
    [CrossRef] [PubMed]
  2. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
    [CrossRef] [PubMed]
  3. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004).
    [CrossRef] [PubMed]
  4. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
    [CrossRef] [PubMed]
  5. S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, Phys. Rev. Lett. 94, 37402 (2005).
    [CrossRef]
  6. H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, Phys. Rev. Lett. 94, 63901 (2005).
    [CrossRef]
  7. N. Katsarakis, G. Konstantinidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, M. Kafesaki, E. N. Economou, Th. Koschny, and C. M. Soukoulis, Opt. Lett. 30, 1348 (2005).
    [CrossRef] [PubMed]
  8. V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
    [CrossRef]
  9. J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
    [CrossRef] [PubMed]
  10. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
    [CrossRef]
  11. A. N. Lagarkov and A. K. Sarychev, Phys. Rev. B 53, 6318 (1996).
    [CrossRef]
  12. L. V. Panina, A. N. Grigorenko, and D. P. Makhnovskiy, Phys. Rev. B 66, 155411 (2002).
    [CrossRef]
  13. V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, J. Opt. A, Pure Appl. Opt. 7, 32 (2005).
    [CrossRef]
  14. D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
    [CrossRef]
  15. Th. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, Phys. Rev. B 71, 245105 (2005).
    [CrossRef]
  16. While completing this manuscript we learned about independent and related work on cut-wire pairs: V. M. Shalaev, in International Conference on Quantum Electronics and Laser Science (QELS) (Optical Society of America, 2005), paper JThA1.

2005 (5)

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, J. Opt. A, Pure Appl. Opt. 7, 32 (2005).
[CrossRef]

Th. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, Phys. Rev. B 71, 245105 (2005).
[CrossRef]

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, Phys. Rev. Lett. 94, 37402 (2005).
[CrossRef]

H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, Phys. Rev. Lett. 94, 63901 (2005).
[CrossRef]

N. Katsarakis, G. Konstantinidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, M. Kafesaki, E. N. Economou, Th. Koschny, and C. M. Soukoulis, Opt. Lett. 30, 1348 (2005).
[CrossRef] [PubMed]

2004 (3)

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

2002 (2)

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

L. V. Panina, A. N. Grigorenko, and D. P. Makhnovskiy, Phys. Rev. B 66, 155411 (2002).
[CrossRef]

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 (1)

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

1996 (1)

A. N. Lagarkov and A. K. Sarychev, Phys. Rev. B 53, 6318 (1996).
[CrossRef]

1968 (1)

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

Basov, D. N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

Brueck, S. R. J.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, Phys. Rev. Lett. 94, 37402 (2005).
[CrossRef]

Casse, B. D. F.

H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, Phys. Rev. Lett. 94, 63901 (2005).
[CrossRef]

Economou, E. N.

Enkrich, C.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

Fan, W.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, Phys. Rev. Lett. 94, 37402 (2005).
[CrossRef]

Fang, N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[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, 37402 (2005).
[CrossRef]

Grigorenko, A. N.

L. V. Panina, A. N. Grigorenko, and D. P. Makhnovskiy, Phys. Rev. B 66, 155411 (2002).
[CrossRef]

Gundogdu, T. F.

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]

Kafesaki, M.

Katsarakis, N.

Konstantinidis, G.

Koschny, T.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

Koschny, Th.

Kostopoulos, A.

Lagarkov, A. N.

A. N. Lagarkov and A. K. Sarychev, Phys. Rev. B 53, 6318 (1996).
[CrossRef]

Linden, S.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

Makhnovskiy, D. P.

L. V. Panina, A. N. Grigorenko, and D. P. Makhnovskiy, Phys. Rev. B 66, 155411 (2002).
[CrossRef]

Malloy, K. J.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, Phys. Rev. Lett. 94, 37402 (2005).
[CrossRef]

Markos, P.

Th. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, Phys. Rev. B 71, 245105 (2005).
[CrossRef]

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, 37402 (2005).
[CrossRef]

Moser, H. O.

H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, Phys. Rev. Lett. 94, 63901 (2005).
[CrossRef]

Narimanov, E. E.

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, J. Opt. A, Pure Appl. Opt. 7, 32 (2005).
[CrossRef]

Padilla, W. J.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

Panina, L. V.

L. V. Panina, A. N. Grigorenko, and D. P. Makhnovskiy, Phys. Rev. B 66, 155411 (2002).
[CrossRef]

Penciu, R. S.

Pendry, J. B.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004).
[CrossRef] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (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]

Podolskiy, V. A.

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, J. Opt. A, Pure Appl. Opt. 7, 32 (2005).
[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]

Sarychev, A. K.

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, J. Opt. A, Pure Appl. Opt. 7, 32 (2005).
[CrossRef]

A. N. Lagarkov and A. K. Sarychev, Phys. Rev. B 53, 6318 (1996).
[CrossRef]

Saw, B. T.

H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, Phys. Rev. Lett. 94, 63901 (2005).
[CrossRef]

Schultz, S.

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

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

Shalaev, V. M.

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, J. Opt. A, Pure Appl. Opt. 7, 32 (2005).
[CrossRef]

While completing this manuscript we learned about independent and related work on cut-wire pairs: V. M. Shalaev, in International Conference on Quantum Electronics and Laser Science (QELS) (Optical Society of America, 2005), paper JThA1.

Shelby, R. A.

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

Smith, D. R.

Th. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, Phys. Rev. B 71, 245105 (2005).
[CrossRef]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004).
[CrossRef] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

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

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

Soukoulis, C. M.

Th. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, Phys. Rev. B 71, 245105 (2005).
[CrossRef]

N. Katsarakis, G. Konstantinidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, M. Kafesaki, E. N. Economou, Th. Koschny, and C. M. Soukoulis, Opt. Lett. 30, 1348 (2005).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

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

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]

Veselago, V. G.

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

Vier, D. C.

Th. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, Phys. Rev. B 71, 245105 (2005).
[CrossRef]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

Wegener, M.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

Wilhelmi, O.

H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, Phys. Rev. Lett. 94, 63901 (2005).
[CrossRef]

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004).
[CrossRef] [PubMed]

Yen, T. J.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

Zhang, S.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, Phys. Rev. Lett. 94, 37402 (2005).
[CrossRef]

Zhang, X.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

Zhou, J.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

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]

J. Opt. A, Pure Appl. Opt. (1)

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, J. Opt. A, Pure Appl. Opt. 7, 32 (2005).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (4)

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

Th. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, Phys. Rev. B 71, 245105 (2005).
[CrossRef]

A. N. Lagarkov and A. K. Sarychev, Phys. Rev. B 53, 6318 (1996).
[CrossRef]

L. V. Panina, A. N. Grigorenko, and D. P. Makhnovskiy, Phys. Rev. B 66, 155411 (2002).
[CrossRef]

Phys. Rev. Lett. (3)

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

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, Phys. Rev. Lett. 94, 37402 (2005).
[CrossRef]

H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, Phys. Rev. Lett. 94, 63901 (2005).
[CrossRef]

Science (4)

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

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

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

Other (1)

While completing this manuscript we learned about independent and related work on cut-wire pairs: V. M. Shalaev, in International Conference on Quantum Electronics and Laser Science (QELS) (Optical Society of America, 2005), paper JThA1.

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic of the adiabatic transition from split-ring resonators (left) to cut-wire pairs (right) as “magnetic atoms” of optical metamaterials. (b) Electron micrograph (oblique-incidence view) of an actual cut-wire pair with w = 150 nm , t = 20 nm , d = 60 nm , and l = 700 nm ; (c) corresponding top view.

Fig. 2
Fig. 2

Measured transmittance (red) and reflectance (blue) spectra for cut-wire pairs for vertical incident polarization (left column) and horizontal polarization (right column). l = ( a ) 500, (b) 400, (c) 300 nm . Fixed parameters for (a)–(c): w = 150 nm , t = 20 nm , d = 80 nm , a x = 500 nm , and a y = 1050 nm . Dotted curves in (a), spectra from a nominally identical structure but without the topmost gold wire. (d) same as (b) but d = 60 nm rather than d = 80 nm . Insets, the corresponding electron micrographs (top views).

Fig. 3
Fig. 3

Measured transmittance (red) and reflectance (blue) spectra for arrays of plate pairs. (a) w = l = 300 nm , (b) w = l = 200 nm . Fixed parameters: t = 20 nm , d = 80 nm , and a x = a y = l + 350 nm . Orientation as in Fig. 2. Dotted curves, transmittance spectra for 45° (left column) and 22.5° (right column) incident polarization.

Fig. 4
Fig. 4

(a) Calculated transmittance T (red) and reflectance R (blue) spectra for the structure shown in Fig. 3(a), i.e., for a single layer. Vertical and horizontal incident linear polarizations are strictly identical. (b) Electric permittivity ϵ, (c) refractive index n, (d) magnetic permeability μ as obtained from the corresponding retrieval for a stack of layers.

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