Abstract

In this letter it is presented a Left-Handed Metamaterial design route based upon stacked arrays of screens made of complementary split rings resonators under normal incidence in the microwave regime. Computation of the dispersion diagram highlights the possibility to obtain backward waves provided the longitudinal lattice is small enough. The experimental results are in good agreement with the computed ones. The physics underlying the Left-Handed behavior is found to rely on electroinductive waves, playing the mutual capacitive coupling the major role to explain the phenomenon. Our route to Left-Handed metamaterial introduced in this paper based on stacking CSRRs screens can be scaled to millimeter and terahertz for future applications.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  22. E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, "Magneto-inductive waveguide," Electron. Lett. 38, 371-373 (2002).
    [CrossRef]
  23. E. Shamonina, V.A. Kalinin, K. H. Ringhofer, and L. Solymar, "Magnetoinductive waves in one, two, and three dimensions," J. Appl. Phys. 92, 6252-6261 (2002).
    [CrossRef]
  24. E. Shamonina and L. Solymar, "Magneto-inductive waves supported by metamaterial elements: components for a one-dimensional waveguide, " J. Phys. D 37, 362-367 (2004).
    [CrossRef]
  25. M. C. K. Wiltshire, E. Shamonina, I. R. Young, and L. Solymar, "Dispersion characteristics of magnetoinductive waves: comparison between theory and experiment," Electron. Lett. 39, 215-217 (2003).
    [CrossRef]
  26. M. Aznabet, M. Navarro-Cía, S. A. Kuznetsov, A. V. Gelfand, N. I. Fedorinina, Yu. G. Goncharov, M. Beruete, O. El Mrabet, and M. Sorolla, "Polypropylene-substrate-based SRR- and CSRR-metasurfaces for submillimeter waves," Opt. Express 16, 18312-18319 (2008).
    [CrossRef] [PubMed]

2008 (4)

N.  Liu, H.  Guo, L.  Fu, S.  Kaiser, H.  Schweizer, and H.  Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nat. Mater.  7, 31-37 (2008).
[CrossRef]

N. Liu, S. Kaiser, and H. Giessen, "Magnetoinductive and Electroinductive Coupling in Plasmonic Metamaterial Molecules," Adv. Mater. 20, 1-5 (2008).
[CrossRef]

N. Liu, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Plasmonic Building Blocks for Magnetic Molecules in Three-Dimensional Optical Metamaterials," Adv. Mater. 20, 3859-3865 (2008)
[CrossRef]

M. Aznabet, M. Navarro-Cía, S. A. Kuznetsov, A. V. Gelfand, N. I. Fedorinina, Yu. G. Goncharov, M. Beruete, O. El Mrabet, and M. Sorolla, "Polypropylene-substrate-based SRR- and CSRR-metasurfaces for submillimeter waves," Opt. Express 16, 18312-18319 (2008).
[CrossRef] [PubMed]

2007 (1)

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D.L. Sivco, and C. Gmachl, "Negative refraction in semiconductor Metamaterials," Nat. Mater. 6, 946-950 (2007).
[CrossRef] [PubMed]

2006 (4)

M.  Beruete, F. Falcone, M. J. Freire, R. Marqués, and J. D. Baena, "Electroinductive Waves in Chains of Complementary Metamaterial Elements," Appl. Phys. Lett. 88, 083503-1-3 (2006).
[CrossRef]

M. Beruete, M. Sorolla, R. Marqués, J. D. Baena, and M. J. Freire, "Resonance and Cross-Polarization Effects in Conventional and Complementary Split Ring Resonator Periodic Screens," Electromag. 26, 247-260 (2006).
[CrossRef]

G.  Dolling, C.  Enkrich, M.  Wegener, C. M.  Soukoulis, and S.  Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science  312, 892-894 (2006).
[CrossRef] [PubMed]

M. Beruete, M. Sorolla, and I. Campillo, "Left-handed extraordinary optical transmission through a photonic crystal of subwavelength hole arrays," Opt. Express 14, 5445-5455 (2006).
[CrossRef] [PubMed]

2005 (3)

R. Marqués, J. D. Baena, M. Beruete, F. Fakcone, T. Lopetegi, M. Sorolla, F. Martin, and J. Garcia, "Ab initio Analysis of Frequency Selective Surfaces Based on Conventional and Complementary Split Ring resonators," J. Opt. A: Pure and Appl. Opt. 7, S38-S43 (2005).
[CrossRef]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404-1-4 (2005).
[CrossRef] [PubMed]

J.D. Baena, J. Bonache, F. Martín, R. Marqués, F. Falcone, T. Lopetegi, M. A. G. Laso, J. García, I. Gil, M. Flores, and M. Sorolla, "Equivalent Circuit Models for Split Ring Resonators and Complementary Split Ring Resonators Coupled to Planar Transmisión Lines," IEEE Trans. Microwave Theory Tech. 53, 1451-1461, (2005).
[CrossRef]

2004 (1)

E. Shamonina and L. Solymar, "Magneto-inductive waves supported by metamaterial elements: components for a one-dimensional waveguide, " J. Phys. D 37, 362-367 (2004).
[CrossRef]

2003 (2)

M. C. K. Wiltshire, E. Shamonina, I. R. Young, and L. Solymar, "Dispersion characteristics of magnetoinductive waves: comparison between theory and experiment," Electron. Lett. 39, 215-217 (2003).
[CrossRef]

R. Marqués, F. Mesa, J. Martel, and F. Medina "Comparative Analysis of Edge- and Broadside- Coupled Split Ring Resonators for Metamaterial Design. Theory and Experiments," IEEE Trans. Antennas Propag. 51, 2572 -2581 (2003).
[CrossRef]

2002 (4)

P. Gay-Balmaz, and O. J. F. Martin, "Electromagnetic resonances in individual and coupled split-ring resonators," J. Appl. Phys. 92, 2929-2936 (2002).
[CrossRef]

R. Marqués, F. Medina, and R. R. El-Idrissi, "Role of Bianisotropy in Negative Permeability and Left-Handed Metamaterials," Phys. Rev. B 65, 144440 1-6 (2002).
[CrossRef]

E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, "Magneto-inductive waveguide," Electron. Lett. 38, 371-373 (2002).
[CrossRef]

E. Shamonina, V.A. Kalinin, K. H. Ringhofer, and L. Solymar, "Magnetoinductive waves in one, two, and three dimensions," J. Appl. Phys. 92, 6252-6261 (2002).
[CrossRef]

2000 (1)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

1968 (1)

V. G. Veselago, "The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Beruete, M.

M.  Beruete, F. Falcone, M. J. Freire, R. Marqués, and J. D. Baena, "Electroinductive Waves in Chains of Complementary Metamaterial Elements," Appl. Phys. Lett. 88, 083503-1-3 (2006).
[CrossRef]

Alekseyev, L.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D.L. Sivco, and C. Gmachl, "Negative refraction in semiconductor Metamaterials," Nat. Mater. 6, 946-950 (2007).
[CrossRef] [PubMed]

Aznabet, M.

Baena, J. D.

M. Beruete, M. Sorolla, R. Marqués, J. D. Baena, and M. J. Freire, "Resonance and Cross-Polarization Effects in Conventional and Complementary Split Ring Resonator Periodic Screens," Electromag. 26, 247-260 (2006).
[CrossRef]

M.  Beruete, F. Falcone, M. J. Freire, R. Marqués, and J. D. Baena, "Electroinductive Waves in Chains of Complementary Metamaterial Elements," Appl. Phys. Lett. 88, 083503-1-3 (2006).
[CrossRef]

R. Marqués, J. D. Baena, M. Beruete, F. Fakcone, T. Lopetegi, M. Sorolla, F. Martin, and J. Garcia, "Ab initio Analysis of Frequency Selective Surfaces Based on Conventional and Complementary Split Ring resonators," J. Opt. A: Pure and Appl. Opt. 7, S38-S43 (2005).
[CrossRef]

Baena, J.D.

J.D. Baena, J. Bonache, F. Martín, R. Marqués, F. Falcone, T. Lopetegi, M. A. G. Laso, J. García, I. Gil, M. Flores, and M. Sorolla, "Equivalent Circuit Models for Split Ring Resonators and Complementary Split Ring Resonators Coupled to Planar Transmisión Lines," IEEE Trans. Microwave Theory Tech. 53, 1451-1461, (2005).
[CrossRef]

Beruete, M.

M. Aznabet, M. Navarro-Cía, S. A. Kuznetsov, A. V. Gelfand, N. I. Fedorinina, Yu. G. Goncharov, M. Beruete, O. El Mrabet, and M. Sorolla, "Polypropylene-substrate-based SRR- and CSRR-metasurfaces for submillimeter waves," Opt. Express 16, 18312-18319 (2008).
[CrossRef] [PubMed]

M. Beruete, M. Sorolla, R. Marqués, J. D. Baena, and M. J. Freire, "Resonance and Cross-Polarization Effects in Conventional and Complementary Split Ring Resonator Periodic Screens," Electromag. 26, 247-260 (2006).
[CrossRef]

M. Beruete, M. Sorolla, and I. Campillo, "Left-handed extraordinary optical transmission through a photonic crystal of subwavelength hole arrays," Opt. Express 14, 5445-5455 (2006).
[CrossRef] [PubMed]

R. Marqués, J. D. Baena, M. Beruete, F. Fakcone, T. Lopetegi, M. Sorolla, F. Martin, and J. Garcia, "Ab initio Analysis of Frequency Selective Surfaces Based on Conventional and Complementary Split Ring resonators," J. Opt. A: Pure and Appl. Opt. 7, S38-S43 (2005).
[CrossRef]

Bonache, J.

J.D. Baena, J. Bonache, F. Martín, R. Marqués, F. Falcone, T. Lopetegi, M. A. G. Laso, J. García, I. Gil, M. Flores, and M. Sorolla, "Equivalent Circuit Models for Split Ring Resonators and Complementary Split Ring Resonators Coupled to Planar Transmisión Lines," IEEE Trans. Microwave Theory Tech. 53, 1451-1461, (2005).
[CrossRef]

Brueck, S. R. J.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404-1-4 (2005).
[CrossRef] [PubMed]

Campillo, I.

Dolling, G.

G.  Dolling, C.  Enkrich, M.  Wegener, C. M.  Soukoulis, and S.  Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science  312, 892-894 (2006).
[CrossRef] [PubMed]

El Mrabet, O.

El-Idrissi, R. R.

R. Marqués, F. Medina, and R. R. El-Idrissi, "Role of Bianisotropy in Negative Permeability and Left-Handed Metamaterials," Phys. Rev. B 65, 144440 1-6 (2002).
[CrossRef]

Enkrich, C.

G.  Dolling, C.  Enkrich, M.  Wegener, C. M.  Soukoulis, and S.  Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science  312, 892-894 (2006).
[CrossRef] [PubMed]

Fakcone, F.

R. Marqués, J. D. Baena, M. Beruete, F. Fakcone, T. Lopetegi, M. Sorolla, F. Martin, and J. Garcia, "Ab initio Analysis of Frequency Selective Surfaces Based on Conventional and Complementary Split Ring resonators," J. Opt. A: Pure and Appl. Opt. 7, S38-S43 (2005).
[CrossRef]

Falcone, F.

M.  Beruete, F. Falcone, M. J. Freire, R. Marqués, and J. D. Baena, "Electroinductive Waves in Chains of Complementary Metamaterial Elements," Appl. Phys. Lett. 88, 083503-1-3 (2006).
[CrossRef]

J.D. Baena, J. Bonache, F. Martín, R. Marqués, F. Falcone, T. Lopetegi, M. A. G. Laso, J. García, I. Gil, M. Flores, and M. Sorolla, "Equivalent Circuit Models for Split Ring Resonators and Complementary Split Ring Resonators Coupled to Planar Transmisión Lines," IEEE Trans. Microwave Theory Tech. 53, 1451-1461, (2005).
[CrossRef]

Fan, W.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404-1-4 (2005).
[CrossRef] [PubMed]

Fedorinina, N. I.

Flores, M.

J.D. Baena, J. Bonache, F. Martín, R. Marqués, F. Falcone, T. Lopetegi, M. A. G. Laso, J. García, I. Gil, M. Flores, and M. Sorolla, "Equivalent Circuit Models for Split Ring Resonators and Complementary Split Ring Resonators Coupled to Planar Transmisión Lines," IEEE Trans. Microwave Theory Tech. 53, 1451-1461, (2005).
[CrossRef]

Franz, K. J.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D.L. Sivco, and C. Gmachl, "Negative refraction in semiconductor Metamaterials," Nat. Mater. 6, 946-950 (2007).
[CrossRef] [PubMed]

Freire, M. J.

M. Beruete, M. Sorolla, R. Marqués, J. D. Baena, and M. J. Freire, "Resonance and Cross-Polarization Effects in Conventional and Complementary Split Ring Resonator Periodic Screens," Electromag. 26, 247-260 (2006).
[CrossRef]

M.  Beruete, F. Falcone, M. J. Freire, R. Marqués, and J. D. Baena, "Electroinductive Waves in Chains of Complementary Metamaterial Elements," Appl. Phys. Lett. 88, 083503-1-3 (2006).
[CrossRef]

Fu, L.

N.  Liu, H.  Guo, L.  Fu, S.  Kaiser, H.  Schweizer, and H.  Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nat. Mater.  7, 31-37 (2008).
[CrossRef]

N. Liu, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Plasmonic Building Blocks for Magnetic Molecules in Three-Dimensional Optical Metamaterials," Adv. Mater. 20, 3859-3865 (2008)
[CrossRef]

Garcia, J.

R. Marqués, J. D. Baena, M. Beruete, F. Fakcone, T. Lopetegi, M. Sorolla, F. Martin, and J. Garcia, "Ab initio Analysis of Frequency Selective Surfaces Based on Conventional and Complementary Split Ring resonators," J. Opt. A: Pure and Appl. Opt. 7, S38-S43 (2005).
[CrossRef]

García, J.

J.D. Baena, J. Bonache, F. Martín, R. Marqués, F. Falcone, T. Lopetegi, M. A. G. Laso, J. García, I. Gil, M. Flores, and M. Sorolla, "Equivalent Circuit Models for Split Ring Resonators and Complementary Split Ring Resonators Coupled to Planar Transmisión Lines," IEEE Trans. Microwave Theory Tech. 53, 1451-1461, (2005).
[CrossRef]

Gay-Balmaz, P.

P. Gay-Balmaz, and O. J. F. Martin, "Electromagnetic resonances in individual and coupled split-ring resonators," J. Appl. Phys. 92, 2929-2936 (2002).
[CrossRef]

Gelfand, A. V.

Giessen, H.

N. Liu, S. Kaiser, and H. Giessen, "Magnetoinductive and Electroinductive Coupling in Plasmonic Metamaterial Molecules," Adv. Mater. 20, 1-5 (2008).
[CrossRef]

N. Liu, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Plasmonic Building Blocks for Magnetic Molecules in Three-Dimensional Optical Metamaterials," Adv. Mater. 20, 3859-3865 (2008)
[CrossRef]

N.  Liu, H.  Guo, L.  Fu, S.  Kaiser, H.  Schweizer, and H.  Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nat. Mater.  7, 31-37 (2008).
[CrossRef]

Gil, I.

J.D. Baena, J. Bonache, F. Martín, R. Marqués, F. Falcone, T. Lopetegi, M. A. G. Laso, J. García, I. Gil, M. Flores, and M. Sorolla, "Equivalent Circuit Models for Split Ring Resonators and Complementary Split Ring Resonators Coupled to Planar Transmisión Lines," IEEE Trans. Microwave Theory Tech. 53, 1451-1461, (2005).
[CrossRef]

Gmachl, C.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D.L. Sivco, and C. Gmachl, "Negative refraction in semiconductor Metamaterials," Nat. Mater. 6, 946-950 (2007).
[CrossRef] [PubMed]

Goncharov, Yu. G.

Guo, H.

N.  Liu, H.  Guo, L.  Fu, S.  Kaiser, H.  Schweizer, and H.  Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nat. Mater.  7, 31-37 (2008).
[CrossRef]

Hoffman, A. J.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D.L. Sivco, and C. Gmachl, "Negative refraction in semiconductor Metamaterials," Nat. Mater. 6, 946-950 (2007).
[CrossRef] [PubMed]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Howard, S. S.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D.L. Sivco, and C. Gmachl, "Negative refraction in semiconductor Metamaterials," Nat. Mater. 6, 946-950 (2007).
[CrossRef] [PubMed]

Kaiser, S.

N. Liu, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Plasmonic Building Blocks for Magnetic Molecules in Three-Dimensional Optical Metamaterials," Adv. Mater. 20, 3859-3865 (2008)
[CrossRef]

N. Liu, S. Kaiser, and H. Giessen, "Magnetoinductive and Electroinductive Coupling in Plasmonic Metamaterial Molecules," Adv. Mater. 20, 1-5 (2008).
[CrossRef]

N.  Liu, H.  Guo, L.  Fu, S.  Kaiser, H.  Schweizer, and H.  Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nat. Mater.  7, 31-37 (2008).
[CrossRef]

Kalinin, V. A.

E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, "Magneto-inductive waveguide," Electron. Lett. 38, 371-373 (2002).
[CrossRef]

Kalinin, V.A.

E. Shamonina, V.A. Kalinin, K. H. Ringhofer, and L. Solymar, "Magnetoinductive waves in one, two, and three dimensions," J. Appl. Phys. 92, 6252-6261 (2002).
[CrossRef]

Kuznetsov, S. A.

Laso, M. A. G.

J.D. Baena, J. Bonache, F. Martín, R. Marqués, F. Falcone, T. Lopetegi, M. A. G. Laso, J. García, I. Gil, M. Flores, and M. Sorolla, "Equivalent Circuit Models for Split Ring Resonators and Complementary Split Ring Resonators Coupled to Planar Transmisión Lines," IEEE Trans. Microwave Theory Tech. 53, 1451-1461, (2005).
[CrossRef]

Linden, S.

G.  Dolling, C.  Enkrich, M.  Wegener, C. M.  Soukoulis, and S.  Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science  312, 892-894 (2006).
[CrossRef] [PubMed]

Liu, N.

N.  Liu, H.  Guo, L.  Fu, S.  Kaiser, H.  Schweizer, and H.  Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nat. Mater.  7, 31-37 (2008).
[CrossRef]

N. Liu, S. Kaiser, and H. Giessen, "Magnetoinductive and Electroinductive Coupling in Plasmonic Metamaterial Molecules," Adv. Mater. 20, 1-5 (2008).
[CrossRef]

N. Liu, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Plasmonic Building Blocks for Magnetic Molecules in Three-Dimensional Optical Metamaterials," Adv. Mater. 20, 3859-3865 (2008)
[CrossRef]

Lopetegi, T.

J.D. Baena, J. Bonache, F. Martín, R. Marqués, F. Falcone, T. Lopetegi, M. A. G. Laso, J. García, I. Gil, M. Flores, and M. Sorolla, "Equivalent Circuit Models for Split Ring Resonators and Complementary Split Ring Resonators Coupled to Planar Transmisión Lines," IEEE Trans. Microwave Theory Tech. 53, 1451-1461, (2005).
[CrossRef]

R. Marqués, J. D. Baena, M. Beruete, F. Fakcone, T. Lopetegi, M. Sorolla, F. Martin, and J. Garcia, "Ab initio Analysis of Frequency Selective Surfaces Based on Conventional and Complementary Split Ring resonators," J. Opt. A: Pure and Appl. Opt. 7, S38-S43 (2005).
[CrossRef]

Malloy, K. J.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404-1-4 (2005).
[CrossRef] [PubMed]

Marqués, R.

M.  Beruete, F. Falcone, M. J. Freire, R. Marqués, and J. D. Baena, "Electroinductive Waves in Chains of Complementary Metamaterial Elements," Appl. Phys. Lett. 88, 083503-1-3 (2006).
[CrossRef]

M. Beruete, M. Sorolla, R. Marqués, J. D. Baena, and M. J. Freire, "Resonance and Cross-Polarization Effects in Conventional and Complementary Split Ring Resonator Periodic Screens," Electromag. 26, 247-260 (2006).
[CrossRef]

J.D. Baena, J. Bonache, F. Martín, R. Marqués, F. Falcone, T. Lopetegi, M. A. G. Laso, J. García, I. Gil, M. Flores, and M. Sorolla, "Equivalent Circuit Models for Split Ring Resonators and Complementary Split Ring Resonators Coupled to Planar Transmisión Lines," IEEE Trans. Microwave Theory Tech. 53, 1451-1461, (2005).
[CrossRef]

R. Marqués, J. D. Baena, M. Beruete, F. Fakcone, T. Lopetegi, M. Sorolla, F. Martin, and J. Garcia, "Ab initio Analysis of Frequency Selective Surfaces Based on Conventional and Complementary Split Ring resonators," J. Opt. A: Pure and Appl. Opt. 7, S38-S43 (2005).
[CrossRef]

R. Marqués, F. Mesa, J. Martel, and F. Medina "Comparative Analysis of Edge- and Broadside- Coupled Split Ring Resonators for Metamaterial Design. Theory and Experiments," IEEE Trans. Antennas Propag. 51, 2572 -2581 (2003).
[CrossRef]

R. Marqués, F. Medina, and R. R. El-Idrissi, "Role of Bianisotropy in Negative Permeability and Left-Handed Metamaterials," Phys. Rev. B 65, 144440 1-6 (2002).
[CrossRef]

Martel, J.

R. Marqués, F. Mesa, J. Martel, and F. Medina "Comparative Analysis of Edge- and Broadside- Coupled Split Ring Resonators for Metamaterial Design. Theory and Experiments," IEEE Trans. Antennas Propag. 51, 2572 -2581 (2003).
[CrossRef]

Martin, F.

R. Marqués, J. D. Baena, M. Beruete, F. Fakcone, T. Lopetegi, M. Sorolla, F. Martin, and J. Garcia, "Ab initio Analysis of Frequency Selective Surfaces Based on Conventional and Complementary Split Ring resonators," J. Opt. A: Pure and Appl. Opt. 7, S38-S43 (2005).
[CrossRef]

Martin, O. J. F.

P. Gay-Balmaz, and O. J. F. Martin, "Electromagnetic resonances in individual and coupled split-ring resonators," J. Appl. Phys. 92, 2929-2936 (2002).
[CrossRef]

Martín, F.

J.D. Baena, J. Bonache, F. Martín, R. Marqués, F. Falcone, T. Lopetegi, M. A. G. Laso, J. García, I. Gil, M. Flores, and M. Sorolla, "Equivalent Circuit Models for Split Ring Resonators and Complementary Split Ring Resonators Coupled to Planar Transmisión Lines," IEEE Trans. Microwave Theory Tech. 53, 1451-1461, (2005).
[CrossRef]

Medina, F.

R. Marqués, F. Mesa, J. Martel, and F. Medina "Comparative Analysis of Edge- and Broadside- Coupled Split Ring Resonators for Metamaterial Design. Theory and Experiments," IEEE Trans. Antennas Propag. 51, 2572 -2581 (2003).
[CrossRef]

R. Marqués, F. Medina, and R. R. El-Idrissi, "Role of Bianisotropy in Negative Permeability and Left-Handed Metamaterials," Phys. Rev. B 65, 144440 1-6 (2002).
[CrossRef]

Mesa, F.

R. Marqués, F. Mesa, J. Martel, and F. Medina "Comparative Analysis of Edge- and Broadside- Coupled Split Ring Resonators for Metamaterial Design. Theory and Experiments," IEEE Trans. Antennas Propag. 51, 2572 -2581 (2003).
[CrossRef]

Narimanov, E. E.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D.L. Sivco, and C. Gmachl, "Negative refraction in semiconductor Metamaterials," Nat. Mater. 6, 946-950 (2007).
[CrossRef] [PubMed]

Navarro-Cía, M.

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Osgood, R. M.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404-1-4 (2005).
[CrossRef] [PubMed]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Panoiu, N. C.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404-1-4 (2005).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Podolskiy, V. A.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D.L. Sivco, and C. Gmachl, "Negative refraction in semiconductor Metamaterials," Nat. Mater. 6, 946-950 (2007).
[CrossRef] [PubMed]

Ringhofer, K. H.

E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, "Magneto-inductive waveguide," Electron. Lett. 38, 371-373 (2002).
[CrossRef]

E. Shamonina, V.A. Kalinin, K. H. Ringhofer, and L. Solymar, "Magnetoinductive waves in one, two, and three dimensions," J. Appl. Phys. 92, 6252-6261 (2002).
[CrossRef]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Schultz, S.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Schweizer, H.

N. Liu, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Plasmonic Building Blocks for Magnetic Molecules in Three-Dimensional Optical Metamaterials," Adv. Mater. 20, 3859-3865 (2008)
[CrossRef]

N.  Liu, H.  Guo, L.  Fu, S.  Kaiser, H.  Schweizer, and H.  Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nat. Mater.  7, 31-37 (2008).
[CrossRef]

Shamonina, E.

E. Shamonina and L. Solymar, "Magneto-inductive waves supported by metamaterial elements: components for a one-dimensional waveguide, " J. Phys. D 37, 362-367 (2004).
[CrossRef]

M. C. K. Wiltshire, E. Shamonina, I. R. Young, and L. Solymar, "Dispersion characteristics of magnetoinductive waves: comparison between theory and experiment," Electron. Lett. 39, 215-217 (2003).
[CrossRef]

E. Shamonina, V.A. Kalinin, K. H. Ringhofer, and L. Solymar, "Magnetoinductive waves in one, two, and three dimensions," J. Appl. Phys. 92, 6252-6261 (2002).
[CrossRef]

E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, "Magneto-inductive waveguide," Electron. Lett. 38, 371-373 (2002).
[CrossRef]

Sivco, D.L.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D.L. Sivco, and C. Gmachl, "Negative refraction in semiconductor Metamaterials," Nat. Mater. 6, 946-950 (2007).
[CrossRef] [PubMed]

Smith, D. R.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Solymar, L.

E. Shamonina and L. Solymar, "Magneto-inductive waves supported by metamaterial elements: components for a one-dimensional waveguide, " J. Phys. D 37, 362-367 (2004).
[CrossRef]

M. C. K. Wiltshire, E. Shamonina, I. R. Young, and L. Solymar, "Dispersion characteristics of magnetoinductive waves: comparison between theory and experiment," Electron. Lett. 39, 215-217 (2003).
[CrossRef]

E. Shamonina, V.A. Kalinin, K. H. Ringhofer, and L. Solymar, "Magnetoinductive waves in one, two, and three dimensions," J. Appl. Phys. 92, 6252-6261 (2002).
[CrossRef]

E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, "Magneto-inductive waveguide," Electron. Lett. 38, 371-373 (2002).
[CrossRef]

Sorolla, M.

M. Aznabet, M. Navarro-Cía, S. A. Kuznetsov, A. V. Gelfand, N. I. Fedorinina, Yu. G. Goncharov, M. Beruete, O. El Mrabet, and M. Sorolla, "Polypropylene-substrate-based SRR- and CSRR-metasurfaces for submillimeter waves," Opt. Express 16, 18312-18319 (2008).
[CrossRef] [PubMed]

M. Beruete, M. Sorolla, R. Marqués, J. D. Baena, and M. J. Freire, "Resonance and Cross-Polarization Effects in Conventional and Complementary Split Ring Resonator Periodic Screens," Electromag. 26, 247-260 (2006).
[CrossRef]

M. Beruete, M. Sorolla, and I. Campillo, "Left-handed extraordinary optical transmission through a photonic crystal of subwavelength hole arrays," Opt. Express 14, 5445-5455 (2006).
[CrossRef] [PubMed]

J.D. Baena, J. Bonache, F. Martín, R. Marqués, F. Falcone, T. Lopetegi, M. A. G. Laso, J. García, I. Gil, M. Flores, and M. Sorolla, "Equivalent Circuit Models for Split Ring Resonators and Complementary Split Ring Resonators Coupled to Planar Transmisión Lines," IEEE Trans. Microwave Theory Tech. 53, 1451-1461, (2005).
[CrossRef]

R. Marqués, J. D. Baena, M. Beruete, F. Fakcone, T. Lopetegi, M. Sorolla, F. Martin, and J. Garcia, "Ab initio Analysis of Frequency Selective Surfaces Based on Conventional and Complementary Split Ring resonators," J. Opt. A: Pure and Appl. Opt. 7, S38-S43 (2005).
[CrossRef]

Soukoulis, C. M.

G.  Dolling, C.  Enkrich, M.  Wegener, C. M.  Soukoulis, and S.  Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science  312, 892-894 (2006).
[CrossRef] [PubMed]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Veselago, V. G.

V. G. Veselago, "The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Wasserman, D.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D.L. Sivco, and C. Gmachl, "Negative refraction in semiconductor Metamaterials," Nat. Mater. 6, 946-950 (2007).
[CrossRef] [PubMed]

Wegener, M.

G.  Dolling, C.  Enkrich, M.  Wegener, C. M.  Soukoulis, and S.  Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science  312, 892-894 (2006).
[CrossRef] [PubMed]

Wiltshire, M. C. K.

M. C. K. Wiltshire, E. Shamonina, I. R. Young, and L. Solymar, "Dispersion characteristics of magnetoinductive waves: comparison between theory and experiment," Electron. Lett. 39, 215-217 (2003).
[CrossRef]

Young, I. R.

M. C. K. Wiltshire, E. Shamonina, I. R. Young, and L. Solymar, "Dispersion characteristics of magnetoinductive waves: comparison between theory and experiment," Electron. Lett. 39, 215-217 (2003).
[CrossRef]

Zhang, S.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404-1-4 (2005).
[CrossRef] [PubMed]

Adv. Mater. (2)

N. Liu, S. Kaiser, and H. Giessen, "Magnetoinductive and Electroinductive Coupling in Plasmonic Metamaterial Molecules," Adv. Mater. 20, 1-5 (2008).
[CrossRef]

N. Liu, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Plasmonic Building Blocks for Magnetic Molecules in Three-Dimensional Optical Metamaterials," Adv. Mater. 20, 3859-3865 (2008)
[CrossRef]

Appl. Phys. Lett. (1)

M.  Beruete, F. Falcone, M. J. Freire, R. Marqués, and J. D. Baena, "Electroinductive Waves in Chains of Complementary Metamaterial Elements," Appl. Phys. Lett. 88, 083503-1-3 (2006).
[CrossRef]

Electromag. (1)

M. Beruete, M. Sorolla, R. Marqués, J. D. Baena, and M. J. Freire, "Resonance and Cross-Polarization Effects in Conventional and Complementary Split Ring Resonator Periodic Screens," Electromag. 26, 247-260 (2006).
[CrossRef]

Electron. Lett. (2)

E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, "Magneto-inductive waveguide," Electron. Lett. 38, 371-373 (2002).
[CrossRef]

M. C. K. Wiltshire, E. Shamonina, I. R. Young, and L. Solymar, "Dispersion characteristics of magnetoinductive waves: comparison between theory and experiment," Electron. Lett. 39, 215-217 (2003).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

R. Marqués, F. Mesa, J. Martel, and F. Medina "Comparative Analysis of Edge- and Broadside- Coupled Split Ring Resonators for Metamaterial Design. Theory and Experiments," IEEE Trans. Antennas Propag. 51, 2572 -2581 (2003).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J.D. Baena, J. Bonache, F. Martín, R. Marqués, F. Falcone, T. Lopetegi, M. A. G. Laso, J. García, I. Gil, M. Flores, and M. Sorolla, "Equivalent Circuit Models for Split Ring Resonators and Complementary Split Ring Resonators Coupled to Planar Transmisión Lines," IEEE Trans. Microwave Theory Tech. 53, 1451-1461, (2005).
[CrossRef]

J. Appl. Phys. (2)

P. Gay-Balmaz, and O. J. F. Martin, "Electromagnetic resonances in individual and coupled split-ring resonators," J. Appl. Phys. 92, 2929-2936 (2002).
[CrossRef]

E. Shamonina, V.A. Kalinin, K. H. Ringhofer, and L. Solymar, "Magnetoinductive waves in one, two, and three dimensions," J. Appl. Phys. 92, 6252-6261 (2002).
[CrossRef]

J. Opt. A: Pure and Appl. Opt. (1)

R. Marqués, J. D. Baena, M. Beruete, F. Fakcone, T. Lopetegi, M. Sorolla, F. Martin, and J. Garcia, "Ab initio Analysis of Frequency Selective Surfaces Based on Conventional and Complementary Split Ring resonators," J. Opt. A: Pure and Appl. Opt. 7, S38-S43 (2005).
[CrossRef]

J. Phys. D (1)

E. Shamonina and L. Solymar, "Magneto-inductive waves supported by metamaterial elements: components for a one-dimensional waveguide, " J. Phys. D 37, 362-367 (2004).
[CrossRef]

Nat. Mater. (2)

N.  Liu, H.  Guo, L.  Fu, S.  Kaiser, H.  Schweizer, and H.  Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nat. Mater.  7, 31-37 (2008).
[CrossRef]

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D.L. Sivco, and C. Gmachl, "Negative refraction in semiconductor Metamaterials," Nat. Mater. 6, 946-950 (2007).
[CrossRef] [PubMed]

Opt. Express (2)

Phys. Rev. B (1)

R. Marqués, F. Medina, and R. R. El-Idrissi, "Role of Bianisotropy in Negative Permeability and Left-Handed Metamaterials," Phys. Rev. B 65, 144440 1-6 (2002).
[CrossRef]

Phys. Rev. Lett. (2)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404-1-4 (2005).
[CrossRef] [PubMed]

Science (1)

G.  Dolling, C.  Enkrich, M.  Wegener, C. M.  Soukoulis, and S.  Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science  312, 892-894 (2006).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, "The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Other (4)

B. A. Munk, Frequency Selective Surfaces: Theory and Design, John Wiley, New York, 2000.

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marqués, F. Martín, and M. Sorolla, "Babinet principle applied to metasurface and metamaterial design," Phys. Rev. Lett. 93, 197401-1-4 (2004).
[CrossRef] [PubMed]

R. Marqués, F. Martín, and M. Sorolla, Metamaterials with Negative Parameters: Theory, Design, and Microwave Applications (John Wiley, New York, 2008).

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, Jr., and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608-1-7 (2004).
[CrossRef]

Supplementary Material (2)

» Media 1: MPG (427 KB)     
» Media 2: MPG (426 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

(a) Schematics of: (left) single CSRR and (right) periodic structure composed of CSRRs metasurfaces. The transverse periodicity are equal ax = ay = 8 mm and dz = 2.145 mm (dz = 0.03λ); the parameters of the unit cell of CSRR are c = d = 0.4 mm, rext = 3.5 mm. (b) Picture of the fabricated stacked CSRR-metasurfaces with the aforementioned parameters.

Fig. 2.
Fig. 2.

(a) Infinite structure dispersion diagram for E-field along x-axis and four different longitudinal lattices. Single-frame excerpts from video recordings of the Ex evolution for stacked CSRR-metasurfaces at 5.3 GHz with dz = 2.145 mm in the xz -plane (Media 1) (b) and yz -plane (Media 2) (c).

Fig. 3.
Fig. 3.

Retrieved constitutive parameters (a) real part of the dielectric permittivity, (b) imaginary part, (c) real part of the magnetic permeability, (d) imaginary part, (e) real part of the refraction index and (f) imaginary part.

Fig. 4.
Fig. 4.

Measurement for several stacked CSRRs metasurfaces of the transmitted amplitude (a) and phase (b) for the structure described in Fig.1 excited as indicated in the amplitude inset.

Equations (4)

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ω 2 ω 0 2 = ( 1 2 C M C + 2 C M cos ( k a ) ) 1
ω 2 ω 0 2 = ( 1 + 2 M L cos ( k a ) ) 1
C M K M
C + 2 C M K L

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