Abstract

By combining experimental and theoretical efforts we study the optical properties of single-layer, double split-ring resonators at oblique incidences for terahertz frequencies and reveal their angular dependent effective properties. Contrary to what is usually anticipated, for incidence angles deviating from normal we do not observe any significant dispersion in the effective permeability. Effective properties are dominated instead by a strong dispersion in the effective permittivity, causing also the wavenumber in the medium to be large. The structure is shown to possess almost invariant effective properties for oblique incidences.

© 2009 Optical Society of America

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2009 (4)

B. Lahiri, A. Z. Khokhar, R. M. De La Rue, S. G. McMeekin, and N. P. Johnson, “Asymmetric split ring resonators for optical sensing of organic materials,” Opt. Express 17, 1107-1115 (2009).
[CrossRef] [PubMed]

M. C. Gwinner, E. Koroknay, L. Fu, P. Patoka, W. Kandulski, M. Giersig, and H. Giessen, “Periodic large-area metallic split-ring resonator metamaterial fabrication based on shadow nanosphere lithography,” Small 5, 400-406 (2009).
[CrossRef] [PubMed]

Z. Li, K. Aydin, and E. Ozbay, “Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coefficients,” Phys. Rev. E 79, 026610 (2009).
[CrossRef]

F. J. Rodriguez-Fortuno, C. Garcia-Meca, R. Ortuno, J. Marti, and A. Martinez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79, 075103 (2009).
[CrossRef]

2008 (7)

2007 (6)

J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic and electric excitations in split ring resonators,” Opt. Express 15, 17881-17890 (2007).
[CrossRef] [PubMed]

A. W. Clark, A. K. Sheridan, A. Glidle, D. R. S. Cumming, and J. M. Cooper, “Tuneable visible resonances in crescent shaped nano-split-ring resonators,” Appl. Phys. Lett. 91, 093109 (2007).
[CrossRef]

C. M. Soukoulis, S. Linden, and M. Wegener, “Physics: negative refractive index at optical wavelengths,” Science 315, 47-49 (2007).
[CrossRef] [PubMed]

V. M. Shalaev, “Optical negative-index metamaterials,” Nature Photon. 1, 41-48 (2007).
[CrossRef]

C. Rockstuhl, T. Zentgraf, E. Pshenay-Severin, J. Petschulat, A. Chipouline, J. Kuhl, T. Pertsch, H. Giessen, and F. Lederer, “The origin of magnetic polarizability in metamaterials at optical frequencies-an electrodynamic approach,” Opt. Express 15, 8871-8883 (2007).
[CrossRef] [PubMed]

T. Driscoll, D. N. Basov, W. J. Padilla, J. J. Mock, and D. R. Smith, “Electromagnetic characterization of planar metamaterials by oblique angle spectroscopic measurements,” Phys. Rev. B 75, 115114 (2007).
[CrossRef]

2006 (1)

2005 (4)

X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E 71, 046610 (2005).
[CrossRef]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett. 30, 3198-3200 (2005).
[CrossRef] [PubMed]

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

2004 (2)

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

2002 (1)

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
[CrossRef] [PubMed]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (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]

1997 (1)

1990 (1)

Aydin, K.

Z. Li, K. Aydin, and E. Ozbay, “Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coefficients,” Phys. Rev. E 79, 026610 (2009).
[CrossRef]

Azad, A. K.

Basov, D. N.

T. Driscoll, D. N. Basov, W. J. Padilla, J. J. Mock, and D. R. Smith, “Electromagnetic characterization of planar metamaterials by oblique angle spectroscopic measurements,” Phys. Rev. B 75, 115114 (2007).
[CrossRef]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Boltasseva, A.

A. Boltasseva and V. M. Shalaev, “Fabrication of optical negative-index metamaterials: Recent advances and outlook,” Metamaterials 1, 1-17 (2008).
[CrossRef]

Brener, I.

Burger, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Cai, W.

Chen, X.

X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E 71, 046610 (2005).
[CrossRef]

Chettiar, U. K.

Chipouline, A.

Clark, A. W.

A. W. Clark, A. K. Sheridan, A. Glidle, D. R. S. Cumming, and J. M. Cooper, “Tuneable visible resonances in crescent shaped nano-split-ring resonators,” Appl. Phys. Lett. 91, 093109 (2007).
[CrossRef]

Cooper, J. M.

A. W. Clark, A. K. Sheridan, A. Glidle, D. R. S. Cumming, and J. M. Cooper, “Tuneable visible resonances in crescent shaped nano-split-ring resonators,” Appl. Phys. Lett. 91, 093109 (2007).
[CrossRef]

Cumming, D. R. S.

A. W. Clark, A. K. Sheridan, A. Glidle, D. R. S. Cumming, and J. M. Cooper, “Tuneable visible resonances in crescent shaped nano-split-ring resonators,” Appl. Phys. Lett. 91, 093109 (2007).
[CrossRef]

Dai, J.

De La Rue, R. M.

de Lustrac, A.

Dolling, G.

Dorfmüller, J.

Drachev, V. P.

Driscoll, T.

T. Driscoll, D. N. Basov, W. J. Padilla, J. J. Mock, and D. R. Smith, “Electromagnetic characterization of planar metamaterials by oblique angle spectroscopic measurements,” Phys. Rev. B 75, 115114 (2007).
[CrossRef]

Economou, E. N.

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

Enkrich, C.

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett. 30, 3198-3200 (2005).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Etrich, C.

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, “Terahertz magnetic response from artificial materials,” Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Fattinger, Ch.

Fu, L.

M. C. Gwinner, E. Koroknay, L. Fu, P. Patoka, W. Kandulski, M. Giersig, and H. Giessen, “Periodic large-area metallic split-ring resonator metamaterial fabrication based on shadow nanosphere lithography,” Small 5, 400-406 (2009).
[CrossRef] [PubMed]

Gadot, F.

Garcia-Meca, C.

F. J. Rodriguez-Fortuno, C. Garcia-Meca, R. Ortuno, J. Marti, and A. Martinez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79, 075103 (2009).
[CrossRef]

Giersig, M.

M. C. Gwinner, E. Koroknay, L. Fu, P. Patoka, W. Kandulski, M. Giersig, and H. Giessen, “Periodic large-area metallic split-ring resonator metamaterial fabrication based on shadow nanosphere lithography,” Small 5, 400-406 (2009).
[CrossRef] [PubMed]

Giessen, H.

Glidle, A.

A. W. Clark, A. K. Sheridan, A. Glidle, D. R. S. Cumming, and J. M. Cooper, “Tuneable visible resonances in crescent shaped nano-split-ring resonators,” Appl. Phys. Lett. 91, 093109 (2007).
[CrossRef]

Grischkowsky, D.

Grzegorczyk, T. M.

X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E 71, 046610 (2005).
[CrossRef]

Gwinner, M. C.

M. C. Gwinner, E. Koroknay, L. Fu, P. Patoka, W. Kandulski, M. Giersig, and H. Giessen, “Periodic large-area metallic split-ring resonator metamaterial fabrication based on shadow nanosphere lithography,” Small 5, 400-406 (2009).
[CrossRef] [PubMed]

Han, J.

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]

Johnson, N. P.

Kafesaki, M.

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

Kandulski, W.

M. C. Gwinner, E. Koroknay, L. Fu, P. Patoka, W. Kandulski, M. Giersig, and H. Giessen, “Periodic large-area metallic split-ring resonator metamaterial fabrication based on shadow nanosphere lithography,” Small 5, 400-406 (2009).
[CrossRef] [PubMed]

Kanté, B.

Katsarakis, N.

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

Keiding, S.

Kern, K.

Khokhar, A. Z.

Kildishev, A. V.

Kong, J. A.

X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E 71, 046610 (2005).
[CrossRef]

Koroknay, E.

M. C. Gwinner, E. Koroknay, L. Fu, P. Patoka, W. Kandulski, M. Giersig, and H. Giessen, “Periodic large-area metallic split-ring resonator metamaterial fabrication based on shadow nanosphere lithography,” Small 5, 400-406 (2009).
[CrossRef] [PubMed]

Koschny, T.

J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic and electric excitations in split ring resonators,” Opt. Express 15, 17881-17890 (2007).
[CrossRef] [PubMed]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

Koschny, Th.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Kuhl, J.

Lahiri, B.

Lederer, F.

Li, L.

Li, Z.

Z. Li, K. Aydin, and E. Ozbay, “Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coefficients,” Phys. Rev. E 79, 026610 (2009).
[CrossRef]

Linden, S.

C. M. Soukoulis, S. Linden, and M. Wegener, “Physics: negative refractive index at optical wavelengths,” Science 315, 47-49 (2007).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett. 30, 3198-3200 (2005).
[CrossRef] [PubMed]

Lourtioz, J.-M.

Markoš, P.

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Marti, J.

F. J. Rodriguez-Fortuno, C. Garcia-Meca, R. Ortuno, J. Marti, and A. Martinez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79, 075103 (2009).
[CrossRef]

Martinez, A.

F. J. Rodriguez-Fortuno, C. Garcia-Meca, R. Ortuno, J. Marti, and A. Martinez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79, 075103 (2009).
[CrossRef]

McMeekin, S. G.

Menzel, C.

C. Menzel, C. Rockstuhl, T. Paul, T. Pertsch, and F. Lederer, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77, 195328 (2008).
[CrossRef]

Meyrath, T. P.

Mock, J. J.

T. Driscoll, D. N. Basov, W. J. Padilla, J. J. Mock, and D. R. Smith, “Electromagnetic characterization of planar metamaterials by oblique angle spectroscopic measurements,” Phys. Rev. B 75, 115114 (2007).
[CrossRef]

O'Hara, J. F.

Ortuno, R.

F. J. Rodriguez-Fortuno, C. Garcia-Meca, R. Ortuno, J. Marti, and A. Martinez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79, 075103 (2009).
[CrossRef]

Ozbay, E.

Z. Li, K. Aydin, and E. Ozbay, “Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coefficients,” Phys. Rev. E 79, 026610 (2009).
[CrossRef]

Padilla, W. J.

T. Driscoll, D. N. Basov, W. J. Padilla, J. J. Mock, and D. R. Smith, “Electromagnetic characterization of planar metamaterials by oblique angle spectroscopic measurements,” Phys. Rev. B 75, 115114 (2007).
[CrossRef]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Patoka, P.

M. C. Gwinner, E. Koroknay, L. Fu, P. Patoka, W. Kandulski, M. Giersig, and H. Giessen, “Periodic large-area metallic split-ring resonator metamaterial fabrication based on shadow nanosphere lithography,” Small 5, 400-406 (2009).
[CrossRef] [PubMed]

Paul, T.

C. Menzel, C. Rockstuhl, T. Paul, T. Pertsch, and F. Lederer, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77, 195328 (2008).
[CrossRef]

Pendry, J. B.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

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]

Pertsch, T.

Petschulat, J.

Pshenay-Severin, E.

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]

Rockstuhl, C.

Rodriguez-Fortuno, F. J.

F. J. Rodriguez-Fortuno, C. Garcia-Meca, R. Ortuno, J. Marti, and A. Martinez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79, 075103 (2009).
[CrossRef]

Sarychev, A. K.

Schmidt, F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Schultz, S.

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Shalaev, V. M.

A. Boltasseva and V. M. Shalaev, “Fabrication of optical negative-index metamaterials: Recent advances and outlook,” Metamaterials 1, 1-17 (2008).
[CrossRef]

V. M. Shalaev, “Optical negative-index metamaterials,” Nature Photon. 1, 41-48 (2007).
[CrossRef]

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Sheridan, A. K.

A. W. Clark, A. K. Sheridan, A. Glidle, D. R. S. Cumming, and J. M. Cooper, “Tuneable visible resonances in crescent shaped nano-split-ring resonators,” Appl. Phys. Lett. 91, 093109 (2007).
[CrossRef]

Singh, R.

Smirnova, E.

Smith, D. R.

T. Driscoll, D. N. Basov, W. J. Padilla, J. J. Mock, and D. R. Smith, “Electromagnetic characterization of planar metamaterials by oblique angle spectroscopic measurements,” Phys. Rev. B 75, 115114 (2007).
[CrossRef]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Soukoulis, C. M.

C. M. Soukoulis, S. Linden, and M. Wegener, “Physics: negative refractive index at optical wavelengths,” Science 315, 47-49 (2007).
[CrossRef] [PubMed]

J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic and electric excitations in split ring resonators,” Opt. Express 15, 17881-17890 (2007).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett. 30, 3198-3200 (2005).
[CrossRef] [PubMed]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

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]

Taylor, A. J.

van Exter, M.

Vier, D. C.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Vogelgesang, R.

Wegener, M.

C. M. Soukoulis, S. Linden, and M. Wegener, “Physics: negative refractive index at optical wavelengths,” Science 315, 47-49 (2007).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett. 30, 3198-3200 (2005).
[CrossRef] [PubMed]

Wu, B.-I.

X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E 71, 046610 (2005).
[CrossRef]

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, “Terahertz magnetic response from artificial materials,” Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Yuan, H.-K.

Zentgraf, T.

Zhang, W.

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, “Terahertz magnetic response from artificial materials,” Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Zhou, J.

Zhou, J. F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett. 30, 3198-3200 (2005).
[CrossRef] [PubMed]

Zschiedrich, L.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

A. W. Clark, A. K. Sheridan, A. Glidle, D. R. S. Cumming, and J. M. Cooper, “Tuneable visible resonances in crescent shaped nano-split-ring resonators,” Appl. Phys. Lett. 91, 093109 (2007).
[CrossRef]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (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]

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

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

Metamaterials (1)

A. Boltasseva and V. M. Shalaev, “Fabrication of optical negative-index metamaterials: Recent advances and outlook,” Metamaterials 1, 1-17 (2008).
[CrossRef]

Nature Photon. (1)

V. M. Shalaev, “Optical negative-index metamaterials,” Nature Photon. 1, 41-48 (2007).
[CrossRef]

Opt. Express (7)

Opt. Lett. (4)

Phys. Rev. B (4)

T. Driscoll, D. N. Basov, W. J. Padilla, J. J. Mock, and D. R. Smith, “Electromagnetic characterization of planar metamaterials by oblique angle spectroscopic measurements,” Phys. Rev. B 75, 115114 (2007).
[CrossRef]

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

C. Menzel, C. Rockstuhl, T. Paul, T. Pertsch, and F. Lederer, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77, 195328 (2008).
[CrossRef]

F. J. Rodriguez-Fortuno, C. Garcia-Meca, R. Ortuno, J. Marti, and A. Martinez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79, 075103 (2009).
[CrossRef]

Phys. Rev. E (2)

X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E 71, 046610 (2005).
[CrossRef]

Z. Li, K. Aydin, and E. Ozbay, “Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coefficients,” Phys. Rev. E 79, 026610 (2009).
[CrossRef]

Phys. Rev. Lett. (2)

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Science (3)

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
[CrossRef] [PubMed]

C. M. Soukoulis, S. Linden, and M. Wegener, “Physics: negative refractive index at optical wavelengths,” Science 315, 47-49 (2007).
[CrossRef] [PubMed]

Small (1)

M. C. Gwinner, E. Koroknay, L. Fu, P. Patoka, W. Kandulski, M. Giersig, and H. Giessen, “Periodic large-area metallic split-ring resonator metamaterial fabrication based on shadow nanosphere lithography,” Small 5, 400-406 (2009).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Sketch of the geometry. (a) Periodic arrangement of the DSRR together with the relevant propagation directions and polarization states. (b) Single DSRR with relevant dimensions.

Fig. 2
Fig. 2

Complex amplitude for the simulated (solid curves) and the measured transmission (dotted lines). The modulus ((a) TE polarization and (b) TM polarization) and the phases ((c) TE polarization and (d) TM polarization) are shown. The different lines correspond to different angles of incidence: blue, 0 deg ; red, 15; black, 30; cyan, 45; magenta, 60. An arbitrary offset was added to each data to separate them in the figure. The frequency resolution of the experimental data is 3.6 GHz and 11.5 GHz for the numerical data.

Fig. 3
Fig. 3

Real and imaginary parts of the effective permittivity and permeability as a function of the frequency and the angle of incidence. (a)–(d) TE polarization, (e)–(h) TM polarization. The effective parameters were retrieved from the numerically obtained complex reflection and transmission coefficients. Note that the Lorentzian resonances in the effective permittivity have very large quality factors, whereas the effective permeability is almost unaffected for all angles of incidence.

Fig. 4
Fig. 4

Real and imaginary parts of the propagation constant k z as a function of the frequency and the angle of incidence as retrieved from the numerically obtained complex reflection and transmission coefficients. (a), (b) TE polarization, (c), (d) TM polarization.

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