Abstract

Experimental investigations of the microscopic electric and in particular the magnetic near-fields in metamaterials remain highly challenging and current studies rely mostly on numerical simulations. Here we report a terahertz near-field imaging approach which provides spatially resolved measurements of the amplitude, phase and polarization of the electric field from which we extract the microscopic magnetic near-field signatures in a planar metamaterial constructed of split-ring resonators (SRRs). In addition to studying the fundamental resonances of an individual double SRR unit we further investigate the interaction with neighboring elements.

© 2009 Optical Society of America

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2008 (8)

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

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature (London) 455, 376-379 (2008).
[CrossRef] [PubMed]

R. Esteban, R. Vogelgesang, J. Dorfmüller, A. Dmitriev, C. Rockstuhl, C. Etrich, and K. Kern, "Direct Near-Field Optical Imaging of Higher Order Plasmonic Resonances," Nano Lett. 8, 3155-3159 (2008)
[CrossRef] [PubMed]

T. Zentgraf, J. Dorfmüller, C. Rockstuhl, C. Etrich, R. Vogelgesang, K. Kern, T. Pertsch, F. Lederer, and H. Giessen, "Amplitude-and phase-resolved optical near fields of split-ring-resonator-based metamaterials," Opt. Lett. 33, 848-850 (2008).
[CrossRef] [PubMed]

G. Acuna, S. F. Heucke, F. Kuchler, H.-T. Chen, A. J. Taylor, and R. Kersting, "Surface plasmons in terahertz metamaterials," Opt. Express 16, 18745-18751 (2008).
[CrossRef]

A. J. L. Adam, J. M. Brok, M. A. Seo, K. J. Ahn, D. S. Kim, J. H. Kang, Q. H. Park, M. Nagel, and P. C. M. Planken, "Advanced terahertz electric near-field measurements at sub-wavelength diameter metallic apertures," Opt. Express 16, 7407-7417 (2008).
[CrossRef] [PubMed]

A. Bitzer and M. Walther, "Terahertz near-field imaging of metallic subwavelength holes and hole arrays," Appl. Phys. Lett. 92, 231101 (2008).
[CrossRef]

A. Bitzer, H. Helm, and M. Walther, "Beam-profiling and wavefront-sensing of thz pulses at the focus of a substrate-lens," IEEE J. Sel. Top. Quantum Electron 14, 476-481 (2008).
[CrossRef]

2007 (4)

N. Liu, H. C. Guo, L. W. Fu, H. Schweizer, S. Kaiser, and H. Giessen, "Electromagnetic resonances in single and double split-ring resonator metamaterials in the near infrared spectral region," Phys. Status Solidi B 244, 1251-1255 (2007).
[CrossRef]

M. A. Seo, A. J. L. Adam, J. H. Kang, J. W. Lee, S. C. Jeoung, Q. H. Park, P. C. M. Planken, and D. S. Kim, "Fourier-transform terahertz near-field imaging of one-dimensional slit arrays: mapping of electric-field-, magnetic-field-, and poynting vectors," Opt. Express 15, 11781-11789 (2007).
[CrossRef] [PubMed]

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative refractive index at optical wavelengths," Science 315, 47-49 (2007).
[CrossRef] [PubMed]

V. M. Shalaev, "Optical negative-index metamaterials," Nat. Photonics 1,41-48 (2007).
[CrossRef]

2006 (1)

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

2005 (2)

S. Zhang, W. J. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95, 203901 (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, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

2002 (1)

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

2000 (3)

R. Hillenbrand and F. Keilmann, "Complex Optical Constants on a Subwavelength Scale," Phys. Rev. Lett. 85, 3029-3032 (2000).
[CrossRef] [PubMed]

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]

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]

1990 (1)

1987 (1)

F. E. Doany, D. Grischkowsky, and C. C. Chi, "Carrier lifetime versus ion-implantation dose in silicon on sapphire," Appl. Phys. Lett. 50, 460-462 (1987).
[CrossRef]

1985 (1)

1968 (1)

V. G. Veselago, "Electrodynamics of substances with simultaneously negative values of sigma and mu," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Acuna, G.

Adam, A. J. L.

Ahn, K. J.

Alexander, R. W.

Bartal, G.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature (London) 455, 376-379 (2008).
[CrossRef] [PubMed]

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

Bell, R. J.

Bitzer, A.

A. Bitzer and M. Walther, "Terahertz near-field imaging of metallic subwavelength holes and hole arrays," Appl. Phys. Lett. 92, 231101 (2008).
[CrossRef]

A. Bitzer, H. Helm, and M. Walther, "Beam-profiling and wavefront-sensing of thz pulses at the focus of a substrate-lens," IEEE J. Sel. Top. Quantum Electron 14, 476-481 (2008).
[CrossRef]

Brok, J. M.

Brueck, S. R. J.

S. Zhang, W. J. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

Burger, S.

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

Chen, H.-T.

Chi, C. C.

F. E. Doany, D. Grischkowsky, and C. C. Chi, "Carrier lifetime versus ion-implantation dose in silicon on sapphire," Appl. Phys. Lett. 50, 460-462 (1987).
[CrossRef]

Dmitriev, A.

R. Esteban, R. Vogelgesang, J. Dorfmüller, A. Dmitriev, C. Rockstuhl, C. Etrich, and K. Kern, "Direct Near-Field Optical Imaging of Higher Order Plasmonic Resonances," Nano Lett. 8, 3155-3159 (2008)
[CrossRef] [PubMed]

Doany, F. E.

F. E. Doany, D. Grischkowsky, and C. C. Chi, "Carrier lifetime versus ion-implantation dose in silicon on sapphire," Appl. Phys. Lett. 50, 460-462 (1987).
[CrossRef]

Dorfmüller, J.

R. Esteban, R. Vogelgesang, J. Dorfmüller, A. Dmitriev, C. Rockstuhl, C. Etrich, and K. Kern, "Direct Near-Field Optical Imaging of Higher Order Plasmonic Resonances," Nano Lett. 8, 3155-3159 (2008)
[CrossRef] [PubMed]

T. Zentgraf, J. Dorfmüller, C. Rockstuhl, C. Etrich, R. Vogelgesang, K. Kern, T. Pertsch, F. Lederer, and H. Giessen, "Amplitude-and phase-resolved optical near fields of split-ring-resonator-based metamaterials," Opt. Lett. 33, 848-850 (2008).
[CrossRef] [PubMed]

Enkrich, C.

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

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Esteban, R.

R. Esteban, R. Vogelgesang, J. Dorfmüller, A. Dmitriev, C. Rockstuhl, C. Etrich, and K. Kern, "Direct Near-Field Optical Imaging of Higher Order Plasmonic Resonances," Nano Lett. 8, 3155-3159 (2008)
[CrossRef] [PubMed]

Etrich, C.

T. Zentgraf, J. Dorfmüller, C. Rockstuhl, C. Etrich, R. Vogelgesang, K. Kern, T. Pertsch, F. Lederer, and H. Giessen, "Amplitude-and phase-resolved optical near fields of split-ring-resonator-based metamaterials," Opt. Lett. 33, 848-850 (2008).
[CrossRef] [PubMed]

R. Esteban, R. Vogelgesang, J. Dorfmüller, A. Dmitriev, C. Rockstuhl, C. Etrich, and K. Kern, "Direct Near-Field Optical Imaging of Higher Order Plasmonic Resonances," Nano Lett. 8, 3155-3159 (2008)
[CrossRef] [PubMed]

Fan, W. J.

S. Zhang, W. J. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

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, C.

Frauenglass, A.

S. Zhang, W. J. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

Fu, L. W.

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

N. Liu, H. C. Guo, L. W. Fu, H. Schweizer, S. Kaiser, and H. Giessen, "Electromagnetic resonances in single and double split-ring resonator metamaterials in the near infrared spectral region," Phys. Status Solidi B 244, 1251-1255 (2007).
[CrossRef]

Genov, D. A.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature (London) 455, 376-379 (2008).
[CrossRef] [PubMed]

Giessen, H.

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

T. Zentgraf, J. Dorfmüller, C. Rockstuhl, C. Etrich, R. Vogelgesang, K. Kern, T. Pertsch, F. Lederer, and H. Giessen, "Amplitude-and phase-resolved optical near fields of split-ring-resonator-based metamaterials," Opt. Lett. 33, 848-850 (2008).
[CrossRef] [PubMed]

N. Liu, H. C. Guo, L. W. Fu, H. Schweizer, S. Kaiser, and H. Giessen, "Electromagnetic resonances in single and double split-ring resonator metamaterials in the near infrared spectral region," Phys. Status Solidi B 244, 1251-1255 (2007).
[CrossRef]

Grischkowsky, D.

D. Grischkowsky, S. Keiding, M. Vanexter, and C. Fattinger, "Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors," J. Opt. Soc. Am. B 7, 2006-2015 (1990).
[CrossRef]

F. E. Doany, D. Grischkowsky, and C. C. Chi, "Carrier lifetime versus ion-implantation dose in silicon on sapphire," Appl. Phys. Lett. 50, 460-462 (1987).
[CrossRef]

Guo, H. C.

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

N. Liu, H. C. Guo, L. W. Fu, H. Schweizer, S. Kaiser, and H. Giessen, "Electromagnetic resonances in single and double split-ring resonator metamaterials in the near infrared spectral region," Phys. Status Solidi B 244, 1251-1255 (2007).
[CrossRef]

Helm, H.

A. Bitzer, H. Helm, and M. Walther, "Beam-profiling and wavefront-sensing of thz pulses at the focus of a substrate-lens," IEEE J. Sel. Top. Quantum Electron 14, 476-481 (2008).
[CrossRef]

Heucke, S. F.

Hillenbrand, R.

R. Hillenbrand and F. Keilmann, "Complex Optical Constants on a Subwavelength Scale," Phys. Rev. Lett. 85, 3029-3032 (2000).
[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]

Jeoung, S. C.

Kaiser, S.

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

N. Liu, H. C. Guo, L. W. Fu, H. Schweizer, S. Kaiser, and H. Giessen, "Electromagnetic resonances in single and double split-ring resonator metamaterials in the near infrared spectral region," Phys. Status Solidi B 244, 1251-1255 (2007).
[CrossRef]

Kang, J. H.

Keiding, S.

Keilmann, F.

R. Hillenbrand and F. Keilmann, "Complex Optical Constants on a Subwavelength Scale," Phys. Rev. Lett. 85, 3029-3032 (2000).
[CrossRef] [PubMed]

Kern, K.

R. Esteban, R. Vogelgesang, J. Dorfmüller, A. Dmitriev, C. Rockstuhl, C. Etrich, and K. Kern, "Direct Near-Field Optical Imaging of Higher Order Plasmonic Resonances," Nano Lett. 8, 3155-3159 (2008)
[CrossRef] [PubMed]

T. Zentgraf, J. Dorfmüller, C. Rockstuhl, C. Etrich, R. Vogelgesang, K. Kern, T. Pertsch, F. Lederer, and H. Giessen, "Amplitude-and phase-resolved optical near fields of split-ring-resonator-based metamaterials," Opt. Lett. 33, 848-850 (2008).
[CrossRef] [PubMed]

Kersting, R.

Kim, D. S.

Koschny, T.

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

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Kuchler, F.

Lederer, F.

Lee, J. W.

Linden, S.

C. M. Soukoulis, S. Linden, and M. Wegener, "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, T. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Liu, N.

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

N. Liu, H. C. Guo, L. W. Fu, H. Schweizer, S. Kaiser, and H. Giessen, "Electromagnetic resonances in single and double split-ring resonator metamaterials in the near infrared spectral region," Phys. Status Solidi B 244, 1251-1255 (2007).
[CrossRef]

Long, L. L.

Malloy, K. J.

S. Zhang, W. J. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

Markos, P.

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

Minhas, B. K.

S. Zhang, W. J. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

Nagel, 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]

Ordal, M. A.

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

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]

Park, Q. H.

Pendry, J. B.

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (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, "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.

Planken, P. C. M.

Querry, M. R.

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.

R. Esteban, R. Vogelgesang, J. Dorfmüller, A. Dmitriev, C. Rockstuhl, C. Etrich, and K. Kern, "Direct Near-Field Optical Imaging of Higher Order Plasmonic Resonances," Nano Lett. 8, 3155-3159 (2008)
[CrossRef] [PubMed]

T. Zentgraf, J. Dorfmüller, C. Rockstuhl, C. Etrich, R. Vogelgesang, K. Kern, T. Pertsch, F. Lederer, and H. Giessen, "Amplitude-and phase-resolved optical near fields of split-ring-resonator-based metamaterials," Opt. Lett. 33, 848-850 (2008).
[CrossRef] [PubMed]

Schmidt, F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. 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. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002).
[CrossRef]

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]

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

Schweizer, H.

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

N. Liu, H. C. Guo, L. W. Fu, H. Schweizer, S. Kaiser, and H. Giessen, "Electromagnetic resonances in single and double split-ring resonator metamaterials in the near infrared spectral region," Phys. Status Solidi B 244, 1251-1255 (2007).
[CrossRef]

Seo, M. A.

Shalaev, V. M.

V. M. Shalaev, "Optical negative-index metamaterials," Nat. Photonics 1,41-48 (2007).
[CrossRef]

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (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, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

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

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]

Soukoulis, C. M.

C. M. Soukoulis, S. Linden, and M. Wegener, "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, T. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

D. R. Smith, S. Schultz, P. Markos, 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.

Ulin-Avila, E.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature (London) 455, 376-379 (2008).
[CrossRef] [PubMed]

Valentine, J.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature (London) 455, 376-379 (2008).
[CrossRef] [PubMed]

Vanexter, M.

Veselago, V. G.

V. G. Veselago, "Electrodynamics of substances with simultaneously negative values of sigma and mu," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

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]

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]

Vogelgesang, R.

R. Esteban, R. Vogelgesang, J. Dorfmüller, A. Dmitriev, C. Rockstuhl, C. Etrich, and K. Kern, "Direct Near-Field Optical Imaging of Higher Order Plasmonic Resonances," Nano Lett. 8, 3155-3159 (2008)
[CrossRef] [PubMed]

T. Zentgraf, J. Dorfmüller, C. Rockstuhl, C. Etrich, R. Vogelgesang, K. Kern, T. Pertsch, F. Lederer, and H. Giessen, "Amplitude-and phase-resolved optical near fields of split-ring-resonator-based metamaterials," Opt. Lett. 33, 848-850 (2008).
[CrossRef] [PubMed]

Walther, M.

A. Bitzer, H. Helm, and M. Walther, "Beam-profiling and wavefront-sensing of thz pulses at the focus of a substrate-lens," IEEE J. Sel. Top. Quantum Electron 14, 476-481 (2008).
[CrossRef]

A. Bitzer and M. Walther, "Terahertz near-field imaging of metallic subwavelength holes and hole arrays," Appl. Phys. Lett. 92, 231101 (2008).
[CrossRef]

Wegener, M.

C. M. Soukoulis, S. Linden, and M. Wegener, "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, T. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (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, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Zentgraf, T.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature (London) 455, 376-379 (2008).
[CrossRef] [PubMed]

T. Zentgraf, J. Dorfmüller, C. Rockstuhl, C. Etrich, R. Vogelgesang, K. Kern, T. Pertsch, F. Lederer, and H. Giessen, "Amplitude-and phase-resolved optical near fields of split-ring-resonator-based metamaterials," Opt. Lett. 33, 848-850 (2008).
[CrossRef] [PubMed]

Zhang, S.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature (London) 455, 376-379 (2008).
[CrossRef] [PubMed]

S. Zhang, W. J. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

Zhang, X.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature (London) 455, 376-379 (2008).
[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, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Zhou, J. F.

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

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Zschiedrich, L.

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

Appl. Opt. (1)

Appl. Phys. Lett. (2)

A. Bitzer and M. Walther, "Terahertz near-field imaging of metallic subwavelength holes and hole arrays," Appl. Phys. Lett. 92, 231101 (2008).
[CrossRef]

F. E. Doany, D. Grischkowsky, and C. C. Chi, "Carrier lifetime versus ion-implantation dose in silicon on sapphire," Appl. Phys. Lett. 50, 460-462 (1987).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron (1)

A. Bitzer, H. Helm, and M. Walther, "Beam-profiling and wavefront-sensing of thz pulses at the focus of a substrate-lens," IEEE J. Sel. Top. Quantum Electron 14, 476-481 (2008).
[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. B (1)

Nano Lett. (1)

R. Esteban, R. Vogelgesang, J. Dorfmüller, A. Dmitriev, C. Rockstuhl, C. Etrich, and K. Kern, "Direct Near-Field Optical Imaging of Higher Order Plasmonic Resonances," Nano Lett. 8, 3155-3159 (2008)
[CrossRef] [PubMed]

Nat. Photonics (1)

V. M. Shalaev, "Optical negative-index metamaterials," Nat. Photonics 1,41-48 (2007).
[CrossRef]

Nature (London) (1)

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature (London) 455, 376-379 (2008).
[CrossRef] [PubMed]

Nature Mater. (1)

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

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. B (1)

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

Phys. Rev. Lett. (5)

R. Hillenbrand and F. Keilmann, "Complex Optical Constants on a Subwavelength Scale," Phys. Rev. Lett. 85, 3029-3032 (2000).
[CrossRef] [PubMed]

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

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. J. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

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

Phys. Status Solidi B (1)

N. Liu, H. C. Guo, L. W. Fu, H. Schweizer, S. Kaiser, and H. Giessen, "Electromagnetic resonances in single and double split-ring resonator metamaterials in the near infrared spectral region," Phys. Status Solidi B 244, 1251-1255 (2007).
[CrossRef]

Science (5)

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]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative refractive index at optical wavelengths," Science 315, 47-49 (2007).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, "Electrodynamics of substances with simultaneously negative values of sigma and mu," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Other (1)

J. Jin, The Finite Element Method in Electromagnetics, (Wiley-IEEE Press 2002), second edn.

Supplementary Material (4)

» Media 1: MOV (3968 KB)     
» Media 2: MOV (3566 KB)     
» Media 3: MOV (3453 KB)     
» Media 4: MOV (3396 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

THz near-field microscope. (a) Overview of the setup. The output of a mode-locked Ti:sapphire laser is split by a beam splitter (BS) into excitation and probe beam which are focused by lenses (L) onto a photoconductive THz emitter and a detector, respectively. The emitted THz pulses are focused by a pair of off-axis paraboloidal mirrors M1 and M2 onto the sample. The THz electric near-field is spatially resolved at the backside of the sample by raster-scanning the detector unit along the x- and y-axis. (b) Cross section of the detector chip with the sample for a measurement of the x-component of the electric field.

Fig. 2.
Fig. 2.

Photograph of the detector unit. Two dimensional raster scans are performed by moving the detector mount with detector chip (D), the laser focusing lens (L) and the probe laser (red line) via the periscope mirrors (P) in x- and y-directions relative to the stationary sample (S) and THz beam (green line).

Fig. 3.
Fig. 3.

Microscope images of the split-ring resonator (SRR) samples. The structures are made from 9 μm thick copper on a 120 μm thick PTFE substrate. (a) Single SRR. (b) Periodic array of SRRs. o= 500 μm; i= 300 μm; g= 100 μm; t= 30 μm; p= 600 μm.

Fig. 4.
Fig. 4.

Power transmission spectrum of the SRR array sample. (a) Spectrum showing four dominant resonances (A1-A4) for orthogonal polarization of the incident electric field relative to the slits. (b) Spectrum for parallel polarization showing only two resonances (B1 and B2).

Fig. 5.
Fig. 5.

Measured electromagnetic near-field distribution and simulation of the current density. The vector plots show the electric in-plane field vectors in the x-y-plane at the backside of the sample at the resonances A 1 - A 4 for (a) the isolated SRR sample (Media 1) and (c) the array sample (Media 2). The color code indicates the time derivative of the out-of-plane component of the corresponding magnetic field, ∂Hz /t , derived from the electric field vectors. All plots show the fields at an individually chosen phase within one oscillation cycle. (b) Simulated surface current density. Polarization and propagation direction of the incident wave is indicated in (b).

Fig. 6.
Fig. 6.

Rotated orientation of the structure. (a) Measured electric and magnetic near-fields at resonances B1 and B2 for the isolated SRR (Media 3) and (c) for the SRR array sample (Media 4)). (b) Simulated current densities.

Fig. 7.
Fig. 7.

Illustration of the fundamental modes. For the three fundamental modes (A1, A3, B1) of the outer ring the currents j⃗ (red arrows), the induced magnetic field H (green arrows) and the resulting charge density are sketched, each at its maximum. The orientation of the magnetic out-of-plane component Hz is indicated by the colored areas.

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