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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 5 — Mar. 2, 2009
  • pp: 3826–3834

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Terahertz near-field imaging of electric and magnetic resonances of a planar metamaterial

Andreas Bitzer, Hannes Merbold, Andreas Thoman, Thomas Feurer, Hanspeter Helm, and Markus Walther  »View Author Affiliations


Optics Express, Vol. 17, Issue 5, pp. 3826-3834 (2009)
http://dx.doi.org/10.1364/OE.17.003826


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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

1. Introduction

Metamaterials constructed from subwavelength resonator structures exhibit unprecedented electromagnetic properties [1

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

, 2

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

, 3

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

] which are based on the microscopic electric and magnetic response of their constituting elements to an incident light wave. As a result artificially engineered metamaterials make possible a range of novel applications such as perfect lensing [4

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

] or invisibility cloaking [5

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

]. Since their first demonstration at microwave frequencies [6

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]

] progress in structure miniaturization allowed to build metamaterials for higher frequencies, ranging from the terahertz [7

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]

] over the mid-infrared [8

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

, 9

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]

] to the near-infrared regime [10

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]

, 11

N. Liu, H. C. Guo, L. W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamate-rials at optical frequencies,” Nature Materials 7, 31–37 (2008). [CrossRef]

, 12

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–U32 (2008). [CrossRef] [PubMed]

]. Typically, they are made of metallic structures, e.g. split-ring resonators (SRRs) [13

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]

, 7

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]

], specifically designed to respond resonantly to the electric and the magnetic fields of an incident light wave. Near resonance the induced fields can exceed the driving fields by orders of magnitude and generate a counteracting response of the medium. This can be expressed in terms of a negative effective permittivity ε eff and permeability μ eff of the metamaterial and can lead to a negative refractive index [14

V. G. Veselago,“Electrodynamics of substances with simultaneously negative values of sigma and mu,” Soviet Physics Uspekhi-Ussr 10, 509–514 (1968). [CrossRef]

]. So far, photonic metamaterials are mostly characterized by far-field measurements. While this provides important information about the characteristic resonances and allows to extract the macroscopic quantities ε eff and μ eff [15

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]

, 10

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]

], such far-field investigations do not provide direct insight into the formation and dynamics of the microscopic internal fields responsible for the material’s negative response. An experimental characterization of the involved electric and in particular the magnetic near-fields which are localized to the microscopic building blocks remains highly challenging and current studies rely mostly on numerical simulations.

Only recently scanning near-field optical microscopy (SNOM) methods have been developed to map optical near-fields of metallic structure on the micro- to nanometer scale [16

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

, 17

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]

] and were also applied to the investigation of near-fields in metamaterial structures [18

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]

, 19

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]

]. Although being extremely powerful, SNOM techniques are mainly sensitive to only the longitudinal electric field component (Ez ) and can not directly provide the magnetic information. Experimental studies of the entire electromagnetic near-fields in metamaterials are still lacking, mainly due to the difficulties involved in measuring electric and in particular magnetic field components with the required subwavelength spatial resolution.

Here, we employ terahertz time-domain imaging [20

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]

, 21

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]

, 22

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

] to investigate the complex resonant activity of a planar metamaterial and trace their localized electric and magnetic near-field response. Our approach 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 metamaterial at terahertz frequencies.

2. Experimental setup and sample fabrication

The experimental setup is illustrated in Fig. 1. Terahertz pulses were emitted and detected by photoconductive antennas optically gated by the output of a mode-locked Ti:sapphire laser (< 20 fs, 800 nm, 75 MHz repetition rate). The pulsed THz beam was focused by a pair of off-axis parabolic mirrors to a frequency dependent spot of about 1 mm diameter (at 0.5 THz) at the position of the sample. The transmitted electric field was detected at the backside of the sample in the 10 μm wide photoconductive gap between the H-shaped electrodes on an ion implanted silicon-on-sapphire substrate [23

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]

]. The detector chip was mounted with its electrodes and photo-active silicon layer facing the backside of the sample and was optically gated by focusing the probe laser beam through the sapphire substrate (Fig. 1(b)). This allows us to perform measurements in direct proximity of the sample, typically at a distance of 30 μm from its surface. Spatial scans were performed by synchronous translation of the probe laser and the detector chip. This is achieved by a pair of mirrors mounted on separate translation stages arranged in a periscope configuration as described elsewhere [24

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]

] (Fig. 2). The spatial resolution of the experiment is mainly limited by the finite dimensions of the probe beam focus and of the photoconductive gap and has been determined to be on the order of 20 μm. Finally, by scanning a variable delay line in the detector beam path the temporal waveform of the electric field was recorded in each spatial pixel.

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. 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).

The transmitted electric field is detected at the backside of our sample which is positioned in the focus of a pulsed THz beam. We perform measurements at a typical distance of 30 μm away from the sample surface, corresponding to λ/25 at 400 GHz, the highest frequency considered in this study. The incident terahertz beam has a fixed polarization along the x-axis. The linearly polarized detector is oriented to be sensitive to both, the x- and the y-component of the transmitted electric field by rotating the entire detector chip by 90 degrees. Spatially resolved measurements are performed by moving the detector (D) together with the probe laser beam and the focusing optics (L) in x- and y-directions relative to the stationary sample (S) by the movable detector mount shown in Fig. 2. At each spatial position the time dependent electric field is measured by scanning an optical delay. From two separate measurements of the electric field polarizations Ex (x,y,t) and Ey(x,y,t) the in-plane vector field Exy (x,y,t) can be reconstructed. By Fourier transforming the time traces we obtain the spectral amplitude and phase distributions. In order to study the oscillation of the vector field at an individual frequency ν 0, the amplitude and phase at the selected frequency, Exy (x,y, ν 0) and ϕxy (x,y, ν 0), are transformed back to the time-domain. By this frequency filtering we obtain the oscillation signature of the field in a narrow frequency window (Δv=15 GHz) around ν 0 without background from other superimposed frequencies, which allows us to unambiguously assign the specific resonances observed in far-field transmission measurements to near-field patterns.

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.

The samples were fabricated by conventional photolithography and etching techniques and were made from 9 μm thick copper on a 120 μm thick polytetrafluoroethene (PTFE) substrate (εr PTFE = 2.28) from Rogers (RT/duroid 5880 ®). A thickness of the substrate smaller than the terahertz wavelength was chosen to avoid multiple reflections within the substrate. We investigate samples consisting of one individual double SRR and of a square array of this structure as shown in Fig. 3(a) and (b) in order to analyze the resonant behavior of an individual element and its interaction with neighboring resonators.

3. Experimental results and simulation

First, the far-field transmission of the SRR array sample has been characterized under normal incidence using a conventional THz time-domain spectrometer [25

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]

]. Figure 4 shows the transmitted power spectra for two perpendicular orientations of the structure relative to the polarization of the incident wave. Four dominant resonances (A1-A4) are observed for orthogonal and two (B1 and B2) for parallel polarization of the electric field relative to the slits in the split-rings. All modes can be interpreted in terms of fundamental excitations of the constituting SRR elements leading to strong reflection peaks and the observed transmission minima [8

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

]. In our case dissipative losses are negligible since in the THz regime metals are almost perfect conductors and the teflon substrate is non-absorbing. Current investigations of the underlying mechanisms leading to these sharp and strong resonances rely almost entirely on numerical simulations which normally assume idealized geometries, material properties, excitation and boundary conditions.

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. 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).

Our THz near-field microscopy approach permits to characterize the electric and magnetic near-field distributions of these structures at their far-field resonances. Figures 5(a) and (c) show the measured near-field distributions of a single SRR and a periodic array of identical SRRs. The electric field vectors are plotted, all at a fixed phase within an oscillation cycle, at the frequencies of the four dominant resonances A1-A4. The complete oscillation cycles for each resonance are available online as movies (Media 1) and (Media 2). For resonances A1 and A2 of the isolated SRR the vector plots indicate the formation of rotational fields oscillating around the center of the structure. These modes correspond to the LC-resonances of the outer and inner split-ring, associated with circulating currents in the metal structures leading to the formation of a magnetic moment normal to the SRR plane [26

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]

]. On the other hand, the modes at 225 and 405 GHz (A3 and A4) show a fundamentally different character. For both modes the field vectors point toward and away from the corners of the resonators indicative of electric quadrupole excitation.

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.

According to Maxwell’s equations a curl of the electric field induces a change in the magnetic field by ∂H⃗/∂t = − μ −1 ∇ × E⃗. This relation allows us to determine the change in the out-of-plane magnetic field component, ∂Hz/∂t, from the measured in-plane electric field vectors, Exy , at each spatial pixel, indicated in the plots in Fig. 5 and 6 by the additional color code. Since the field is harmonically oscillating the magnetic field distribution Hz (x,y,t) simply corresponds to its time derivative phase-shifted by π/2. The magnetic field distributions shown in Fig. 5 reveal that the LC-resonances, A1 and A2, are associated with the formation of magnetic dipoles normal to the sample plane whereas the higher order modes, A3 and A4, exhibit a fourfold magnetic field pattern.

Complementary numerical simulations based on finite element method (FEM) modeling [27

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

] reproduce all four fundamental resonances, albeit slightly shifted (< 10%) to higher frequencies. In the simulation an individual double SRR structure was positioned in the center of a 3-dimensional simulation box of refractive index n=1. Drude conductivity was assumed for the rings using the literature values of copper for the plasma frequency and the damping rate [28

M. A. Ordal, R. J. Bell, R. W. Alexander, L. L. Long, and M. R. Querry, “Optical-properties of 14 metals in the infrared and far infrared - al, co, cu, au, fe, pb, mo, ni, pd, pt, ag, ti, v, and w,” Appl. Opt. 24, 4493–4499 (1985). [CrossRef] [PubMed]

]. A plane harmonic wave normally incident onto the SRR plane was excited on one boundary. Scattering boundary conditions have been imposed on the remaining sides of the simulation volume. This simplified model does not account for the frequency-dependent Gaussian THz beam focus nor the changing position of the detector close to the sample surface. Therefore, instead of the fields we consider the surface currents in the rings which are extracted from the simulation, since they proved to be less dependent on excitation conditions and external influences. The current densities were determined from the simulated electric field in the rings by j⃗ = σE⃗, where E⃗ is the field in the metal 50 nm below the surface.

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 H⃗ (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.

The simulated surface current densities at each resonance are shown in Fig. 5(b). We find that the measured magnetic field distributions are fully consistent with the directions of the driving currents predicted by the simulation for each resonance, the magnetic dipole mode (A1 and A2) and the fourfold magnetic field pattern of an electric quadrupole (A3 and A4). An illustration of the relative orientation of the current flux and associated magnetic fields is shown in Fig. 7 for the three characteristic resonances of the outer ring.

The lower panel of Fig. 5 shows the respective fields observed for the SRR-array sample. Since the resonances significantly extend into the surrounding area of the SRRs field interference between neighbors has to be considered for the array sample. Destructive field interference between neighboring SRRs for the LC-resonance A1 is observed considerably attenuating the field rotations. In contrast, for the higher order mode A3 constructive interference significantly enhances the rotation patterns predominantly in-between the structures. We attribute the remarkably stronger resonance at A3 observed in the far field transmission spectrum in Fig. 4 to this mechanism. The modes of the inner ring (A2 and A 4) remain relatively unperturbed by influence from neighboring structures due to their larger separation and the screening by the outer rings.

Figure 6 shows the field patterns and simulated currents when the SRRs are rotated by 90°. Both modes B1 and B2 arise from currents symmetrically induced in the horizontal sides of the outer and the inner ring, respectively, leading to charge accumulations on the vertical sides and the formation of a depolarization field. The measured magnetic fields are again consistent with the orientation of the simulated current flux in the rings as illustrated for the resonance of the outer ring in Fig. 7. For the periodic array sample constructive interference between neighbors leads to enhanced field patterns, albeit slightly distorted due to the inhomogeneous illumination in particular at higher frequencies [24

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]

].

4. Conclusion

In summary we have utilized THz near-field microscopy to investigate a planar metamaterial based on double split-ring resonator structures. By our approach we are able to trace the in-plane electric and out-of-plane magnetic fields at the metamaterial’s characteristic resonances which are responsible for its extraordinary optical properties. We find that for our structure three fundamental resonances occur for the outer and the inner ring, respectively, leading to the six dominant resonances observed in the far-field transmission spectra. Using our imaging technique we map the electromagnetic near-field signature of each fundamental mode for the first time. The ability to visualize near-field distributions of microstructured surfaces opens a unique way to experimentally investigate and optimize metamaterials and their complex interaction with light.

Acknowledgments

This work was supported by the Deutsche Forschungsgemeinschaft (DFG) through grant No. WA 2641/3. The authors are grateful to A. Fauler from the Freiburg Materials Research Center (FMF) for assistance in sample fabrication.

References and links

1.

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

2.

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

3.

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

4.

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

5.

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

6.

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]

7.

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]

8.

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

9.

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]

10.

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]

11.

N. Liu, H. C. Guo, L. W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamate-rials at optical frequencies,” Nature Materials 7, 31–37 (2008). [CrossRef]

12.

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–U32 (2008). [CrossRef] [PubMed]

13.

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]

14.

V. G. Veselago,“Electrodynamics of substances with simultaneously negative values of sigma and mu,” Soviet Physics Uspekhi-Ussr 10, 509–514 (1968). [CrossRef]

15.

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]

16.

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

17.

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]

18.

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]

19.

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]

20.

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]

21.

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]

22.

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

23.

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]

24.

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]

25.

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]

26.

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]

27.

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

28.

M. A. Ordal, R. J. Bell, R. W. Alexander, L. L. Long, and M. R. Querry, “Optical-properties of 14 metals in the infrared and far infrared - al, co, cu, au, fe, pb, mo, ni, pd, pt, ag, ti, v, and w,” Appl. Opt. 24, 4493–4499 (1985). [CrossRef] [PubMed]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(160.3918) Materials : Metamaterials
(180.4243) Microscopy : Near-field microscopy
(300.6495) Spectroscopy : Spectroscopy, teraherz

ToC Category:
Microscopy

History
Original Manuscript: January 22, 2009
Revised Manuscript: February 20, 2009
Manuscript Accepted: February 20, 2009
Published: February 26, 2009

Citation
Andreas Bitzer, Hannes Merbold, Andreas Thoman, Thomas Feurer, Hanspeter Helm, and Markus Walther, "Terahertz near-field imaging of electric and magnetic resonances of a planar metamaterial," Opt. Express 17, 3826-3834 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-5-3826


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