1. Introduction

Metamaterials offer outstanding opportunities for designing the electromagnetic properties of matter [1, 2]. Their response to light is determined by the structure embossed into the material rather than by its composition. The most common approach for tailoring electrical and magnetic properties of the metamaterials is to design metallic resonators and arrange them in periodic patterns [3]. Obviously, the unit cells of such patterns have to be smaller than the light’s wavelength if a spatially homogeneous response in the far-field is desired. The primary resonances of both, the dielectric permittivity and the magnetic susceptibility are determined by the geometric properties of the elements within the unit cells. Examples are LC-resonances of circuits comprising inductances and capacitances or Mie resonances within the individual microscopic elements [4, 5]. Besides these modes the periodicity of the structures itself may lead to further excitations with distinct resonances. Periodic patterns are known to support collective excitations such as dielectric plasmon polaritons [6] and magneto plasmon polaritons [7, 8]. These collective excitations can reach oscillator strengths, which are comparable to that of the elements within the unit cell. In this work we identify the modes of metamaterials using THz microscopy with extreme subwavelength resolution. Our experimental data show, that one mode, which is commonly attributed to a Mie resonance, in fact results from surface plasmon excitations. It is assumed that surface plasmon resonances are a generic property of virtually all metamaterials, because the only requirement for the excitation of these surface waves is the periodicity of the metal structure.

2. Method

The experiments were performed on metamaterials that allow for switching the dielectric resonances by electronic means [9]. The schematic in Fig. 1(a) shows a typical structure and summarizes the most important dimensions. The array of electric split-ring resonators is fabricated on a GaAs substrate with a 1 µm thick n-doped epitaxial layer. Further details of the structure can be found in Ref. [9]. Electronic control over the optical properties is achieved by switching the width of the depletion zone underneath the surface of the structure. The metallic structure forms a Schottky contact to the electron gas in the GaAs as shown in Fig. 1(b). Without applied bias, mobile electrons are close to the metallic structure, and short-circuit the element’s central capacitor. When a positive bias is applied, the increased depletion width prevents shortcircuiting and the structure reveals a resonance given by the capacitances and inductances of the loops. Far-field transmission data show two resonances when the polarization of the exciting field is oriented as illustrated in Fig. 1(c). The resonance f_A=0.7 THz is due to the fundamental mode, which oscillates between the terminals of the capacitor (mode α in the inset of Fig 1(c)). The resonance f_B=1.6 THz agrees with numerical calculations of a Mie-type mode at the side of the element (mode β in Fig. 1(c)). In the following, we show that the resonance at this frequency in fact results from the collective excitation of the elements. The oscillator strength of this collective mode exceeds that of the Mie resonance and dominates the spectral response in this frequency range.

The advance of near-field microscopy makes it possible to resolve the modes along the elements of a metamaterial [10]. In this study, we apply apertureless terahertz near-field microscopy with a spatial resolution of about 1 µm [11]. Further details of our technique and the electro-optic detection can be found in [12]. Figure 2(a) illustrates the microscope head. The incident THz pulses are concentrated by the tungsten probe to a spot size of about 1 µm underneath the tip. This spot size is comparable to the lateral resolution of the microscope. It should be emphasized that the image contrast in apertureless THz microscopy is proportional to the capacitive coupling of the near-field into the structure underneath [13]. Thus, the spot size also defines the area where the metamaterial is locally excited by the near-field. This differs from apertureless techniques operated in the near infrared and visible, where non-metallic probes pick up field energy and emit it into the far-field [10, 14]. One outstanding strength of apertureless THz microscopy is its band width. With our recently developed THz emitter [15], it extends over more than 2 octaves from 0.5 THz to about 2.5 THz and covers the entire response spectrum of the metamaterials investigated. This property allows for the spectral characterization of the local response, which is the main merit of this work.

 

Fig. 1. (a) Top view onto the metamaterial, which consists of a metallic structure fabricated on n-doped GaAs, with a=50 µm and b=c=36 µm. (b) Cross section through the device. Application of a bias between ohmic contact and Schottky contact enlarges the depletion zone, which prevents short-circuiting of the capacitor. (c) Far-field transmission spectra for two different biases. The inset illustrates the polarization of the incident light and two possible modes within one element.

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3. Results

Figure 2(b) shows the THz image of one element. All details of the metallic structure are resolved with an image contrast of about 3%. Further insight into the spatial distribution of modes is obtained by differential THz imaging. The differential signal is recorded while the metamaterial is electronically switched between the on- and off-state. This image shows an enhanced contrast close to the central capacitor, while other regions of the device show no measurable signal. We interpret the data in terms of the capacitive coupling between scanning probe and structure. The capacitive coupling is most efficient at the anti-nodes of the resonator, which are located at the capacitor. Here, the fundamental modeα is excited. Following this interpretation, the excitation of mode β should be visible at the edges of the structure. In contrast, no significant signal is recorded here, as Fig. 2(c) shows. From this unexpected fact we conclude that the Mie-type mode β has an oscillator strength, which is much smaller than that of the fundamental modeα. Apparently, the strong resonance at f_B (see Fig. 1(c)) results from another mechanism, which couples much more efficiently to radiation.

 

Fig. 2. (a) Schematic of the apertureless THz microscope. The tungsten probe concentrates the incident radiation to the area underneath the tip. (b) Terahertz near-field image of one unit cell. The lateral resolution is about 1 µm. (c) Differential image obtained by switching the structure on and off. The dotted lines illustrate the position of the element.

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In the following, we will show that the resonance at f_B=1.6 THz results from the collective response of the entire metamaterial. The extreme bandwidth of apertureless THz microscopy allows for recording the entire spectral response at distinct positions of the structure, as shown in Fig. 3. At position 1 the response of the fundamental mode at 0.7 THz should be strongest while the response of the Mie mode at 1.6 THz is expected to appear at position 2. However, this is not observed. No measurable response is observed at position 2, which confirms that the Mie-mode β has a smaller oscillator strength than the fundamental mode α. In fact, both resonances are found at position 1, which makes a reinterpretation of the resonance at 1.6 THz necessary.

 

Fig. 3. Spectrally resolved coupling of the near-field to the metamaterial. The spectra were obtained at two different positions of the metamaterial.

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Fig. 4. Dispersion relation for surface plasmon excitations propagating on a metal/air interface and on a metal/GaAs interface. Coupling between light and surface plasmons is possible at 1.6 THz, when an inverse lattice vector $G=\frac{2\pi }{a}$ is gained from the grating.

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4. Discussion

The resonance at 1.6 THz results from the excitation of surface plasmons along the surface of the structure. Figure 4 illustrates the surface plasmon dispersion, which can be approximated for the THz range by ω=kc/√ε, where c is the speed of light. At perpendicular incidence, the THz radiation has a wave vector component in the surface plane of k_x ≈ 0, which prevents direct excitation of the surface plasmons. The incident radiation can gain the required wave vector from the inverse lattice vector G=2π/a of the metamaterial, where a=50 µm is the metamaterial’s period. This Bragg-type scattering leads to a surface plasmon excitation that propagates parallel to the surface in the GaAs substrate. Considering the permittivity of GaAs (ε=13) leads to a resonance at 1.6 THz in agreement with the data shown in Figs. 1(c) and 3. We have performed further measurements and finite-element numerical simulations of metamaterials with 50 µm and 60 µm periodicity. The results shown in Fig. 5 reveal that the frequency of the second resonance depends on the periodicity which agrees well with the interpretation of surface plasmon excitations.

 

Fig. 5. (a) Simulated and (b) measured far-field transmission spectra for two different periodicities, 50 µm and 60 µm. The samples were fabricated on intrinsic Si.

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The experimental data of Fig. 1(c) show that the surface plasmon resonance can be switched by electronic means. A detailed description of the modulation of the central capacitor can be found in [9]. But in contrast to such individual components of the structure, surface plasmons are delocalized excitations. Thus, the switching of the surface plasmon resonance cannot be assigned to a specific element or sub-circuit of the structure. It requires a discussion in reciprocal space rather than in the original lattice. The electro-modulation of any periodic lattice property leads to a modulation at wave vector G=2π/a in reciprocal space. At this inverse lattice vector the surface plasmon couples to light. This modulation of Fourier components in reciprocal space suffices for electromodulating the surface plasmon. In the micrographs (Fig. 2) and in the spectral measurements in Fig. 3 the surface plasmon resonance has an enhanced visibility in the region of the capacitor because here the electrical field energy is stored every half cycle.

Finally, it should be mentioned that the framework of surface plasmons in metamaterials agrees with resonances reported in other works [16, 17, 18]. The fact that these works cover a variety of metamaterial structures emphasizes the generic role of surface plasmons in THz metamaterials.

5. Conclusions

In summary, we have shown that plasmonic resonances significantly affect the optical properties of metamaterials. The strength of plasmonic resonances can exceed that of Mie resonances within the unit cell. The finding suggests that future design and interpretation of metamaterials should consider collective excitations.