1. Introduction

Metamaterial has attracted substantial attention due to the exotic electromagnetic response to the incident light. It consists of a periodic unit cell, called meta-atom, whose physical dimension is typically much smaller than the wavelength of the light [1,2]. When the incident light is illuminated on the meta-atoms, electromagnetic dipoles are formed on the metallic surface, in which the light excites collective oscillations of free electrons that lead to the surface plasmon mode [2,3]. These dipoles strongly interact with the adjacent ones, resulting in interesting and yet unnatural phenomenon such as negative [4–8] or extremely high refractive index [9]. Numerous studies conducted so far have included optical properties of meta-structures focusing on the spectral region of specific resonance with narrow bandwidth. For example, split-ring resonator (SRR), one of the most widely investigated metamaterials, has been explored and has achieved tunable resonance frequency and bandwidth by adjusting the dipole coupling via controlling the geometrical parameters [10,11], periodicity [2,12,13] and stacking layers [14,15]. Although the SRR have been extensively studied [1,2,10,12,14–18], not much explored structure is its complementary one where the metallic (open) patterns in SRR are replaced with the corresponding open (metallic) patterns [17,19,20].

Complementary split-ring resonator (C-SRR) is a reversed structure of the SRR. Since it is composed of periodic unit slit where the metallic surfaces in the SRR are replaced with the open slit, the electromagnetic dipole coupling in the C-SRR structure is based on the localized guided mode of magnetic dipole rather than the surface plasmon mode [20]. So far, the electromagnetic response of the C-SRR structures have been analyzed and compared with the SRR structure using Babinet’s principle [19,20]. According to the Babinet’s principle, the electromagnetic response of reflection and transmission of the C-SRR is reversed to that of the SRR under complementary light illumination. However, the principle strictly holds only for the isolated two-dimensional planar layer, and it is expected that the dipole coupling in the layered C-SRR exhibits different coupling behaviors as compared to the layered SRR. Although the interpretation of the C-SRR response could be relied on the optical symmetry of the SRR electric dipole, there exists no simple complementary optical quantity in determining the reverse behaviors of the layered C-SRR as to the layered SRR, and no experimental studies have been reported on the vertically stacked C-SRR metamaterials.

Here, we report direct experimental measurements of the coupling effect in the double-layered C-SRR. We present the terahertz (THz) time-domain spectroscopy (THz-TDS) measurements of the dipole coupling mechanism in the layered C-SRR structures, and the result is compared to that of the layered SRR structures. Specifically, the top and bottom layer of both C-SRR and SRR samples are laterally shifted to control the amount of coupling strength between adjacent unit cells. By increasing the spatial shift between the two layers (top and bottom layers), we have observed a large spectral shift over 40% in the resonance frequency of both layered C-SRR and SRR structures. In addition, we show that the bandwidth can be tunable as much as 30% compared to the structures with no lateral shift, all of which can be explained by the interaction of the electric or magnetic dipole with the adjacent meta-atoms.

2. Sample design and experimental method

The proposed metamaterial structures are fabricated by conventional photolithography. First, 5 μm of polyimide is spin coated on silicon wafer and then 200 nm-thick gold with 20 nm-thick chromium adhesion layer is deposited by an electron-beam evaporator. The bottom layer is patterned by the lift-off technique to form C-SRR structures. As a spacer layer, 3μm of polyimide is spin coated over the bottom metallic structure. After the spacer layer is cured, the second C-SRR array structures are deposited and patterned. The layer-to-layer alignment is achieved by the conventional aligner system (EVG 640). Finally, 5 μm of polyimide is spin coated and cured as a passivation layer, and the completed polyimide filter is peeled off from the silicon wafer.

The dimensions of the periodic C-SRR are designed to have a peak resonance frequency ranging from 1.26 THz to 1.83 THz (depending on the lateral shift), considering the transmission characteristics of the polyimide film that shows a high transparent optical property at frequency range of 0.5 ~3 THz. The geometrical parameters of the proposed double-layered C-SRR structure are shown in Fig. 1(a). In order to compare with the SRR, we also fabricate the inverse structure with same geometry. Figure 1(b) shows the double-layered SRR: the unit-cell width is w = 30 μm and the length is l = 90 μm. The overlap distance along the lateral direction between the bottom and the top meta-atom array is s = 0, 15, 30, and 45 μm. The insets of Fig. 1(a) and 1(b) are the optical microscopy images of the C-SRR and the SRR structures with periodicity p = 135 μm at s = 0 μm. The polarization of the incident THz field to the C-SRR is rotated by 90° compared to the SRR’s as shown in Fig. 1 by the Babinet’s principle [19,20].

 

Fig. 1 Geometry of proposed metamaterial structures. Schematics of the double-layered C-SRR (a) and SRR (b) are shown with the following geometrical parameters: width w = 30 μm, length l = 90 μm, and overlap distance s = 0, 15, 30, and 45 μm. Insets are the optical microscopy images of both structures with periodicity p = 135 μm. The incident THz field is directed downwards with the rotated polarization of 90 ° for the C-SRR compared to the SRR.

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For the THz-TDS measurement, we have employed an ultrafast regenerative amplifier system with a repetition rate of 250 kHz (Coherent RegA 9050). Ultrashort 50 fs pulse with 800 nm central wavelength are focused on a 500 μm thick <110> ZnTe crystal. It produces THz pulses covering 0.5 ~3 THz range by optical rectification. The THz field is focused with a 90° off-axis parabolic mirror onto the samples with the focus diameter of about 1 mm. For the THz detection, an identical pair of the ZnTe is used for the electro-optic sampling measurement. In order to keep the humidity level below 1%, the whole THz set-up is the enclosed and purged with dry air. To characterize the electromagnetic responses of the proposed arrays over THz range, we have used conventional THz-TDS measurement [21,22]. Transmission in THz frequency-domain is obtained from THz field through the samples $E(\omega )$ divided by the THz reference field $E_0(\omega )$.

3. Results and discussion

The measured THz transmission spectra of the double-layered C-SRR with respect to the overlap distance s are plotted in Fig. 2(a). The incident magnetic field is vertically polarized as shown in the right inset of Fig. 2(a). As shown in Fig. 2(a), we observe the resonant transmission enhancement in the C-SRR structures [17,19,20]. Blue shift of the resonance frequency is qualitatively well reproduced by the finite-element numerical simulation shown as thin solid lines in Fig. 2(a). In the left inset of Fig. 2(a), we present the transmission spectra of the double-layered SRR to compare the spectral characteristics between the two structures. The data show that the SRR structures show the resonant transmission decrease, as expected from the Babinet’s principle.

 

Fig. 2 Measured transmission spectra of the double-layered C-SRR (symbols) with various s = 0, 15, 30, and 45 μm and the simulation results (lines) performed by high frequency structure simulator (HFSS) (a). Inset of (a) is the measured transmission spectra of the double-layered SRR with the same s. The resonance frequency (b) and the 3 dB bandwidth (c) of both structures with the simulation results (lines) are shown as a function of the s.

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In order to investigate the effect of the s, we plot the resonance frequency and the 3 dB bandwidth as a function of s in Fig. 2(b) and 2(c), respectively. The slight discrepancies between the experiment and the simulations (solid lines) are attributed to deviations of the geometry and surface roughness of the structures [10]. By increasing s, we find that the resonance frequency is blue-shifted over 44% in the double-layered C-SRR. On the other hand, a large red-shift is observed in the double-layered SRR. For the spectral broadening, the 3dB bandwidths of the split-ring resonators (both C-SRR and SRR) show opposite behaviors, namely the bandwidth gets narrower with increasing s for the C-SRR while it shows a broader feature with increasing s for the SRR. These observations indicate that the coupling mechanism of two structures is different with respect to s.

For further analysis of the dipole coupling effects, we compare the measured transmission spectra of the single and the double layered structures for the two split-ring resonators with s = 0 μm. The measured THz transmission spectra for the single- and double-layer structures (both C-SRR and SRR) are shown in Fig. 3. For the SRR, two plasmon resonances at 0.9 THz and 1.61 THz are observed as depicted in Fig. 3(a). These plasmon modes can be understood by the plasmon hybridization of the electric dipole [18,23–27]. The induced electric dipoles on the metallic rings by THz excitation are strongly coupled transversely along the vertical direction, and this coupling generates so called antisymmetric plasmon mode ω_a (0.9 THz) and symmetric plasmon mode ω_s (1.61 THz) via stacking exactly the same structure. As shown in the Fig. 3(a), the transverse coupling between the top and the bottom layer causes a frequency blue-shift compared to the single-layer SRR. However, Fig. 3(b) shows that the resonance ω_c in the double layered C-SRR does not change in contrast to the single layer C-SRR. Because light is confined inside the open slits in the C-SRR, no charge oscillations are excited in the C-SRR (due to the absence of metallic rings) and the magnetic dipoles are induced between the effective slits in the layered C-SRR [19,20]. The fact that there is negligible shift of the resonance frequency in the C-SRR at s = 0 μm underlies the apparently different coupling mechanism between the SRR and the C-SRR structures.

 

Fig. 3 Measured transmission spectra of the single and the double layered SRR (a) and the corresponding C-SRR structures (b) at s = 0 μm. The antisymmetric plasmon mode ω_a and the symmetric plasmon mode ω_s (both arise from the coupling of the two meta-atoms between the stacked layers) are clearly shown in the SRR; however, the resonance frequency ω_c is hardly changed for the single and the double layered C-SRR.

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The central issue to address in this paper is the dependence of coupling effect on s. In Fig. 4(a), we plot the top and cross-sectional views of the layered structures with their induced electromagnetic dipoles (indicated by arrow). Here, we consider only the major resonance mode for the SRR (the symmetric plasmon mode ω_s in the SRR). By increasing s, while the transverse electric-dipole coupling between the upper and the lower plane becomes weak, the longitudinal coupling becomes strong since the electric-dipole coupling length d_x is reduced for the SRR. Both the transverse and the longitudinal coupling thus lead to the decreased resonance frequency (a red-shift feature) with increased broadening in the double-layered SRR [26,27]. On the other hand, the magnetic dipole length a_C-SRR in the double-layered C-SRR is reduced with increasing s, which leads to the resonance blue-shift; note that the electric dipole length a_SRR in the double-layered SRR does not change with respect to the s. In contrast to the double-layered SRR, we note that the coupling length d_x in the C-SRR increases, thereby the spectral bandwidth of the double-layered C-SRR becomes narrower [27].

 

Fig. 4 Top and cross-sectional views of both split-ring resonators with s (a). The length of electric dipole a_SRR (red arrows) in the SRR does not change with s; whereas the length of magnetic dipole a_C-SRR varies because the magnetic dipoles are induced in the effective slits. By increasing s, the coupling distance d_x is decreased (increased) in SRR (C-SRR). (b) Calculated local magnetic field distribution of the double-layered C-SRR and the corresponding optical microscopy images. Strong field enhancements at the edge of the effective slits represent the induced magnetic dipoles. The effective slit length l_eff decreases with increasing s as shown in optical microscopy images.

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More insight can be obtained from the local field distribution. In Fig. 4(b), we shows the calculated results of the local magnetic field distribution based on the finite difference time domain (FDTD) method and the corresponding optical microscopy images of the layered C-SRR with respect to the s. As expected, the local field enhancement at the edge of the effective slits is clearly observed, confirming the induced magnetic dipoles in the C-SRR. Note that the length between field-enhancement spots decreases as increasing s because the effective slit length l_eff is decreased as shown in the optical microscopy images of Fig. 4(b). Therefore, we can confirm that the magnetic field is confined in the effective slits and the dipole coupling of the C-SRR shows different behaviors compared to the double-layered SRR with respect to the s.

4. Conclusion

In conclusion, we have investigated electromagnetic dipole coupling in layered SRR and C-SRR. Using identical meta-atom arrays of the layered C-SRR and SRR, we have observed that the electromagnetic dipoles are strongly coupled with adjacent unit cells with the overlap distance. Since excited modes in both structures cannot be attributed to the same mode, the resonance features show qualitatively different coupling behaviors with respect to the s. In the layered SRR, it is the surface plasmon mode by the electric charge oscillation on the metallic surface. On the other hand, the localized guided mode via the confined magnetic dipole plays an important role in determining the spectral characteristics of the layered C-SRR. Our results are expected to provide experimental basis for designing layered three-dimensional metamaterial devices.