Design and characterization setups

The schematic from top with design parameters, and the photograph of the proposed EIT-like structure are shown in Fig. 1. The metallic CRR and ER structures was patterned over Rogers RT/duroid® 5880 substrate with relative permittivity ε _r = 2.2 and dielectric loss tangent tan δ = 0.0009. Herein, the thickness of the dielectric substrate is 0.762 mm and the thickness of the metallic conductor (i.e., copper, modeled by conductivity of 58 MS/m) is 17.5 µm. The dimensions of the substrate and the structure are given as L_x = 72.136 mm, L_y = 34.036 mm, l_cv = 24 mm, l_ch = 24 mm, l_ev = 10 mm, l_eh = 10 mm, w_c = 1 mm, w_l = 1 mm, l_s = 3 mm, g = 1 mm.

Figure 1. The studied EIT-like metamaterial design. (a) The schematic from top with design parameters. (b) The photograph of the fabricated structure.

The numerical analyses of the design are carried out by using CST Studio Suite® frequency domain solver by using the simulation setup, as shown in Fig. 2(a). Herein two waveguide ports are placed in the z-axis direction, and perfect electrical conductors (E _t = 0) are used as the boundary conditions in the remaining directions to limit the computational domain [58]. In simulations, the background medium is modeled by ${\varepsilon _r} = 1$ and ${\mu _r} = 1$. For the experimental process, the structure is placed inside the sample holder as shown in Fig. 2(b–d). As the description of the applications a series of photographs, each taken in the sample holder, are presented in Fig. 3(c) illustrating the horizontal sliding application (HSA) as the example. During the experiments, to prevent the unwanted displacements of the dielectric loadings and to minimize the unwanted air gaps between the EIT-like metamaterial and the dielectric loadings, extruded polystyrene (XPS) materials (i.e., pink foams observed in Fig. 2(d)) are used as support material. Our previous laboratory analyses revealed that effect of the XPS material might be negligible since it had similar dielectric properties with air [Reference Ekmekci, Kose, Cinar, Ertan and Ekmekci59]. Moreover, WR-284 coaxial to waveguide adaptors are used to connect the waveguide transmission line to the Agilent FieldFox N9926A vector network analyzer. Considering the cutoff frequencies of the first two propagating modes of a rectangular waveguide [Reference Pozar60] together with the frequency band under investigation, only TE₁₀ mode propagates in the simulation and experimental setups, where the wave propagation is along z direction, the electric field is along y direction, and the magnetic field is along x and z directions. However, the effects of H_z field, which has cosine variation [Reference Pozar60], on the excitation of the structure may be neglected since the metallic structure is placed around the center of the waveguide cross section [Reference Karacan, Ekmekci and Turhan-Sayan61].

Figure 2. (a) Simulation and (b) experimental setups for EIT-like metamaterial characterization; (c) a series of photographs, each taken in the sample holder, illustrating the horizontal sliding application; and (d) the layout of EIT-like metamaterial together with dielectric loadings inside the sample holder with supporting pink XPS materials.

Figure 3. The schematic illustrations of the dielectric loading pairs composed of two identical a × b sized rectangular dielectric pieces in (a) horizontal sliding application and (b) vertical sliding application in six steps.

Figure 3 illustrates the two proposed dielectric loading mechanisms schematically, namely HSA and vertical sliding application (VSA) for tuning of the transmission window or tuning the of transmission peak frequency. HSA and VSA represent the applications where the loadings are positioned vertically and horizontally, respectively. As seen in the figure, the dielectric loadings are shifted gradually toward the geometric center of structure (i.e., inward) with the shift parameter s_h for HSA and s_v for VSA. For the proof of concept, the dielectric materials used as the dielectric loadings are uncladded Rogers RT/duroid® 5880 (ε _r = 2.2 and tan δ = 0.0009), Rogers CLTE-AT™ (ε _r = 3 and tan δ = 0.0013), Arlon AD450 (ε _r = 4.5 and tan δ = 0.0035), and Rogers RO4360G2™ (ε_r = 6.15 and tan δ = 0.0038) having thicknesses of 1.58, 1.524, 1.524, and 1.524 mm, respectively. During the analyses, the side lengths of the loadings are kept constant at a = 22 mm and b = 6 mm (see Fig. 3). In the simulations, the loadings are lifted as much as the metallic line thickness (i.e., 17.5 µm) to avoid any intersections between the dielectric loadings and the metallic resonator line. Considering the two proposed sliding applications; it can be said that it is important for the EIT-like metamaterial unit-cell to be symmetrical in the design along horizontal and vertical directions.

Figure 4. Transmission spectra of (a) individual ER and CRR structures in simulations and (b) EIT-like metamaterial in simulation and measurement.

Results and discussion

The transmission (i.e., |S ₂₁|) spectra of the individual unloaded (i.e., bare) CRR and ER structures in simulations and the unloaded EIT-like metamaterial structure in simulations and measurements are presented in Fig. 4(a) and (b), respectively. In Fig. 4(a), the individual CRR and ER are shown to possess a transmission dip at 3.372 and 3.607 GHz, respectively. On the other hand, the composition of them, i.e., the EIT-like metamaterial, has two transmission dips and one transmission peak in the frequency band of investigation. In more detail, the dips are observed at 3.197 and 3.772 GHz in simulations and observed at 3.193 and 3.779 GHz in measurements. In addition, the transmission peak frequency f ₀ is observed at 3.479 GHz in simulation and at 3.484 GHz in measurement. Figure 4(b) reveals that the simulated and the measured transmission spectra agree very well. In the design, CRR and the ER have the role of the bright and the quasi-dark mode resonators, respectively.

To figure out the resonance behavior of the EIT-like metamaterial, the surface current densities are plotted at 3.197, 3.479, and 3.772 GHz, as shown in Fig. 5. The plots at each frequency support that the ER has circulating current densities, which is the identifier of an LC resonance [Reference Bai, Chen, Liu, Bu, Cai, Xu and Zhu19, Reference Tian, Hu, Huang, Yu, Lin and Yang22, Reference Arritt, Adomanis, Khraishi and Smith44] and the CRR has stronger surface currents at the vertical edges which are parallel to direction of the incident electric field vector; hence, this resonance can be described as an electric dipole resonance [Reference Chiam, Singh, Rockstuhl, Lederer, Zhang and Bettiol40]. In all, the surface current densities are strongest at 3.479 GHz where the transmission peak is observed.

Figure 5. The surface current densities on EIT-like metamaterial structure. (a) At 3.197 GHz; the first transmission dip frequency, (b) at 3.479 GHz; the transmission peak frequency, and (c) at 3.772 GHz; the second transmission dip frequency.

The |S ₂₁| plots regarding the tuning application for HSA at the shift values s_h = 0 mm and s_h = 5 mm, and for VSA at the shift values s_v = 0 mm and s_v = 5 mm are shown in Figs. 6 and 7, respectively. Since the transmission plots for s_h and s_v values from 2 to 4 present similar behaviors with the those observed for the extremes (i.e., 0 and 5 mm), the transmission spectra are only presented for 0 and 5 mm shift values for four dielectric loading cases together with the bare ones. However, all aggregate results will be discussed through Fig. 9.

Figure 6. Transmission spectra of the bare and the dielectric-loaded EIT-like metamaterials in horizontal sliding application. (a) s_h = 0 mm simulations, (b) s_h = 0 mm measurements, (c) s_h = 5 mm simulations, and (d) s_h = 5 mm measurements.

Figure 7. Transmission spectra of the bare and the dielectric-loaded EIT-like metamaterials in vertical sliding application. (a) s_v = 0 mm simulations, (b) s_v = 0 mm measurements, (c) s_v = 5 mm simulations, and (d) s_v = 5 mm measurements.

In Figs. 6 and 7, the bare MUT designates the air which is chosen as the starting point of the permittivity level (i.e., ε _r = 1). For HSA at s_h = 0 mm, as the real part of relative permittivity of the MUT is increased from 1 to 6.15 (i.e., from bare to RO4360G2™), f ₀ reduces from 3.479 to 3.175 GHz in simulations and from 3.484 to 3.195 GHz in measurements, systematically. Alternatively, for VSA at s_v = 0 mm, as the real part of relative permittivity of the MUT is changed from bare to RO4360G2™, the frequency of the transmission peak reduces from 3.479 to 3.118 GHz in simulations and from 3.484 to 3.182 GHz in measurements. The behavior of f ₀ is very similar for the two applications; however, the transmission bandwidths get effected differently. In more detail, although the transmission bandwidths are nearly the same as the MUT is changed from the bare to RO4360G2™ for HSA at s_h = 0 mm, they obviously broaden for VSA at s_v = 0 mm. This behavior can be explained by the use electric field distributions over the bare EIT-like metamaterial as shown in Fig. 8. First, the electric field distributions at the first null of the EIT-like transmission (i.e., at 3.197 GHz) are especially higher at the top and bottom edges of the CRR and around the gap positions of the ER. Second, the field distributions at the EIT-like transmission peak frequency f ₀ (i.e., at 3.479 GHz) are higher mainly on ER but also on the top and bottom edges of the CRR. Moreover, the field distributions are the highest here in strength among the three cases. Lastly, the electric field distributions at the second null of the EIT-like transmission (i.e., at 3.772 GHz) are higher at the gap positions of the ER, on the other hand there are still high electric field distributions around the top and bottom edges of the CRR. However, the field distributions around the top and bottom edges are observed to be significantly reduced as compared with that of the first null. Since in HSA at s_h = 0 mm case, the dielectric loadings are along the vertical arms of the CRR (see Fig. 3(a)) and tangent to the gaps of the ER, all the two dips and the transmission peak get effected similarly and simultaneously, and the transmission bandwidth is not affected significantly. However, in VSA at s_v = 0 mm case, the dielectric loadings lie in-between the horizontal edges (i.e., top and bottom) of the CRR and the ER. Therefore, the frequencies of the first transmission minimum and the transmission peak slides down more than the second transmission minimum. This application yields a band broadening. As a measure of change in the transmission bandwidth, the quality factor is calculated by Q-factor = f ₀/FWHM, where FWHM is the full width at half maximum, and it is calculated as the frequency band between the value corresponding to the average of the maximum and minimum values of the transmitted power [Reference Christopoulos, Tsilipakos, Sinatkas and Kriezis62, Reference Tang, Zhang, Wang, Hai, Xue, Zhang and Yan63]. Figure 9 shows the calculated Q-factor values by using the simulation and the measurement results for both HSA and VSA at several shift values. Supporting the above observations, for HSA at s_h = 0 mm case, Q-factor does not significantly change; however, it gradually decreases for VSA at s_v = 0 mm case.

Figure 8. Electric field distribution on the bare EIT-like metamaterial. (a) At 3.197 GHz; the first transmission dip frequency, (b) at 3.479 GHz; the transmission peak frequency, and (c) at 3.772 GHz; the second transmission dip frequency.

Figure 9. Calculated Q-factors. (a) Horizontal sliding application simulations, (b) horizontal sliding application measurements, (c) vertical sliding application simulations, and (d) vertical sliding application measurements.

Now, we investigate the behaviors of the EIT-like transmission window in response to the change in real part of relative permittivity of the MUT at the second extremes, i.e., at s_h = 5 mm and s_v = 5 mm for the HSA and VSA, respectively. For HSA at s_h = 5 mm, as the real part of relative permittivity of the MUT is increased from 1 to 6.15 (i.e., from bare to RO4360G2™), f ₀ reduces from 3.479 to 2.343 GHz in simulations and reduces from 3.484 to 2.513 GHz in measurements, systematically. Alternatively, for VSA at s_v = 5 mm, as the real part of relative permittivity of the MUT is changed from bare to RO4360G2™, the frequency of the transmission peak reduces from 3.479 to 2.393 GHz in simulations and reduces from 3.484 to 2.622 GHz in measurements. Here we have three important observations: First, f ₀ of the EIT-like metamaterial becomes more sensitive to the real part of relative permittivity of the dielectric loadings at 5 mm shift cases than that at 0 mm shift cases for both applications. This is not a surprising behavior if we consider Fig. 8 again, since the electric field distribution is highly concentrated on the ER at f ₀. At 5 mm shift cases, the dielectric loadings completely cover up the ER, and hence they have greatest effect on the f ₀ change, i.e., sensitivity. In literature, the sensitivity (S) is used as a measure which is defined by the ratio difference between the resonance frequencies to the difference between the real part of relative permittivities of the loadings [Reference Xu, Wang and Fang27, Reference Liu, Deng, Meng and Sun31–Reference Ebrahimi, Scott and Ghorbani33]. Second, for both HSA and VSA at 5 mm shift cases, as the real part of relative permittivity of the dielectric loadings increases, the overall structure tends to behave like a CRR-only resonator since the resonance frequency of the individual ER reduces much rapidly than that of CRR and the effect of the CRR become more dominant on the transmission characteristics. Ultimately, EIT-like transmission peak almost disappears in the simulations of RO4360G2™-loaded EIT-like metamaterial at s_v = 5 mm. There still exists a reduced transmission peak in the related measurement result (see Fig. 7(b)); however, its trend reveals that further increment in the real part of relative permittivity will destroy the EIT-like transmission. Lastly, for 5 mm shift cases, there are obvious changes in the Q-factor observed even by naked eye in Fig. 6(c) and (d) for HSA and in Fig. 7(c) and (d) for VSA. This observation is supported by Fig. 9. In addition to that, Fig. 9 clearly reveals that the Q-factor is dependent on the shift values; however, this dependence is highest in 5 mm shift cases.

The simulation results given in Fig. 10 show that for both HSA and VSA, f ₀ chances faster in response to the change in the real part of relative permittivity as the shift amount increases. According to sensitivity, defined above, this means that the sensitivity increases as the shift amount increases and ultimately the sensitivities become maximum for 5 mm shift cases. Moreover, change in f ₀ with respect to the real part of relative permittivity change gradually increases with increasing s_h value in HSA. However, it increases significantly in VSA starting with s_v = 4 mm. In other words, it can be said that f ₀ in HSA is more sensitive than that of VSA to the shift value and the real part of relative permittivity of the dielectric loadings. This observation makes HSA more advantageous in terms of sensitivity and makes it a preferable candidate for a sensing application. On the other hand, Fig. 10 is another indicator showing that the proposed approach is clearly sensitive to the changes in s_h and s_v at fixed relative permittivity values. Although some experimental measurement errors are noticeable, the measurement results in Fig. 10 are consistent with the simulation results.

Figure 10. Frequency of transmission peak (i.e., f ₀) versus real part of relative permittivity of the dielectric loadings. (a) Horizontal sliding application simulations, (b) horizontal sliding application measurements, (c) vertical sliding application simulations, and (d) vertical sliding application measurements.

Table 1 shows the f ₀ values obtained by simulations and measurements for s_h = 5 mm case of HSA, where f ₀ is most dependent on the permittivity of the dielectric loadings ε _r. The data show that the f ₀ of HSA for s_h = 5 mm is reduced from 3.479 to 2.343 GHz in simulations and it is reduced from 3.484 to 2.513 GHz in measurements as ε _r is increased from 1 to 6.15 which correspond to 1.136 GHz (32.65%) and 0.971 GHz (27.87%) shifts in f ₀ in simulations and experiments, respectively.

In this study, we performed analyses in both simulations and experimental measurements. In general, the results show good agreements. However, it is important to discuss here that there are some discrepancies in terms of resonance frequencies, transmission amplitudes, or bandwidths. These discrepancies are supposed to be mainly due to the unavoidable additional air gaps between the dielectric loading and the EIT-like metamaterial since the structures do not have ideally flat surfaces. Although using an XPS material in the measurements as a support structure to avoid these additional air gaps is an effective approach depending on our laboratory experiences, it cannot fully provide the ideal simulation setup. Another reason of the discrepancies may be deviations in the dielectric properties of the dielectric loadings with respect to the catalog values. We cannot see fabrication errors as a factor here because, there is nearly a perfect agreement between the simulation and experimental results of the bare (unloaded) EIT-like metamaterial.

Table 1. Dependence of f ₀ on ε _r in the case of s_h = 5 mm of horizontal sliding application

Figure 11. Sensing performance of the 10-mm-thick dielectric-loaded EIT-like metamaterial. (a) Transmission spectra for several refractive indexes. (b) Perspective and (c) side views of 10-mm-thick dielectric-loaded EIT-like metamaterial.

To complete the study, additional numerical analyses were performed for a fairer comparison with the related literature. This time, the resonator side of the studied EIT-like metamaterial unit cell surface was completely loaded (i.e., covered) with a 10-mm-thick lossless dielectric (i.e., 72.136 mm × 34.036 mm × 10 mm) just on the Rogers RT/duroid^® 5880 substrate in the simulation environment. The usage of EIT-like designs for refractive index (n) sensing applications is common [Reference Li, Kong, Liu, Liu and Li21–Reference Pan, Yan, Ma and Shen26, Reference Gao, Yuan, Gao, Deng, Sun, Jin, Zeng and Yan53–Reference Meng, Wu, Erni, Wu and Lee56]. Therefore, the refractive index of the dielectric is increased from 1 to 1.5, which corresponds to an increase in ${\varepsilon _{\textrm{r}}}$ from 1 to 2.25, since $n = \sqrt {{\varepsilon _{\textrm{r}}}} $ considering ${\mu _{\textrm{r}}} = 1$ [Reference Lin, Chen, Yu, Liu, Li and Chen23], as the parametric study and transmission spectra are obtained. The simulation results and schematics of the application are shown in Fig. 11. The results reveal that the frequency of transmission peak lowers from 3.479 to 2.841 GHz as the refractive index increases from 1 to 1.5 which corresponds to 0.638 GHz (18.34%) shift in f ₀.

Table 2. Comparison of EIT-like sensors in terms of various parameters

COR = completely on the resonator, POR = partially on the resonator, SM = surrounding medium, MSTL = microstrip transmission line

To clarify the structural and performance differences of this study as compared to the related EIT-like sensor studies given in the literature, whose mechanism are based on sensing the dielectric constant or refractive index changes of the dielectric loadings (i.e., MUT), Table 2 is presented. The comparison parameters in the table are refractive index n or dielectric constant ε _r range, frequency region, test setup, MUT settling, position adjustability of MUT, and absolute percentage sensitivity (% |S|). For Table 2, the % S values are calculated using equation (1) [Reference Xu, Wang and Fang27].

(1)\begin{equation}\% S = {{\Delta f} \over {\Delta {\varepsilon _{\textrm{r}}} \cdot {f_0}}} \times 100\end{equation}

where $\Delta f = {f_2} - {f_1}$ is the spectral change in the EIT-like peaks in the transmission, $\Delta {\varepsilon _{\textrm{r}}} = {\varepsilon _{{\textrm{r2}}}} - {\varepsilon _{{\textrm{r1}}}}$ is change in the permittivity, and ${f_0}$ is EIT-like peak frequency of the bare (i.e., unloaded) case. In the table, given n values are converted to permittivity by using $n = \sqrt {{\varepsilon _{\textrm{r}}}} $ considering ${\mu _{\textrm{r}}} = 1$ [Reference Lin, Chen, Yu, Liu, Li and Chen23]. In the formulation, ${f_1}$ corresponds to the resonance frequency where MUT’s permittivity is ${\varepsilon _{{\textrm{r1}}}}$, and similarly ${f_2}$ corresponds to the resonance frequency where MUT’s permittivity is ${\varepsilon _{{\textrm{r2}}}}$. For the case of ${\varepsilon _{{\textrm{r1}}}} = 1$, ${f_0}$ will be equal to ${f_1}$; however, this is not a requirement as can be seen in reference [Reference Liu, Weiss, Mesch, Langguth, Eigenthaler, Hirscher, Sönnichsen and Giessen25]. If the percentage sensitivity values were given in the articles compared in Table 2, we used it directly, if not, we calculated it by using the data or graphs in the related article. For this reason, there may be small deviations due to reading errors from the graph.

Table 2 reveals that there are three prominent directions of our study. First, the partial coverage of the unit-cell by MUT (i.e., referred to as POR in the table) instead of complete coverage. Second, sensing mechanism based on position adjustability of the MUT, and third, relatively high sensitivity values for the complete coverage scenario (i.e., referred to as COR in the table). The first is believed to be an advantage in sensing applications terms of using small amount of analyte material (i.e., MUT), the second provides an important flexibility for adopting the design in mechanical sensing approaches, and the last is obviously preferred in many sensing applications. For the COR scenario, our EIT-like metamaterial shows 14.67% sensitivity, and it is the second highest percentage sensitivity in the table. For the POR scenario, the sensitivity is reduced in both simulations (6.34%) and experiments (5.41%) as expected with respect to the COR case, since the amount of MUT is reduced. However, these sensitivities are still comparable to references [Reference Lin, Chen, Yu, Liu, Li and Chen23, Reference Shen, Wang and Lu24, Reference Pan, Yan, Ma and Shen26] and [Reference Xu, Wang and Fang27]. In addition to those benefits, we use a rectangular hollow waveguide setup for the characterization of EIT-like sensor performance. The main advantage of the waveguide setup is presenting an array behavior with a single unit cell [Reference Karacan, Ekmekci and Turhan-Sayan61] which again provides an important advantage to reduce the applied total MUT amount.