1. Introduction

Metamaterials are synthetic designer composites with subwavelength-size features that collectively exhibit properties not usually found in natural materials. Owing to these outlandish properties, metamaterials have undergone rapid development during the past decade [1–4]. As a result, researchers found ways to surpass some of the known physical barriers and invented methods for super-resolution [5], perfect light absorption [6–8], complete tunneling [9], and invisibility cloaking [10, 11]. Unfortunately, due to the resonant and highly dispersive nature of metamaterials, the metamaterial-based devices inevitably suffer from narrow operating bandwidths, greatly limiting their utility in practical applications.

The narrowband operation of metamaterials stems from resonant interactions among their meta-atoms. It is sometimes possible to vary the internal resonance frequencies of the meta-atoms and change the electromagnetic response of a metamaterial. Some of the tried and proven methods include having active elements, such as varactor diodes [12, 13], gain-enabling semiconductors [14,15], ferroelectrics [16], ferrites [17,18], and anisotropic liquid crystals [19,20]. These methods in many instances only shift the frequency response to another frequency range. One may also feature-wise replicate the dominant characteristics of the frequency response at multiple points on the frequency scale, by either using multiple resonant units [21, 22] or introducing defects into the metamaterial lattice [23]. Although such approaches are quite efficient and practicable at microwave frequencies, the sophisticated techniques required for the associated metamaterial synthesis complicate the fabrication process and make these approaches less relevant for broadening and tuning of the metamaterial spectrum at optical frequencies.

In this paper, we propose and experimentally demonstrate a metamaterial absorber that can shift its central frequency by using mechanical means. The shift is achieved by varying the gap between the metamaterial and an auxiliary dielectric slab parallel to its surface. We also show that one may create multiple absorption peaks by adjusting the size and/or shape of the dielectric slab, and shift them by moving the slab relative to the metamaterial. As an example, we synthesize double and triple absorption peaks by halving the dielectric slab area. With this modification to the absorber’s design, its spectrum can be altered from a congregate of well-separated maxima to a single absorption peak extending over a wider frequency range.

2. Translation of absorption spectrum

The considered metamaterial structure and its unit cell are schematically shown in Fig. 1. The structure consists of three functional layers: (i) an FR4 substrate of thickness t; (ii) 5×2 array of ten square electric-LC (ELC) resonators [24] fabricated at the front of the substrate; and (iii) full-size copper film at the back of the structure. If geometric parameters of the unit cell are appropriately chosen to eliminate reflection at the frequency of interest, then this metamaterial structure exhibits almost total absorption regardless of the incident angle [7]. General physical considerations suggest that the position of the absorption peak can be influenced by dielectric objects in the close vicinity of the metamaterial. In order to exploit the potential of this feature to translate the absorption peak along the frequency axis, we place an auxiliary FR4 dielectric slab parallel to the metamaterial absorber. The electromagnetic properties of the resulting system may be altered on the fabrication stage by varying the size of the slab, or mechanically controlled by changing the distance d between the slab and metamaterial.

 

Fig. 1 (a) Metamaterial absorber inside a microwave waveguide and (b) its unit cell. The parameters of the unit cell are l = 4.5 mm, a = 3.3 mm, b = 1.0 mm, g = w = 0.2 mm, and t = 0.8 mm. See text for details.

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Using the standard printed circuit board technology, we fabricated a 22.9×10.2 mm² rectangular metamaterial absorber precisely fitting the cross section of the X-band waveguide. We modeled its absorption spectrum using the commercial CST Microwave Studio solver, and then measured the spectrum with the Agilent N5230A vector network analyzer. It was assumed that the walls of the waveguide are made of a perfect electric conductor and the permittivity of the FR4 substrate is 4.2, with a loss tangent of 0.025. The thickness of the copper film was 18 μm and the electric conductivity of copper was 5.8 ×10⁷ S/m. The other geometric parameters employed in the simulations are listed in the caption of Fig. 1. They were numerically optimized to provide the maximum absorption at 10.69 GHz in the absence of the slab.

We first examine the situation where the squares of the metamaterial and auxiliary slab are equal, as shown in Fig. 2(a). The numerically calculated absorption spectrum of the bare metamaterial, with its peak centered at 10.69 GHz, is plotted in Fig. 2(b). For the absorber covered by the slab (d = 0), the same peak is located at 8.78 GHz (see the red curve). As the slab is moved away from the absorber, the absorption peak successively shifts to 10.02, 10.33, and 10.53 GHz for d = 0.1, 0.2, and 0.4 mm, respectively. The shift of the spectrum towards shorter wavelengths is explained by the decrease in the effective permittivity of the nearby background medium leading to the decrease in the effective capacitance of the unit cell. When d is increased well above the substrate thickness (d ≫ t), the absorption spectrum overlaps with the spectrum of the bare metamaterial. It is of significance that the frequency tuning range of 1.91 GHz, theoretically predicted for the present geometry, is much larger than what was demonstrated previously with other approaches [14, 18–20].

 

Fig. 2 (a) Metamaterial absorber parallel to an auxiliary dielectric slab and its (b) theoretical and (c) experimental absorptivities for different separation distances d between the two layers. For simulation parameters, see the text.

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The experimentally measured spectra shown in Fig. 2(c) are in good qualitative agreement with the simulation results. The small blue shifts of the absorption peaks corresponding to d ≫ t (no cover slab), d = 0.2 mm, and d = 0.4 mm with respect to similar peaks in Fig. 2(b) are explained by the approximations of the numerical model. A slightly larger red shift of the peak in the case of d = 0, which is now located at 9.02 GHz, is due to the imperfection of the contacting surfaces resulting in a small effective gap between the metamaterial and auxiliary slab even at their close contact. Despite the described deviations, the experiment shows a substantial peak-frequency shift of about 1.6 GHz.

3. Creation of multiple absorption peaks

The size and shape of the auxiliary dielectric slab in the vicinity of the metamaterial profoundly affects the absorber’s spectral response. In this section, we show that multiple absorption peaks may be created by varying the area of the dielectric slab.

Consider the configuration shown in Fig 3(a), where a horizontal half-slab is placed next to the metamaterial. Since this slab covers only half of the ELC resonators, effectively it reduces the symmetry of the entire structure and enables the absorber to operate in two regimes determined by different patterns of the surface current circulating over the structure. The representative patterns of the two regimes shown in Figs. 3(b) and 3(c) correspond to a pair of resonant peaks in the absorption spectra in Fig. 3(d). By looking at Fig. 2(b), it is easy to conclude that the low-frequency peak (at 8.99 GHz) arises due to the excitation of the mode shown in Fig. 3(b), while the high-frequency peak (at 10.85 GHz) is associated with the mode in Fig. 3(c). As expected, the peaks’ separation is the largest for d = 0 where the impact of the auxiliary slab is maximal (see the red curve). When the half-slab is moved away from the metamaterial, the peaks in the absorption spectra approach each other and eventually merge into one for d ≫ t. This transformation is illustrated by Fig. 3(d). Notice that the absolute shift is much larger for the low-frequency peak than for the high-frequency peak, because of the stronger coupling of the auxiliary slab to the surface plasmon mode in the first case. The experimental spectra presented in Fig. 3(e) exhibit a similar behavior with the changing d and qualitatively agree with the numerical data.

 

Fig. 3 (a) Metamaterial absorber with a horizontal half-slab. Distribution of the surface current at (b) 8.99 and (c) 10.85 GHz for d = 0, and (d) theoretical and (e) experimental absorption spectra for different d. Simulation parameters are the same as in Fig. 2.

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The picture becomes a bit more intricate in the case of a vertical half-slab shown in Fig. 4(a). The reason for this is an additional plasmon mode that may be excited at the edge of the auxiliary slab extending over the central resonators. This mode does not have an analogue in the previous two configurations, and has a frequency that lies between the frequencies of the two modes in Figs. 3(b) and 3(c). As a result, the absorptivity spectrum of the metamaterial features three distinct peaks, with their positions dependant on d. Figures 4(d)–4(f) show the dominant surface currents for each of the peaks. In the event that the slab touches the metamaterial, the theoretical spectrum peaks at 8.92, 9.87, and 10.97 GHz [see Fig. 4(b)]. As before, the theory underestimates the positions of the low-frequency resonances and overestimates the position of the high-frequency peak [see Figs. 4(b) and 4(c)].

 

Fig. 4 (a) Metamaterial absorber with a vertical half-slab, its (b) theoretical and (c) experimental spectra, and distribution of the surface current at (d) 8.92, (e) 9.87, and (f) 10.97 GHz for d = 0. Simulation parameters are the same as in Fig. 2.

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Using the above examples, it is not hard to predict the number of peaks in the metamaterial absorption spectrum when the vertical cover extends over an integer number of ELC resonators. Namely, if one, two, three, or four pairs of the resonators are fully covered by the auxiliary slab, then two absorption peaks corresponding to the mode patterns similar to those shown in Fig. 3(b) and 3(c) would occur. On the other hand, three absorption peaks appear when the slab covers only a half of any pair of ELC resonators, in which case the mode profile would be analogous to that in Fig. 4(e). These predictions are fully confirmed by numerical simulations.

As a concluding remark, we would like to notice that our results hold true not only for the TE mode of a microwave waveguide, but also upon normal incidence of a TEM plane wave polarized in the y direction. The only difference of the absorption spectra in the latter case will be minor red shifts of its resonant peaks, due to the different lateral profile of the incident wave.

4. Conclusions

We have shown that the absorption peak of a metamaterial may be translated by placing a dielectric slab in close proximity to the subwavelength structures making up the metamaterial. If such a placement leads to the symmetry breaking of the overall structure, then it is possible to create multiple absorption peaks and effectively widen the absorption region by bringing them to partially overlap. Essentially, we showed that the effective index variation seen by the metamaterial due to the presence of the the dielectric slab enables the absorption peak translation, whereas the symmetry breaking in the index leads to the appearance of multiple absorption peaks. This concept may be readily extended to THz frequencies by optically controlling the effective index of a dielectric slab in the close vicinity of a metamaterial (e.g., by using Kerr effect for index change and intensity control for symmetry breaking).