1. Introduction

With the advent of metamaterials, a rich variety of unique optical materials and devices that cannot be obtained from natural materials have been developed in recent years [1–3]. Resonant metamaterials are composed of an array of artificially designed subwavelength resonant elements (meta-atoms) such as split-ring resonators (SRRs) [4]. Meta-atoms can be designed to respond to not only the electric field but also the magnetic field of incident electromagnetic (EM) waves. The macroscopic response of metamaterials to EM waves should be described as effective media via effective electric permittivity and magnetic permeability. Novel concepts such as negative index, super- and hyper-lens, and optical cloaks have attracted much attention in the early stage of metamaterials’ research. More recently, many studies have been devoted to inventing novel materials with optical effects for more practical device applications, and among these, metamaterial perfect absorbers (MPAs) [5–13] are promising. Here, we demonstrate metamaterial absorber that shows frequency-selective absorption and low reflection in a wide spectral range.

Let us consider a situation in which many people use their Wi-Fi devices in a very crowded environment such as an expo. We may need to consider using EM wave absorbers between booths to prevent interfering with others. At the same time, we do not want to disturb EM waves in the cellular frequencies in such a situation. Geometric transition absorbers made of wedged-shaped lossy materials or very porous low-density absorbers are commonly used. They are broadband absorbers and thus do not meet our demand considered here. They are also bulky, and we may want to use thin sheet or film absorbers between booths. Recently invented MPAs can be thin; however, the vast majority of MPAs reported so far are also not suitable here. They are usually composed of a metal-insulator-metal (MIM) three-layer structure, in which metallic resonant elements are fabricated on a thin insulator layer backed by an opaque metallic ground plane. Such MIM structure acts as a perfect reflector outside of the absorption band. Only a few studies on the ground-plane-less absorber have been reported to date. Balmokou et al. reported on the ground-plane-less near-perfect terahertz (THz) absorber based on omega resonators [14]. In their device, pairs of omega resonators are orthogonally arranged in such a way that no EM waves can reradiate owing to the destructive interference. They numerically demonstrated a wide-band reflection-less property and absorption of 94% at around 2.9 THz. Here, we demonstrate a subwavelength-thick metamaterial absorber that shows frequency-selective narrow-band near-perfect absorption at a Wi-Fi band of 2.4 GHz. Inspired by the work of Balmokou et al., we investigated a square array of orthogonally arranged paired resonators but more simplified C-shaped SRRs as shown in Fig. 1. We chose to use this simplified shape because we are planning to develop thin absorbers as a next step in the future. Here, we show preliminary results that may lead to the development of an ultrathin metamaterial sheet or film absorber. We successfully designed ground-plane-less subwavelength-thick metamaterial absorbers by numerical simulation and also show the results of proof-of-concept experiments.

 

Fig. 1. Schematic of the unit cell of an orthogonally arranged square array of pairs of C-shaped split-ring resonators (SRRs). The SRRs lie in the common plane (xy-plane) are shown in blue. Those placed perpendicular to the blue SRRs are shown in red. These blue and red rings in each pair are isolated from each other. (a) Front view, (b) top view, (c) side (left) view, (d) perspective view.

Download Full Size | PDF

Figure 1 shows a schematic of the unit cell of the designed metamaterial absorber. Each unit cell is composed of four pairs of orthogonally arranged C-shaped SRRs. The SRRs that lie in the common plane of the array (xy-plane) are shown in blue, and those placed perpendicular to them are in red. As discussed below, the gap width of the SRRs ( = 3.2 mm) is larger than the wire diameter ( = 0.07 mm), and the blue and red rings in each pair are isolated from each other. The orientations of these pairs are also perpendicular in the xy-plane such that the array possesses fourfold rotational symmetry about the z-axis.

We note that, in addition to omega resonators, there are several reports on the ground-plane-less metamaterial absorber. Chiral particles [15] are the original ones to the best of our knowledge. Very recently, MPAs with high functionalities on the basis of various types of ground-plane-less geometries have been reported. Zhang et al. demonstrated unidirectional absorption by utilizing three-dimensional (3D) SRRs with broken symmetry [16]. Li et al. developed a tunable metasurface with switchable functionalities from perfect transparency to perfect absorption utilizing a trilayer metasurface loaded with PIN diodes [17]. The geometry and working principle of our device are rather simple and designed to work as a passive absorber. It is designed to work specifically at a Wi-Fi band that is widely and will be increasingly utilized for portable electronic devices, Internet of Things (IoT) devices, and so forth. We are aiming at developing portable, foldable, and disposable thin sheet or film absorbers in the future. Therefore, we chose to use C-shaped SRRs with a rather simple geometry. We believe that our device will find practical applications in these areas.

2. Modeling, numerical simulation, and experiments

2.1 Modeling and numerical simulation

In this study, the devices and analysis of their microwave responses were modeled using 3D EM field analysis software, CST Studio (Dassault Systèmes). A schematic of the numerical simulation is shown in Fig. 2. The absorber is constructed with a square array of pairs of C-shaped SRRs orthogonally arranged in such a way that induced electric and magnetic dipoles destructively interfere and no reradiation of EM waves can be observed. Here, we assume that the SRRs are made of nichrome with high ohmic loss so that EM energy is dissipated as heat. Its conductivity is 0.926 × 10⁶ S/m. The EM properties of metamaterials are quite sensitive to the geometric parameters of the SRRs, such as the radius of the rings (r), the gap width of the SRRs (g), the wire diameter (d), and the spacing between SRRs (s) [Fig. 2(a)]. A schematic of the analyzed model is shown in Fig. 2(b). To model a periodic array of paired SRRs, periodic boundary conditions are applied in the x and y directions, and a unit cell is shown in the figure. EM plane waves whose electric and magnetic fields are uniform over the unit cell and polarized in the y and x directions, respectively, are launched to the device from port 1 from the normal (along z) direction to the SRR array, and the complex scattering parameters S₂₁ and S₁₁ are evaluated. From transmission (T = |S₂₁|²) and reflection (R = |S₁₁|²) spectra, absorption (A) is evaluated as A = 1 – T – R. The impedance Z of a metamaterial slab for normal incidence can be retrieved from its complex transmission (S₂₁) and reflection (S₁₁) coefficients as follows [18,19].

The sign should be chosen such that a real part of Z to be positive value.

 

Fig. 2. Schematic diagram of the analyzed model. (a) Unit cell of an orthogonally arranged square array of pairs of C-shaped split-ring resonators (SRRs) and their geometrical parameters: the radius of the rings (r), the gap width of the SRRs (g), the wire diameter (d), and the spacing between SRRs (s). (b) Unit cell model with periodic boundary conditions and direction and polarization of incident EM wave.

Download Full Size | PDF

2.2 Microwave measurement

For microwave measurement, a broadband horn antenna with 2–18.0 GHz frequency range (LB-20180, A-INFO Inc.) is used to launch directional and linearly polarized EM waves to the sample and the transmitted signal is probed with a Wi-Fi dipole antenna. The transmitted EM signals are measured using a vector network analyzer (KEYSIGHT N9925A). For the measurement of the incident angle dependence, the sample is rotated around the y-axis. Measurements are performed for both transverse electric (TE) and transverse magnetic (TM) polarizations by changing the orientation of both the horn antenna and probe antenna 90° about the common z-axis.

3. Results and discussion

3.1 Optimization of geometrical parameters of metamaterial absorber

As discussed above, the EM properties of metamaterials as an effective medium can be engineered by changing the geometric parameters. As a rough approximation, the wavelength associated with the resonant frequency is twice the unwound length of an SRR. To obtain such a half-wavelength resonance at 2.4 GHz, we chose to fix r and g to be 10 mm and 3.2 mm, respectively. Then, we performed numerical simulations using the remaining parameters d and s as the design parameters to find the optimum conditions to achieve high absorption. As a first step, we fixed s to be 8.5 mm and varied d to obtain a rough estimate of the optimum wire diameter.

In Fig. 3(a), spectra of magnitude of the scattering parameters |S₂₁| and |S₁₁| for various d values are shown. If d is too small, the dip in transmission at resonance is too shallow to expect high absorption. However, by increasing d, the dip in transmission becomes deeper and sharper and |S₂₁| reaches the smallest value. In Fig. 3(b), the magnitude of |S₂₁| at resonance is plotted as a function of d. The smallest value of |S₂₁| is obtained for d = 0.07 mm, which we assume as a rough estimate of the optimum value. This tendency can be simply interpreted as follows: the thinner wire should be favorable for obtaining a higher ohmic loss in the rings for higher absorption; however, if the wires are too thin, the SRRs cannot have sufficient volume to interact with the EM waves. In Fig. 3(b), the resonant frequency (f_res) is also plotted as a function of d. Only a slight shift is seen around the roughly estimated optimum value of d. Next, we fixed d to be 0.07 mm and varied s. In Fig. 3(c), spectra of |S₂₁| and |S₁₁| for various values of s are shown, and in Fig. 3(d), the magnitude of |S₂₁| and its resonant frequencies are plotted as functions of s. For a smaller s, the dip in transmission at resonance is shallow and shows high reflection. In Fig. 3(e), snapshots of the electric field and surface current at resonance are shown for s = 0.5 mm. It can be seen that adjacent rings strongly interact, and it is difficult to expect the SRRs to work as isolated meta-atoms. In contrast, if the spacing between rings is sufficiently large, the SRRs can be well separated to work as meta-atoms, which can be recognized from snapshots of the electric field and surface current at resonance for s = 9.5 mm shown in Fig. 3(f). The dip in transmission becomes deeper and sharper by making s larger and reach the minimum value for s = 9.5 mm. When s is further increased, the dip in transmission becomes shallower again, which might be attributed to the lower density and thus a smaller absorption cross section of SRR arrays. Here, we assume 9.5 mm as a rough estimate of the optimum s.

 

Fig. 3. Summary of the simulation for the optimization of the geometrical parameters d and s for the reflection-less metamaterial absorber working at 2.4 GHz. Results are all for normal incidence. (a) Spectra of |S₂₁| and |S₁₁| as functions of the diameter of the wire (d). (b) Magnitude of |S₂₁| and resonant frequency as functions of d. (c) Spectra of |S₂₁| and |S₁₁| as functions of the spacing between SRRs (s). (d) Magnitude of |S₂₁| and resonant frequency as functions of s. Snapshots of the spatial distribution of the electric field and surface current for (e) s = 0.5 mm and (f) s = 9.5 mm.

Download Full Size | PDF

To optimize geometrical parameters, we further evaluated absorption by varying d and s around the roughly estimated optimum values obtained above. Figure 4 shows a contour map of the absorption A at the resonance as a function of d and s. From this result, we found the optimum geometrical parameters of d = 0.07 mm and s = 9.2 mm.

 

Fig. 4. Contour map of the absorption at the resonance as a function of the wire diameter (d) and the spacing between split ring resonators (s), which indicates that d = 0.07 mm and s = 9.2 mm are the optimum geometrical parameters.

Download Full Size | PDF

3.2 Optical properties of optimized metamaterial absorber

Spectra of transmission (T), reflection (R), and absorption (A) of the device designed with these optimum parameters are summarized in Fig. 5(a). The high absorption of 0.97 is achieved at 2.394 GHz. In addition, the reflection is well suppressed over the wide spectral range of interest; therefore, we succeeded in designing a reflection-less and highly absorbing metamaterial working at 2.4 GHz. The full width at half maximum (FWHM) bandwidth of the absorption band (Δf) is 139 MHz, and the relative bandwidth (Δf / f_res) is 0.058. In Fig. 5(b), the retrieved effective impedance Z of our device is shown. It can be seen that the real part of the impedance matches well with that of free space in the entire frequency range of interest, which also supports the observation that the reflection is well suppressed in our device. We also investigated how the resonators respond to the EM wave by visualizing surface current at 2.394 GHz. In Fig. 5(c), the simulated surface current is shown. The snapshots in the left and right panels have a phase difference of π/2. The left panel of Fig. 5(c) shows that the adjacent electric dipoles cancel each other, showing a purely magnetic response. In contrast, the right panel of Fig. 5(c) shows a purely electric response as expected. No EM wave can reradiate from such resonators owing to the destructive interference; therefore, both transmission and reflection are well suppressed at resonance. Under such condition, the incident EM energy can well dissipate as heat in the nichrome wire with high ohmic loss. This working principle is quite similar to that of the omega resonators reported by Balmakou et al. [14]. We also investigated how tolerant our device is to fabrication imperfection. We have already seen that slight deviations of d [Fig. 3(b)] and s [Fig. 3(d)] do not have much effect on the resonant frequency. We varied only g, keeping the other parameters unchanged. In Fig. 5(d), the absorption and resonant frequency of the device are plotted as functions of g. A roughly 10% deviation of g (∼ 0.3 mm) results in a less than 1% shift of the resonant frequency (< 0.02 GHz). Therefore, our device is quite tolerant to fabrication imperfection.

 

Fig. 5. Summary of the simulation of the device performance of the reflection-less metamaterial absorber working at 2.4 GHz with the optimized geometrical parameters. Results are all for normal incidence. (a) Spectra of transmission (T), reflection (R), and absorption (A) of the metamaterial absorber. (b) Spectra of the effective impedance Z. (c) Snapshots of the spatial distribution of the surface current at different timings, which corresponds to the phase difference of π/2. (d) Absorption and resonant frequency as functions of g.

Download Full Size | PDF

We also investigated the angular dependences of the transmission, reflection, and absorption spectra of the optimum device as summarized in Fig. 6 for (a) TE and (b) TM polarizations. The main response at 2.40 GHz does not show a remarkable change in oblique incidence; however, other sharp resonant responses appeared at higher frequencies of 3.76 GHz for 20° and 3.40 GHz for 30°. We also observed non-negligible cross-polarization responses for oblique incidences, which was negligible for normal incidence. Both co-polarization and cross-polarization responses are summarized in the figure. Here, T_pp (= |S_2p1p|²) and R_pp (= |S_1p1p|²) denote co-polarized transmittance and reflectance, and T_sp (= |S_2s1p|²) and R_sp (= |S_1s1p|²) denote cross-polarized transmittance and reflectance, respectively, for TE polarization. Similarly, for TM polarization, T_ss (= |S_2s1s|²) and R_ss (= |S_1s1s|²) denote co-polarized transmittance and reflectance, and T_ps (= |S_2p1s|²) and R_ps (= |S_1p1s|²) denote cross-polarized transmittance and reflectance, respectively. These polarization conversions are widely observed in various types of anisotropic metamaterial, and even device applications such as polarization manipulation are proposed [20,21]. In our device, the cross-polarization terms appeared at around the main resonance at 2.40 GHz and at other new sharp resonant responses that appeared for oblique incidence. However, the magnitudes of these cross-polarization terms are not significant and almost negligible at the main resonance at 2.40 GHz. Nevertheless, we evaluated absorbance taking these cross-polarization terms into account. Thus, here A = 1 – T_pp – T_sp – R_pp – R_sp for TE polarization and A = 1 – T_ss – T_ps – R_ss – R_ps for TM polarization. Our device maintains high absorption in a certain range of incident angles, which may be useful for the practical applications considered here.

 

Fig. 6. Summary of the simulated spectra of transmission, reflection, and absorption for normal and oblique incidences for (a) TE and (b) TM polarizations. Both co-polarized and cross-polarized responses are summarized: (a) co-polarized transmission (T_pp = |S_2p1p|²) and reflection (R_pp = |S_1p1p|²), and cross-polarized transmission (T_sp = |S_2s1p|²) and reflection (R_sp = |S_1s1p|²), and absorption (A = 1 – T_pp – T_sp – R_pp – R_sp) for TE polarization, and (b) co-polarized transmission (T_ss = |S_2s1s|²) and reflection (R_ss = |S_1s1s|²), and cross-polarized transmission (T_ps = |S_2p1s|²) and reflection (R_ps = |S_1p1s|²), and absorption (A = 1 – T_ss – T_ps – R_ss – R_ps) for TM polarization.

Download Full Size | PDF

We further investigated polarization stability characteristics as summarized in Fig. 7. Here, we define polarization conversion ratio for transmission (PCRt) and for reflection (PCRr) as PCRt = T_sp/(T_pp + T_sp) and PCRr = R_sp/(R_pp + R_sp) for TE polarization, and similarly, PCRt = T_ps/(T_ss + T_ps) and PCRr = R_ps/(R_ss + R_ps) for TM polarization, respectively. Both PCRt and PCRr are almost zero in the entire frequency range of interest for normal incidence. In contrast, for oblique incidence, sharp responses can be observed in both PCRt and PCRr at around the main peak at 2.40 GHz and at other sharp resonant responses at 3.76 GHz for 20° and at 3.40 GHz for 30° for both TE and TM polarizations. However, these effects at the main resonance at 2.40 GHz do not mean much owing to the near-perfect absorption characteristics of the device. Similarly, PCRr values at 3.76 GHz for 20° and at 3.40 GHz for 30° do not show significant effects owing to the low magnitude of the reflectance. PCRt values at these frequencies are low; therefore, the polarization state of transmitted EM waves is almost maintained. Note that both PCRt and PCRr are negligibly small at off-resonant frequencies between these resonant responses even for the oblique incidence. This implies that EM waves can be transmitted stably maintaining the polarization state outside of the resonant frequencies, which we think is favorable for the practical applications discussed above.

 

Fig. 7. Summary of the simulated spectra of polarization conversion ratio for transmission (PCRt) and reflection (PCRr) for normal and oblique incidences for (a) TE and (b) TM polarizations.

Download Full Size | PDF

Since a new sharp resonant response appeared at a higher frequency for the oblique incidence, we further explored the physical origin of these modes. In Fig. 8, snapshots of the surface current for normal incidence at 2.40 GHz and for oblique incidence from 30° at 3.40 GHz are summarized. These snapshots in each panel have a phase difference of π/4. For normal incidence, SRRs whose electric or magnetic dipoles are orthogonal to the electric or magnetic fields of the incident EM waves cannot interact with [22], and therefore, only half of the SRRs can respond to the incident EM waves as shown in Figs. 8(a) and 8(b). In contrast, for oblique incidence, all SRRs can respond to the incident EM waves as shown in Figs. 8(c) and 8(d). The hybridized mode can be induced in each paired SRRs, and they work as meta-molecules, which might be the physical origin of the new high-frequency mode that appeared and also of the polarization conversion properties observed at these frequencies. For normal incidence, only loop currents are observed in each ring at 2.40 GHz [Figs. 8(a) and 8(b)], which implies that the so-called half-wavelength resonance are induced in this condition. In contrast, other types of current flow can be seen for oblique incidence from 30° at 3.40 GHz [Figs. 8(c) and 8(d)], which might be attributed to the dipole-like responses in the hybridized modes.

 

Fig. 8. Snapshots of the spatial distribution of the surface current at different timings, which corresponds to the phase (ϕ) difference of π/4. For normal incidence (θ = 0°) at 2.40 GHz for (a) TE and (b) TM polarizations and for oblique incidence (θ = 30°) at 3.40 GHz for (c) TE and (d) TM polarizations. The direction of the incident angle and the polarization of the EM wave are also indicated.

Download Full Size | PDF

3.3 Experimental verification

On the basis of the optimized parameters obtained above, we fabricated a metamaterial absorber sample using nichrome wire of 0.07 mm diameter for experiments. Since such thin wires are too soft to maintain their shape, we used styrene foam spheres of 20 mm diameter as supports. A pair of coiled C-shaped nichrome wires are orthogonally bonded to the spheres and are periodically attached to the supporting styrene foam plate as designed. A photograph of our sample is shown in Fig. 9(a). Although thin wires are floating in vacuum in our numerical modeling, the dielectric constant of the styrene foam is nearly unity, and therefore, we believe that our sample well reproduces the condition considered in the numerical simulation. A schematic of the experimental setup for the microwave transmission measurement is shown in Fig. 9(b).

 

Fig. 9. Summary of microwave measurements. (a) Photograph of the sample. (b) Schematic of the experimental setup. Spectra of measured transmission for normal and oblique incidences for (c) TE and (d) TM polarizations.

Download Full Size | PDF

In Figs. 9(c) and 9(d), the measured transmission spectra of the metamaterial absorber are presented. For both TE and TM polarizations, a huge decrease in transmission of over 6 dB is obtained at around 2.30 GHz, and no significant difference is detected by changing the incident angle from normal up to 20°. Apart from the resonant frequency, almost no decrease in transmittance is observed; thus, reflection-less characteristics were also realized. The FWHM bandwidths of the absorption band are 135 and 157 MHz, and the relative bandwidths (Δf / f_res) are 0.059 and 0.069 from normal incidence for TE and TM polarizations, respectively. These values are quite similar to those obtained in the numerical simulation. Although the resonant frequency of the sample is slightly different from the designed one, we believe that our results clearly show sufficient performances as a preliminary demonstration.

We do not expect such a large disagreement of 0.1 GHz from the designed value from the fabrication imperfection as discussed above. The dielectric constant of the styrene foams is small (nearly unity) at THz or lower frequencies, which depends on the density of foam [23]. Therefore, we numerically investigated how the resonant characteristics can be affected by the presence of dielectric supporting materials with low dielectric constant. The transmission and reflection are simulated assuming a small dielectric constant of nearly unity for the supporting dielectric materials, and the results are summarized in Fig. 10. When the dielectric constant of the supporting material was slightly increased, the resonant frequency became lower, and the value of ∼ 2.30 GHz was attained for a dielectric constant of 1.25. Therefore, the difference in the resonant frequency between the experimental measurements and the numerically designed values might be attributed to the presence of the supporting styrene foam spheres. The value of |S₂₁|² remains low, which implies that the nearly perfect absorption characteristics are not affected by the presence of the supporting styrene foams with low dielectric constants.

 

Fig. 10. Summary of the simulation of transmission and reflection assuming a small dielectric constant of nearly unity for the supporting dielectric materials. (a) Transmission (T) and reflection (R) spectra. (b) Magnitude of |S₂₁|² and resonant frequency as functions of the dielectric constant of the supporting dielectric materials.

Download Full Size | PDF

4. Conclusions

We successfully demonstrated a reflection-less metamaterial absorber that shows frequency-selective narrow-band near-perfect absorption at a Wi-Fi band of 2.4 GHz. Our device is constructed with an orthogonally arranged square array of pairs of C-shaped SRRs and does not have a ground plane. The induced electric and magnetic dipoles destructively interfere and no reradiation of EM waves is possible; therefore, reflection is well suppressed in our device. When nichrome wire with high ohmic loss is used, EM energy can well dissipate as heat. On the basis of the numerical simulation, we obtained the optimum geometrical parameters of SRRs and obtained absorption of 97% at 2.4 GHz. We also fabricated a proof-of-concept device using nichrome wire and obtained a huge decrease in transmission at a resonance of – 6 dB and observed no reflection over the entire frequency range of the interest. The thickness of our device is 20 mm ( = 2r) without a supporting styrene foam plate, which is roughly λ/6. The basic principle demonstrated here can be easily extended to higher frequencies, possibly up to THz [14]. Our subwavelength-thick reflection-less metamaterial absorber may have a wide variety of practical applications in a wide variety of circumstances such as next-generation wireless communications, IoT, and so forth.