1. Introduction

Metamaterial perfect absorbers are composed of periodically arranged subwavelength artificial “atoms” with predesigned dimensions. With the ability of explicit design of the effective parameters, metamaterial perfect absorber with near unity absorptivity can be achieved. The first narrow band metamaterial perfect absorbers working in the terahertz and microwave regimes were demonstrated in 2008 [1,2]. The key issue to design a perfect absorbor is to satisfy the impedance-matched condition ε(ω) = μ(ω) at the working frequency by generating electric and magnetic resonances simultaneously. These absorbers consisted of two distinct metallic elements: electric ring resonators and split-wires. The electric and magnetic responses derived from the electric ring resonators and the anti-parallel currents between the electric ring resonators and split-wires, respectively. Since then, a large number of metamaterial perfect absorbers have been demonstrated numerically or experimentally from microwave to optical realm [3–9]. The narrow band metamaterial absorbers have stimulated tremendous interests due to its important applications in terms of sensing [10], thermal imaging [8] and emitting [11], and optical switching [12]. However, almost all of these metamaterial absorbers have been based on patterned metal “atoms” to produce electric and magnetic responses so far. Actually, besides of metal “atoms”, dielectric “atoms” can also be used to build perfect absorbers because a single dielectric “atom” can support a series of electric and magnetic resonance modes owing to multiple Mie resonances [13]. Metamaterials composed of dielectric spheres [14–23], cubes [24–30] and rods [30–35] have been widely utilized to achieve exotic electromagnetic properties. Here, we numerically designed and experimentally verified a metamaterial perfect absorber consisting of dielectric ceramic material (SrTiO3) cubic “atoms” and a metallic ground plane. The dielectric “atoms” couple strongly to the incident electric and magnetic fields at the Mie resonance mode, leading to a narrow absorption band with simulated and experimental absorptivities of 99% and 98.5% at 8.96 GHz, respectively. Mie resonances of dielectric “atoms” provide a novel and simple method to construct metamaterial perfect absorbers. This dielectric “atoms” based metamaterial perfect absorber is polarization insensitive and can work in wide-angle incidence.

2. Metamaterial structure and numerical design

The metamaterial absorber consisted of a metallic ground plane and dielectric “atoms” embedded in a background matrix (acrylonitrile butadiene styrene: ABS) as shown in Fig. 1(a). The unit cell of the metamaterial absorber had the dimensions, in millimeters, of: a = 1.8, p = 8. The background matrix with low permittivity ε₁ = 2.67 with loss tangent tanδ₁ = 0.006 was used to fix the position of the dielectric “atoms” which possessed high permittivity ε₂ = 341 with loss tangent tanδ₂ = 0.002. The metallic ground plate (thickness d = 0.1 mm) was made of copper with conductivity σ = 5.8 × 10⁷ s/m. $R(f)={\left|S_{11}(f)\right|}^2$, $T(f)={\left|S_{21}(f)\right|}^2$, S₁₁ and S₂₁ were the scattering S parameters. T(f) was zero across the entire frequency range because the metallic ground plane was thicker than the penetration depth. Therefore,

 

Fig. 1 (a) The designed dielectric metamaterial absorber and its unit cell. (b) Dielectric metamaterial absorber sample.

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Numerical simulations were performed using the finite-difference time domain (FDTD) method with the unit cell boundary conditions along the x and y axis. The electromagnetic plane wave with incident angle θ, polarization angle φ was illuminated on the sample shown in Fig. 1(a). When the incident angle θ = 0 and the polarization angle φ = 0, the simulated S₁₁ and S₂₁ spectra were demonstrated in Fig. 2(a). According to Eq. (1), the absorptivity spectrum was shown in Fig. 2(b) (solid line) which indicated that we achieved an absorption peak with A = 99% at 8.96 GHz.

 

Fig. 2 (a) The simulated S₁₁ and S₂₁ spectra, (b) absorptivity spectra,and (c) μ/ε with the incident angle θ = 0 and the polarization angle φ = 0.

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3. Absorption mechanism

According to the relationship among absorptivity A, reflectivity R, and transmissivity T, A = 1-R-T, near unity absorptivity can be obtained at predesigned frequency when both reflectivity R and transmissivity T are minimized. In our design, T is zero across the entire frequency range because the metallic ground plane is thicker than the penetration depth. Therefore, near unity absorptivity can be achieved when the reflectivity R is near zero. The reflectivity R can be calculated by $R={\left|\frac{Z-Z_0}{Z+Z_0}\right|}^2$when the incident electromagnetic wave is normal to the metamaterial absorber. Where, $Z=\sqrt{\mu {\mu }_{\text{0}}/\epsilon {\epsilon }_0}$ is the impedance of the metamaterial absorber. $Z_0=\sqrt{{\mu }_0/{\epsilon }_0}$ is the impedance of free space. ε and μ are the effective permittivity and permeability of the metamaterial absorber. ε₀ and μ₀ are the permittivity and permeability of free space. With the explicit design of the effective permittivity ε and permeability μ, this metamaterial absorber can be impedance-matched to free space μ/ε = 1, which makes a reflectivity R of 0 at the working frequency. The values of the effective permittivity ε and permeability μ of the metamaterial absorber can be changed by electric and magnetic resonances, respectively. Therefore, when both electric and magnetic resonances are generated, the impedance-matched condition can be satisfied leading to near unity absorptivity at working frequency. We monitored the electric and magnetic field distributions in the dielectric “atom” at 8.96 GHz. Figure 3(a) showed the circular electric field distribution surrounded the incident magnetic field generating the magnetic resonance. At the same time, the circular magnetic field distribution surrounded the incident electric field illustrated in Fig. 3(a) proved that the electric resonance was also produced. For a single dielectric “atom” without metal plate, the electric and magnetic fields are symmetric at resonances. In order to block the transmission, we added a metal plate behind the dielectric “atoms”. The generated current in the metal plate coupling to the electric and magnetic fields in the dielectric “atoms” lead to the asymmetry of the electric and magnetic fields in the dielectric “atom” as shown in Fig. 3(a). Therefore, the values of the effective permittivity ε and permeability μ of the metamaterial absorber can be modulated in electric and magnetic resonances. Now the key issue to design the perfect absorption peak is to satisfy the impedance-matched condition μ/ε = 1.

 

Fig. 3 Numerical results of the metamaterial absorber at 8.96 GHz.(a) The electric and magnetic field distributions in the dielectric “atom”. (b) The electric and magnetic energy density distributions in dielectric “atoms”. (c) The power loss density distributions in dielectric “atoms”, ABS and the copper.

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The effective permittivity ε and permeability μ of the metamaterial absorber can be extracted from the simulated scattering S parameters using a well-developed retrieval algorithm as follows [36–38]:

Where, S₁₁ and S₂₁ are the scattering S parameters which can be achieved directly from simulation and experiment. d, z and n are the thickness, impedance and refractive index of the metamaterial absorber. k₀ denotes the wave number of the incident wave in free space. From Eqs. (2)-(4), the impedance z and refractive index n of the metamaterial absorber can be calculated. Then the value of the effective permittivity ε and permeability μ of the metamaterial absorber can be calculated according to Eq. (5). Figure 2(c) showed the value of μ/ε around 8.96 GHz. It indicated that the impedance-matched condition μ/ε = 1 was satisfied at 8.96 GHz leading to the reflectivity R of 0, near unity absorptivity can be achieved. The electric and magnetic energy density distributions were demonstrated in Fig. 3(b) which indicated that these two resonances ensured that the incident electromagnetic power was totally trapped in the dielectric “atoms” and transferred to heat without transmitting or scattering. The power loss density distributions in dielectric “atoms”, ABS and the copper at 8.96 GHz were demonstrated in Fig. 3(c). The energy absorbing ratios between the dielectric “atoms”, ABS, and copper plate was 91.5: 3.2: 5.3, which was calculated by the volume integration of power loss density. The main loss was produced by the dielectric loss of the resonance “atoms”.

4. Aborsoption with different polarization and incident angle

The Mie resonances of dielectric cubic atoms is polarization insensitive as the induced electric and magnetic resonances in the cube is intrinsically isotropic. We simulated the absorption property of the dielectric metamaterial absorber in different polarization angles. The absorptivity remained 99% when the polarization angle φ changed from 0 to 75 degrees as demonstrated in Fig. 4. The electric and magnetic resonances insensitive to polarization angles took place due to circular magnetic and electric field distributions surrounded the incident electromagnetic fields leading to the narrow absorption peak (A = 99%) at 8.96 GHz. The simulated absorptivity at working frequency with different incident angle θ of the transverse electric (TE) and transverse magnetic (TM) waves were demonstrated in Fig. 4. With TE incident wave, the absorptivity decreased slowly from 99% to 97% when the incident angle θ changed from 0 to 30 degrees. Then the absorptivity decreased dramatically from 97% to 60% as θ varied from 30 to 75 degrees. While, with TM incident wave, the absorptivity remained 99% when incident angle θ changed from 0 to 40 degrees. Then the absorptivity decreased slowly from 99% to 81% as θ varied from 30 to 75 degrees. The absorptivity was still above 90% when the incident angle was 45 degrees with both TE and TM incident waves. We found that the absorptivity in TE mode was more sensitive to the incident angle than TM mode. When the incident angle was above 45 degrees, the absorptivity in TE mode reduced drastically. However, the absorptivity in TM mode decreased slowly. Actually, the absorbing frequency 8.96 GHz is near the first Mie resonance of the dielectric “atoms”. The first Mie resonance is magnetic resoance which is more sensitive to the incident magnetic field. In TM mode, the direction of the incident magnetic field doesn’t change, leading to high absorptivity above 45 degrees.

 

Fig. 4 Absorptivity spectra with polarization angle φ, and incident angle θ in TE and TM modes.

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5. Experimental verification

A dielectric ceramic material SrTiO₃ (ε₂ = 341, tanδ₂ = 0.002) was fabricated by the solid state reaction method and then cut into cubes with the same geometric parameters of the numerical simulation. We inserted the cubes into the ABS matrix and added a piece of copper with the thickness of 0.1 mm under the matrix to form a 150 cm × 150 cm metamaterial absorber sample (Fig. 1(b)). The microwave absorption performance was measured experimentally in free space by a network analyzer (Agilent HP8720ES). Two linearly polarized focused antennas were connected to the network analyzer with low-loss coaxial cable to emit and receive electromagnetic waves in the frequency band of 8.2–12.4 GHz. We placed the sample at the focus of the two antennas in a microwave anechoic chamber. When the incident angle θ = 0 and the polarization angle φ = 0, the measured absorptivity spectrum was shown in Fig. 2(b)(dash dot line) which indicated that we achieved an absorption peak with A = 98.5% at 8.96 GHz. We rotated the sample to measure the reflectivity at different polarization angles. The experimental absorptivity at 8.96 GHz with different polarization angle φ was shown in Fig. 4. It indicated that we achieved an absorption peak with A = 98.5% at 8.96 GHz which didn’t change when the polarization angle φ changed from 0 to 75 degrees. Then we moved the emitting and receiving antennas along the arc line to measure the reflectivity at different incident angles. The experimental at 8.96 GHz with different incident angle θ of the transverse electric (TE) and transverse magnetic (TM) waves were demonstrated in Fig. 4. With TE incident wave, the absorptivity decreased slowly from 98.5% to 97% when the incident angle θ changed from 0 to 30 degrees. Then the absorptivity decreased dramatically from 97% to 57.2% as θ varied from 30 to 75 degrees. While, with TM incident wave, the absorptivity remained 98.5% when incident angle θ changed from 0 to 40 degrees. Then the absorptivity decreased slowly from 98.5% to 80.7% as θ varied from 30 to 75 degrees. The absorptivity was still above 90% when the incident angle was 45 degrees with both TE and TM incident waves. We achieve good agreement between experimental and simulated results.

6. Summary

In conclusion, a dielectric “atoms” based metamaterial perfect absorber with near unity absorbance in microwave is experimentally and numerically demonstrated. The metamaterial absorber consists of a metallic ground plane and 484 dielectric cubic “atoms” embedded in ABS matrix. The dielectric “atoms” couple strongly to the incident electric and magnetic fields at the Mie resonance mode, leading to the narrow absorption band with simulated and experimental absorptivity 99% and 98.5% at 8.96 GHz, respectively. The absorptivity remained 99% when the polarization angle φ changed from 0 to 75 degrees and above 90% when the incident angle was 45 degrees with both TE and TM incident waves. The designed metamaterial absorber is polarization insensitive and can operate in wide-angle incidence. Unlike patterned metal blocks, dielectric cubes as artificial “atoms” can support a series of electric and magnetic resonance modes and offer a simpler route for the production of metamaterial perfect absorber.