Dual band metamaterial perfect absorber based on artificial dielectric “molecules”

Dual band metamaterial perfect absorbers with two absorption bands are highly desirable because of their potential application areas such as detectors, transceiver system, and spectroscopic imagers. However, most of these dual band metamaterial absorbers proposed were based on resonances of metal patterns. Here, we numerically and experimentally demonstrate a dual band metamaterial perfect absorber composed of artificial dielectric “molecules” with high symmetry. The artificial dielectric “molecule” consists of four “atoms” of two different sizes corresponding to two absorption bands with near unity absorptivity. Numerical and experimental absorptivity verify that the dual-band metamaterial absorber is polarization insensitive and can operate in wide-angle incidence.


Results
Design and numerical simulations. The unit cell of the dielectric "molecules" based dual-band metamaterial absorber is demonstrated in Fig. 1a. It consists of dielectric "atoms" with two different sizes ("atoms" A and "atoms" B) periodically embedded into a background matrix (acrylonitrile butadiene styrene: ABS) on the metallic ground plane. The unit cell of the metamaterial absorber has the dimensions, in millimeters, of: The background matrix ABS with permittivity ε 1 = 2.67 and loss tangent tanδ 1 = 0.006 is used to fix the position of the dielectric "atoms". The permittivity and loss tangent of the dielectric cubes are ε 2 = 341, tanδ 2 = 0.002, respectively. The metallic ground plane is made of copper with conductivity σ = 5.8 × 10 7 s/m. Numerical simulations were performed using the finite-difference time domain (FDTD) method. The electromagnetic plane wave with incident angle θ, polarization angle ϕ was launched from Port 1 to the absorber sample along y direction. Periodic boundary conditions were set along the x and z axis. The simulated reflection spectrum (θ = 0, ϕ = 0) shown in Fig. 1b indicated that we achieved two reflection minimum with R = 2% at 9.4 GHz and R = 1% at 11.7 GHz. The transmission T is zero across the entire frequency range due to the metallic ground plane. Therefore, two absorption peaks with A = 98% at 9.4 GHz and A = 99% at 11.7 GHz were achieved according to A = 1-R-T.
To explore how the two absorption bands were generated, we then simulated the electric and magnetic field distributions in the dielectric "atoms" at 9.4 and 11.7 GHz. As shown in Fig. 2a, there was a strong electric field distribution in "atoms" A with bigger size at lower frequency 9.4 GHz, which coupled strongly to the incident electric field leading to an intense electric resonance. At the same time, it is shown in Fig. 2c that there was also a strong magnetic field distributions in "atoms" A which generate a magnetic resonance at the same frequency. The similar electric and magnetic resonances were also found in "atoms" B with smaller size at 11.7 GHz, as demonstrated in Fig. 2b,d. The simultaneous resonances of electric permittivity ε(ω) and magnetic permeability μ(ω) made our metamaterial absorber impedance-matched to free space ε(ω) = μ(ω) at two absorption frequencies.
The incident electromagnetic wave was trapped in the dielectric "atoms" without reflection R. The transmissivity T is zero across the entire frequency range due to the metallic ground plane. Therefore, two absorption peaks with near unity absorptivity A were achieved. The power loss density of this metamaterial absorber at 9.4 and 11.7 GHz in Fig. 2e,f indicated that the main loss was produced by the dielectric loss of the resonant dielectric "atoms". Experimental results. We built a dielectric "molecules" based dual-band metamaterial absorber sample according to the predesigned structure. The dielectric "atoms" was made by strontium titanate ceramic SrTiO 3 (ε 2 = 341, tanδ 2 = 0.002), the absorber sample was composed of 289 artificial "molecules" (1156 artificial "atoms") inserted into an ABS matrix on a metallic ground plane shown in Fig. 3a. The absorption performance was    with R = 3% at 9.4 GHz and R = 2.5% at 11.7 GHz. Therefore, two absorption peaks with A = 97% at 9.4 GHz and A = 97.5% at 11.7 GHz were experimentally achieved, which was in reasonable agreement with the simulation though the absorption peaks were lower than expected and there were some small split peaks due to fabrication imperfections.

Discussion
Absorptivity with different polarization angle ϕ, and incident angle θ in transverse electric (TE) and transverse magnetic (TM) modes were further considered to evaluate the absorption properties. Figure 4a,b demonstrated the simulated and experimental absorptivity with different polarization angle ϕ at 9.4 and 11.7 GHz, respectively. It indicated that the two absorption peaks were independent on the polarization angle ϕ changing from 0 to 75 degrees. With TE incident wave, the absorptivity at 9.4 GHz was above 94% when the incident angle θ changed from 0 to 60 degrees. Then the absorptivity decreased dramatically from 94% to 65% as θ varied from 60 to 75 degrees shown in Fig. 4c. Figure 4d indicated that the absorptivity at 11.7 GHz was above 85% when the incident angle θ changed from 0 to 60 degrees. Then decreased from 85% to 60% as θ varied from 60 to 75 degrees. With TM incident wave, the absorptivity at 9.4 GHz decreased from 98% to 55% and the absorptivity at 11.7 GHz decreased from 99% to 60% when the incident angle θ changed from 0 to 75 degrees as shown in Fig. 4e,f. Simulated and experimental absorptivity was always above 78% when the incident angle below 60 degree in both TE and TM modes showing efficient function in wide-angle incidence.
In conclusion, a dual-band metamaterial perfect absorber based on artificial dielectric "molecules" was experimentally and numerically demonstrated. The metamaterial absorber consisted of a metallic ground plane and 289 dielectric cubic "molecules" (1156 dielectric "atoms") embedded in ABS matrix. The dielectric "atoms" of different sizes coupled strongly to the incident electric and magnetic field at different frequencies leading to two absorption bands with simulated absorptivity of 98% and 99%, experimental absorptivity of 97% and 97.5% at 9.4 and 11.7 GHz. Numerical and experimental absorption spectra verified that the dule-band metamaterial absorber was polarization insensitive and could operate in wide-angle incidence.

Methods
Sample fabrication. High temperature solid-state reaction method was used to synthesize the ceramic material strontium titanate SrTiO 3. We added 5% polyvinyl alcohol (PVA) to SrTiO 3 powders with the mass ratio of 1:10 and mixed them homogeneously. The mixture was then uniaxially pressed into cylinders at 20 MPa, cold isostatically pressed at 200 MPa, and pressurelessly sintered at 873K for 2h and 1673 K for 4 h in air. Then we cut the ceramic cylinders into cubes with geometric parameters obtained from numerical simulations. We inserted dielectric cubes into the background matrix ABS and added a copper plate at the back to achieve the due-band dielectric metamaterial absorber.