Polarization-Independent and Angle-Insensitive Metamaterial Absorber Using 90-Degree-Rotated Split-Ring Resonators

We present the design, simulation, and measurement of a polarization-independent and angle-insensitive metamaterial absorber (MA) in X-band. Since the unit cell of the MA consists of four subwavelength split-ring resonators with 4-fold symmetric rotation, the MA is insensitive to the variation of both polarization and incident angle of the planar electromagnetic wave. The electromagnetic performances of the MA are studied by full-wave simulations based on finite-element method and the Naval Research Laboratory arch experimental measurements.The electric field distributions are numerically investigated, which confirm the polarization-insensitive property of the MA, as expected from the symmetric nature of the structure. When the incident angles vary from 0 to 45 degrees, the MA remains at full width at half maximum of 0.4GHz (0.5GHz) with peak absorptions of 99.9% (95.2%) at 10.27GHz (10.3 GHz) by simulations (measurements).

In this study, an X-band polarization-independent and angle-insensitive MA based on 90-degree-rotated split-ring resonators (SRRs) is designed and proposed.The MA is designed and optimized by full-wave simulations using finiteelement method (FEM) based commercial software ANSYS HFSS and verified by the Naval Research Laboratory (NRL) arch experimental measurements.We will show that the proposed MA yields not only a compact structure that can be readily fabricated through standard printed circuit board (PCB) technology, but also good polarization-independent and angle-insensitive absorption characteristics from both simulation and experiment results.

MA Design
For our MA design, we chose unit cell with 4-fold rotational symmetric configuration, which leads to polarizationindependent property.Meanwhile, the MA constructed with subwavelength unit cells can offer angle-insensitivity property.Figure 1 where reflection  = | 11 | 2 and transmission  = | 21 | 2 are obtained from simulated and measured -parameters.
From this equation, reflection  and transmission  should be minimized to achieve maximum absorption .The transmission  of the proposed MA is equal to zero,  21 = 0, due to the presence of the metallic ground plane in our design.Therefore, the absorption  of the MA can be maximized by minimization of the reflection .
To better understand the mechanism of the perfect absorption of the MA, the effective impedance of the MA can be obtained from effective medium theory [31][32][33]: Combination of ( 1) and ( 2) results in the general expression of the absorption: In case of perfect absorption,  = 1, the real part of the effective impedance should match the free-space value, Re() = 1, and the imaginary part is supposed to be vanished, Im() = 0, according to (3).

Simulations and Measurements
The MA with three layers is modelled with full-wave FEM solver ANSYS HFSS.The top layer is made of 90-degreerotated SRRs in a periodic pattern.The middle layer is dielectric substrate FR4.The bottom layer is a solid metallic ground plane.The simulation is based on a MA unit cell along with Floquet ports and Master/Slave periodic boundary condition (PBC).The usage of PBC can mimic an infinite extended periodic structure.
The simulated  11 of the MA is shown in Figure 2. A minimal reflection of near zero is observed at 10.27 GHz.By using (1) and (2), the absorption and effective impedance can be easily calculated.The effective impedance is calculated and shown in Figure 3.The inset in Figure 3 shows the zoomed view of the effective impedance.It can be observed that the real part of the effective impedance of the MA is near unity (matched to the air), Re() ≅ 1, and imaginary part of the MA is near zero, Im() ≅ 0 at 10.27 GHz, corresponding to the perfect absorption.Figure 4 shows the absorption as a function of polarization angle with step of 10 ∘ at 10.27 GHz.The absorption amplitude for different polarization angles varies by less than 1‰.The detailed discussion on angleinsensitive property of the proposed MA is presented in the fifth paragraph of this section.
Figure 5 shows the simulated electric field distribution at 10.27 GHz for normal incident TE and TM waves, as well as the 45 ∘ condition.It is seen that the MA performs almost the same electric field distributions, except a 90-degree rotation, for normal incident TE and TM waves, as shown in Figures 5(a) and 5(b).This indicates that the symmetrical structure of the MA with the unit cell of 4-fold rotational SRRs possesses a polarization-independent performance, in accordance with our predication.In Figure 5(c), the electric field distribution for 45 ∘ incident electromagnetic waves is shown at 10.27 GHz.In this condition, we discovered that all of the incident electromagnetic waves are absorbed by the four 90-degreerotated SRRs.To verify the numerical results, we fabricate the MA by using PCB technique, as shown in Figure 1(b).The absorption characteristics of the fabricated MA at different incident angles are measured with the NRL arch, as shown in Figure 6.NRL arch is a reliable standard for characterizing the reflection and absorption of materials [34].In our measurements, a vector network analyzer (Agilent N5244A) is used to measure the reflection of the proposed MA.
Figure 7 shows the simulated and measured absorption at incident angles from 0 to 45 degrees in X-band.It can be seen that when the incident angle of the electromagnetic wave is altered from 0 to 45 degrees, the absorption does not change significantly, which proves that our proposed MA possesses angle-insensitive property.It is known that a periodic structure with subwavelength dimensions of unit cell is equivalent to a homogenous and isotropic medium.The effective impedance of a homogenous and isotropic medium is stable for wide angles of incident electromagnetic waves.Therefore, the strong subwavelength dimensions of the lattice constant of unit cell ( = 5 mm) and dielectric thickness (0.8 mm) of the MA make it absorb wide angles of incident electromagnetic waves.The measured results are in good agreement with numerical simulations.The small discrepancy of the peak absorption with the change of incident angle might be due to nonidealities of fabrication, such as the surface roughness of the metal pattern and nonuniformity of the dielectric substrate.
Furthermore, the full width at half maximum (FWHM) and fractional bandwidth (FBW) are very important parameters to describe the performance of the MA.Fractional bandwidth (FBW) was calculated as where   is the center frequency of FWHM.For incident angles varying from 0 to 45 degrees, the MA remains at the FWHM of 0.4 GHz with peak absorptions of 99.9% at 10.27 GHz in simulations, while in experiments the MA remains at an FWHM of 0.5 GHz with peak absorptions  of 95.2% at 10.3 GHz, as shown in Figure 7.It is worth noting that the difference between the simulations and measurements can be attributed to the fabrication tolerance and measurement calibration.
The measured FBW of the MA is about 5% (FWHM ≅ 0.5 GHz,   ≅ 10.3 GHz), which is good enough for many practical applications.For example, both the microstrip patch antenna and the waveguide slot antenna generally need less than 3% FBW for efficient operations [35,36].Hence, this MA is a promising candidate for radar cross section reduction of antennas and antenna arrays.

Conclusions
The theoretical analysis, full-wave FEM simulation, fabrication, and measurement of an X-band polarizationindependent and angle-insensitive MA are demonstrated.The MA employs 90-degree-rotated SRRs as a unit cell, which shows the absorption FBW of 5% with incident angles ranging from 0 to 45 degrees by experiment.The measured results are in good agreement with the theoretical analysis and the full-wave FEM simulated ones, which provide effectively design guidelines for MAs.The proposed MA exhibits simple planar structure, easy fabrication using PCB technology, polarization-independence, angle-insensitiveness, and sufficient effective band.These remarkable features allow the MA to be a promising candidate for future applications, such as bolometer, perfectly matched layer, and scattering reductions.
(a)  shows the geometry of the unit cell of the MA, and the fabricated prototype of the proposed MA is illustrated in Figure1(b).The unit cell of the MA consists of four symmetric subwavelength 90-degree-rotated SRRs, and it is fabricated by etching an 18 m thick copper (conductivity 5.8 × 10 7 S/m) pattern on an FR4 (relative permittivity 4.4 and dielectric loss tangent 0.02) epoxy dielectric substrate with 0.8 mm thickness.The optimized geometrical parameters of the unit cell are listed in the caption of Figure1(a).The absorption  of the MA can be determined by the expression[30]

Figure 2 :Figure 3 :
Figure 2: The simulated  11 of the proposed MA from a normal incident planar wave.

Figure 4 :
Figure 4: Simulated absorption as a function of polarization angle with step of 10 ∘ at 10.27 GHz.

Figure 6 :Figure 7 :
Figure 6: NRL arch used to measure the absorption of the MA at different incident angles.(a) Front and (b) side view of the experimental setup.The insert in (b) shows the zoomed view of the MA under measurement.