# Wide Bandwidth Angle- and Polarization-Insensitive Symmetric Metamaterial Absorber for X and Ku Band Applications

#### ByAUTHOR

Jun 25, 2020

Metamaterial (MM) absorbers are recent developments in the field of electromagnetic wave applications like 5 G antenna, Radar cross-section reduction, remote sensing, stealth technology and photo-electron absorption in THz range, etc. MM absorbers are those materials that usually exhibit either negative permittivity or negative permeability or both are negative when electromagnetic (EM) waves pass through them1,2,3. As a result, they absorb most of the EM waves, as the transmission coefficient of MM absorber is negligible, and the reflection coefficient is very small. These properties are not present in any material generally used for EM wave applications unless they are engineered4,5. Research is going on to achieve absorbance of certain selective range or entire incident EM waves for purpose-wise applications6,7,8,9,10. Different types of substrate materials are used for appropriate di-electric properties for the desired absorbance of the EM waves11. FR4 (fire retardant 4) is one of the most popular and widely used substrates for MM absorber design12. Although FR4 is not appropriate because of high dielectric loss13 at high-frequency range like X and Ku band, it is popular because of low cost, availability and most importantly, absorber applications due to high dielectric loss.

The absorption capability of an MM absorber depends not only on the unit cell design but also on the angle of incidence of the incident EM wave and their polarization types. EM waves are sometimes needed to be absorbed for sensing devices or frequency-selective antenna where the type of polarization and incident angle is important for the absorption capacity of the absorber.

Research is going on to design MM absorbers with features like angle and polarization insensitiveness. The unit cell should also be symmetrically shaped like a split-ring cross resonator, circular sector, Jerusalem cross-section, four-fold symmetric and so on14,15,16,17,18,19. These absorbers can absorb EM waves with high efficiency at some certain frequencies with very low bandwidth. Hence, they are not appropriate for mass deployment into places for wide bandwidth absorption like radar cross-section reduction, remote sensing, unwanted frequency absorption in antennae, stealth capability in modern military airplanes and so on. To overcome all these challenges in this modern age, the MM absorbers should be designed with such precision that, they will be polarization and wide-angle insensitive, symmetric in structural design, capable of high absorption and most importantly, they must have broad bandwidth of absorption efficiency. For both X and Ku band, only a few absorbers are designed with FR4 to date. The efficiency of those absorbers is not at a satisfactory level concerning the afore-mentioned performance indicators.

In this paper, we propose an MM absorber which satisfies all these properties for X and Ku band applications. We also have compared the performance of the unit cell with recently published relevant absorbers and found it better in all aspects of the above-mentioned performance categories. The most popular FR4 substrate is used as the dielectric barrier for the unit cell, where the copper patch is backed up by a copper ground with the substrate in between them.

### Design of unit cell

Usually, absorption with broad bandwidth and negative value of either permittivity or permeability or both, are the key objectives of designing an MM absorber. Any substrate can be used to design the patch on it with or without a ground at the opposite side of the patch. Commercially and widely used FR4 is not found much with broad bandwidth absorption in the X and Ku band regions. In this project, FR4 substrate (loss tangent = 0.025, dielectric constant = 4.3 and relative permeability = 1) with 1.578 mm thickness was used to design the proposed MM absorber unit cell. Fortunately, a broadband frequency absorption was achieved with so many attempts in the patch and the ground plane design with ending up to the following design shown in Fig. 1. The shape of the patch became like this from the intention of keeping square-shaped inductive and rectangular-shaped capacitive ring elements with 90-degree symmetric rotations. The metallic square rings are continuous for ensuring inductance and the rectangular rings are discontinuous by splits for capacitance. The entire unit cell is four-fold symmetrical as each quadrant are equivalent and rotated by 90 degrees. The size of the unit cell is 10 × 10 mm. The detailed dimension of the unit cell and a quadrant is shown in Fig. 2. Each quadrant is shown in different colors for the understanding of the patch design with the central square associated with all quadrants.

Each quadrant acts as an associate resonator to demonstrate the single negative value of either permittivity or permeability. The center of the total patch acts as a bridge to ensure equivocal current flow from any direction throughout the unit cell. The slits at the square border act as a capacitive load to perform for absorption in the lower frequencies (X band), whereas the discontinuities in the body of the patchwork for absorption in the higher frequencies (Ku band). Each quadrant with the center square and the perimeter lines act as inductive loads with complex values for reflection and transmission coefficients. The ground was chosen to reflect EM waves only to the quadrants except for the circumferential border transmission lines for better performance. This was because, the EM waves (any type of polarized) were needed to be rippled back from the ground to the patch so that the transmission coefficient of the unit cell is not negligible, which is essential to ensure negative values of permittivity and permeability.

The unit cell was fabricated (as shown in the top inset of Fig. 2) and data were taken using the cell in the PNA Network analyzer (N5227A).

### Metamaterial fundamentals and results

The absorption capability of an MM absorber can be calculated by

$$A(omega )=1-R(omega )-T(omega )$$

(1)

if the reflection coefficient R (ω) and transmission coefficient T(ω) are zero, the highest absorption can be achieved. In the case of normal incidence of EM wave, the reflection coefficient can be achieved by

$$R(omega )=frac{Z(omega )-{Z}_{o}}{Z(omega )+{Z}_{o}}$$

(2)

where Z(ω) is the impedance of the MM absorber and zo is the impedance of the free space (air). When Z(ω) = Zo = 377 Ω, the reflection coefficient becomes zero. The characteristic or built-in impedance of the absorber can be found by

$$Z(omega )=sqrt{frac{{(1+{S}_{11}(omega ))}^{2}-{S}_{21}{(omega )}^{2}}{{(1-{S}_{11}(omega ))}^{2}-{S}_{21}{(omega )}^{2}}}$$

(3)

as the designed unit cell has a symmetric patch, the dependence of characteristic impedance of the cell on the incident angle was not an issue. Furthermore, the groundsheet at the back of the substrate didn’t allow any EM waves to be transmitted through it. Hence the transmission coefficient was negligible and any amount of it was dissipated due to the dielectric loss tangent of the substrate medium. The simulated values of the reflection (S11) and transmission (S21) coefficients were found below −10dB at the resonance frequencies.

The refractive index (η) of the unit cell was calculated by two different methods: the Nicolson-Ross-Weir (NRW) method and the Direct Refractive Index (DRI) method as shown in the Eqs. (4) and (7) below.

$${rm{By}},{rm{NRW}},{rm{method}},,{rm{eta }}=-real[sqrt{{in }_{r}{mu }_{r}}]$$

(4)

Where,

$${in }_{r}({rm{relative}},{rm{permittivity}})=frac{2}{sqrt{-frac{omega }{c}d}}frac{1-({S}_{21}+{S}_{11})}{1+({S}_{21}+{S}_{11})}$$

(5)

And

$${mu }_{r}({rm{relative}},{rm{permeability}})=frac{2}{sqrt{-frac{omega }{c}d}}frac{1-({S}_{21}-{S}_{11})}{1+({S}_{21}-{S}_{11})}$$

(6)

here ω = 2πf (f is the frequency of applied EM wave), d = thickness of the substrate and c = speed of light.

$${rm{By}},{rm{DRI}},{rm{method}},,{rm{eta }}={rm{real}}left[frac{c}{ipi fd}sqrt{frac{{({S}_{21}-1)}^{2}-{({S}_{11})}^{2}}{{({S}_{21}-1)}^{2}+{({S}_{11})}^{2}}}right]$$

(7)

using Eq. (1) and (4) to (7), the results were found using simulated S11 and S21 parameters in transverse electric and magnetic (TEM) mode, which are tabulated in Table 1. The S parameters were found for 3 different polarized incident EM waves.

It is clear from Table 1 that, highest possible absorptions were found with a negative value of either permittivity or permeability. As a result, the refractive index became negative as per Eq. (5) & (6), which confirmed the metamaterial (MM) characteristics of the proposed unit cell. Also, the absorption bandwidth was calculated for frequencies with more than 70% absorption (for ensuring −10dB value of S11 and S21 parameters), which are quite good values and proved the design as a wide bandwidth MM absorber. The simulated absorption for plane-polarized EM waves at different normal incidences is plotted in Fig. 3, which shows similar performance with negligible distortions.

The simulated absorptions for plane-polarized EM waves at different oblique incidences for TE (transverse electric) mode and TM (transverse magnetic) mode of applied incident waves are plotted in Fig. 4(a,b) respectively.

It is observed in Fig. 4(a) that, a considerable bandwidth of absorption (≈1.75 GHz) is ensured from the oblique incidence of applied EM waves on the proposed absorber in TE mode. Broadband absorption is achieved from 12.7 GHz to 13.46 GHz, 14.72 GHz to 15.19 GHz and 16.45 GHz to 16.97 GHz considering −10dB value of S11 and S21 parameters. Whereas in TM mode of applied EM wave at oblique incidence (Fig. 4(b)), the bandwidth of absorption reduces significantly to ≈1.24 GHz. It is important to mention that, in both TE and TM mode for oblique incidence, the proposed absorber can absorb only at Ku band, but bandwidth is increased compared to normal incidence.

At the resonance frequencies, the value of either relative permittivity or relative permeability was found negative as shown in Fig. 5, which ensures the negative value of the refractive index as per Eq. 4 & 7. Hence the absorption of applied EM waves at normal and oblique incidences is justified from the negative value of the refractive index.

The impedance of the unit cell in the whole operating frequencies is shown in Fig. 6. Impedance was determined by Eq. 320.

From Fig. 6 it is clear that the impedance of the unit cell at the resonance frequencies aligns with the impedance of air, as a result, the reflection coefficient is less in these resonance frequencies as shown in Fig. 7. In association with transmission blocked by the metal ground, four absorption peaks were found at 11.31 GHz, 14.11 GHz, 14.23 GHz, and 17.79 GHz respectively.

The behavior of the patch along with the ground at the resonance frequencies can be better understood by the following Fig. 8. The perfect electric field was applied along the x-axis, perfect magnetic field along the y-axis and the EM wave propagated along the z-axis. Hence Ez = 0 and Hz = 0 It is essential to mention that, the distributed fields and surface current are lying on the x-y plane. Hence the electric field has components Ex and Ey. Similarly surface current and magnetic fields have Hx, Hy, and Jx, Jy components respectively in Fig. 8. The electric field, magnetic field and current distributions at resonance frequencies show the respective dense amounts at some specific portions of the patch. The redder color shows the dense field and current density. Green color shows medium dense areas and blue means less dense. At the lowest resonance frequency (11.31 GHz), the lower-left corner of the patch seems to be agitated much than the upper right corner. And the right bottom and the upper left corners are comparatively less agitated. But in medium resonance frequencies (14.11 GHz and 14.23 GHz), all four corners are agitated. Hence highest absorption was found in these frequencies. Again, in the highest resonance frequency (17.79 GHz), all the corners except the lower-left corner are agitated. These happen because of the current flow throughout the patch transmission lines, which were changing directions with respect to frequencies. The distributions shown in Fig. 6 are polarization insensitive due to the symmetric geometry of the unit cell. In other words, the magnetic dipoles are aligned with the incident polarized magnetic field and hence the energy due to the incident magnetic field is trapped, which led to less reflection of EM waves and intense absorption inside the lossy dielectric material.