# A Polarization Independent Quasi-TEM Metamaterial Absorber for X and Ku Band Sensing Applications
## 3 Absorption and Pressure Sensor Results and Discussion
### Absorption Based on Simulation  
In this proposed metamaterial absorber, unit cell design, analysis, and simulation were performed on CST Microwave Studio using the FIT method. Boundary conditions were applied periodically on the waveguide port. All other conditions like substrate thickness, patching pattern, outer and inner resonator spacing have been analyzed based on the design methodology. In Figure 7a, simulated absorption as well as a reflection of EM energy concerning frequency are shown. As from Equation (3), it is evident that absorption depends on the admittance formed by the patch from the equivalent circuit considered for the prototype. Figure 6: Absorption of quasi-TEM polarization independence of the proposed absorber. Peak absorption (Figure 7a) is rated at 99.6% and 99.14% with a respective frequency of 13.78 GHz and 15.3 GHz in the presence of LHM properties. Theoretically, a perfect absorber should have zero reflection (R = 0) to get an ideal absorption of 100% at the resonance frequency. In the experimental measurement, simulated absorption and measured absorption have proximity as depicted in Figure 7b. It is evident that measured data have roughly 5\(\sim\)10% variation than the simulated one at the resonance frequency. As the MM absorber simulation shows two resonance frequency (13.78 GHz and 15.3 GHz), energies at that time dissipated by the substrate and patch model on it, so the energy consumption may result in heating on the absorber. For the time being this factor was not considered in the proposed model, but a non-linear recursive feedback optical-thermodynamic numerical analysis in [43] showed that optical absorption induced temperature affects metamaterial absorber performance. However, the inner and outer resonator model have a mutually coupled E-field and H-field region at the splits and between ring resonators. Another significant point is that the proposed absorber shows quasi-TEM properties with LHM characteristics which are not available in usual material absorbers. Figure 1c depicts that the unit cell has a layer of the dielectric substrate placed between quasi-TEM systems. We know a relationship from [PERSON] and his research group [44] that was used to study Nicolson-Ross-Weir (NRW) method, which is:  
\[S_{21}=j_{50}S_{11}M \tag{12}\]  
where, \(s_{0}=\pm 1\) and \(M=\sqrt{\frac{1-\left|S_{11}\right|^{2}}{\left|S_{11}\right|^{2}}}\). So, if there is any change in polarity of \(s_{0}\) then the real value of \(S_{11}\) remains unchanged. Producing four distinct symmetric polarization angles \(\varphi\) which vary from \(-\pi\) to \(+\pi\) having no identical value. As a result, Equation (12) and Figure 8a,b illustrate that at the resonance frequency, especially at 13.78 GHz, both transmission (\(S_{21}\)) and reflection (\(S_{11}\)) real parts, have negative values of \(\varepsilon\) (\(-1.48\)) and \(\mu\) (\(-0.36\)) (in Figure 8c,d) that signify DNG metamaterial properties. Similarly, at 15.3 GHz, positive values of transmission and reflection gives negative permittivity and permeability, but at this point, the permittivity becomes very close to positive. On the other hand, based on the \(S\)-parameter retrieval from the simulated environment of the proposed MM absorber, the refractive index (\(\
u\)) performance is being shown in Figure 9.  
Figure 7: (**a**) reflection vs. absorption performance, (**b**) simulated and measured absorption of proposed MM absorber. The traditional Direct Refractive Index (DRI) method [45] was used for calculating the parameter which is:  
\[\
u\approx\frac{c}{j\pi ft^{\prime}}\sqrt{\frac{\left[\left(S_{21}-1\right)^{2}-S _{11}{}^{2}\right]}{\left[\left(S_{21}+1\right)^{2}-S_{11}{}^{2}\right]}} \tag{13}\]  
Figure 8: Reflection and Transmission properties in simulated design (**a**) Reflection vs. Transmission, (**b**) Transmission characteristics, (**c**) Permititivity (\(\varepsilon\)), (**d**) Permeability (\(\mu\)) with Frequency spectrum. Figure 9: Refractive Index of designed MM absorber in a simulated environment using DRI method.