# A Polarization Independent Quasi-TEM Metamaterial Absorber for X and Ku Band Sensing Applications
## 3 Absorption and Pressure Sensor Results and Discussion
### E-Field, H-Field and Surface Current Analysis
The similar trivial solution gives two components of the H-field where both of them couple to each other in the outer two rings as well as in the mirror reflexed C-shape portion in the inner side. It is evident from Figure 4 that, a split and vertical section of the inner resonator gives a significant response at the resonance frequency. Also, the magnetic dipole moment created at that instant shows a highlighted portion which approximately ranges from 10 to 24 A/m in a logarithmic scale. Similar to E-field distribution, the H-field propagation constant is dependent on \(\varepsilon\), \(\mu\), and \(\sigma\) for which field distribution become stable at the resonance frequency with LHM properties. \begin{table}
\begin{tabular}{c c c c} \hline
**Resonance Frequency (GHz)** & **Permittivity, \(\varepsilon\)** & **Permeability, \(\mu\)** & **Reflection Co-Efficient, \(\eta\)** \\ \hline
13.78 & \(-\)1.484 & \(-\)0.362 & \(-\)0.887 \\ \hline
15.3 & \(-\)0.048 & \(-\)1.054 & \(-\)0.460 \\ \hline \end{tabular}
\end{table} 
Table 2: LHM characteristics values of proposed MM absorber at resonance. Figure 4: H-field distribution at the resonance frequency (**a**) 13.78 GHz, (**b**) 15.3 GHz of proposed MM absorber. Surface current distributions are shown in Figure 5a,b, where two distinct distributions with high density are observed at the resonance frequency. At 13.78 GHz and 15.3 GHz, the outer and inner resonators have a significant amount of surface current roaming around the edges. An important point to remember is that, the microstrip pattern uses Cu (thickness of 0.035 mm) on top of a FR-4 substrate, so a traveling wave may face a situation where at low frequency the wave has a good conductor medium but with increasing frequency the dielectric property of the same medium decreases. In order to explain such surface, current distribution at these specific frequencies some basic equations like [PERSON]'s law for EM field should be recapped:  
\[\
abla\times\overset{\rightarrow}{H}=\overset{\rightarrow}{J}+\frac{ \partial\overset{\rightarrow}{D}}{\partial t} \tag{9}\]  
where, \(\overset{\rightarrow}{J}\) = conduction current density  
\(\frac{\partial\overset{\rightarrow}{D}}{\partial t}\) = displacement current density = \(\overset{\rightarrow}{J}_{d}\). The currents \(\overset{\rightarrow}{J}\) and \(\overset{\rightarrow}{J}_{d}\) form the loss tangent \(\tan\theta\), \(\tan\theta=\frac{\sigma}{\omega\kappa}\). On the other hand, patching of unit completed with Cu (which is a good conductor) also plays a role for this surface current. As we know, when an E-field or H-field wave travels in a conducting medium, its amplitude is attenuated by the factor \(e^{-\alpha z}\) where, \(\alpha\) is the attenuation constant. The distance the wave travels till attenuation is called skin depth or penetration depth, \(\delta=\frac{1}{\alpha}\), so as the MM absorber reaches the resonance frequency, this loss angle moves to its maximum value while curving the traveling wave at the edge of each patch portion. Moreover, Equation (9) indicates that the maximum loss tangent will enhance the right-hand side of the equation to show the dominant value of the magnetic field. Additionally, in the GHz range frequency, copper shows a skin depth of approximately 6.6 \(\times\) 10\({}^{-4}\) mm and the skin depth decreases as the frequency increases [41]. That is why both mirror reflexed C-shaped inner resonators have high values of surface current.