# 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  
Before we start the analysis, some prominent research papers must be consulted to explore the unit cell behavior. At the visible frequency range, a collaborative research group from National University  
Figure 2: Prototype analysis (**a**) simulated boundary condition, (**b**) Experimental arrangement for measurement. of Singapore (NUS) have proposed an ultrathin flat bilayer metasurface design to work over the broadband range [38]. An interesting feature of surface wave application is control and manipulation of electromagnetic wave propagation that can achieve cloaking features [39]. Herein, we have analyzed the design according to basic field distribution, specifically the voltage and current distribution. The EM field distribution at maximum absorption rating (at resonance frequency), which is 99.6%, has to be explained regarding both physics and mathematics. To do so, we will consider the well-known Helmholtz equation or the vector wave equations for both the E-field and the H-field. We know that:  
\[\
abla^{2}E_{m}-\gamma^{2}E_{m}=0 \tag{6}\]  
where, \(E_{m}=\) E-field propagation or distribution component  
\(\gamma\) = propagation constant,  
where, \(\left|\gamma^{2}\right|=\omega\mu\sqrt{\sigma^{2}+\omega^{2}\epsilon^{2}}\). According to the Helmholtz equation (assuming standard conditions), both the E-field and the H-field propagation are dependent on the propagation constant \(\gamma\) of the medium. Also, \(\gamma\) is dependent on permittivity (\(\varepsilon\)), permeability (\(\mu\)), frequency (\(\omega\)), and conductivity (\(\sigma\)) as we can see in the Equation (6). The proposed metamaterial absorber substrate FR-4 has \(\varepsilon=4.6\) and \(\mu=1.0\). Combing all these parameters, Equation (6) reduces to:  
\[\left[\frac{d^{2}}{dz^{2}}-\gamma^{2}\right]E_{xm}(z)=0 \tag{7}\]  
which is a linear homogeneous differential equation. Taking a trivial solution, it gives two components of this E-field, so, at resonance frequency, say at 13.78 GHz, assuming the wave propagation along the +\(z\) direction it gives an optimum distribution around the inner mirror reflexed C-shape resonator. Not only that, some E-field components are also present at the vertical edge of the two-ring resonator at the outer side of the unit cell absorber. Highly dense electric fields couples mutually with each other to form a strong dipole moment. This moment is equally shared by the upper and lower split sections at the resonance frequency as shown in Figure 3a. Figure 3: E-field distribution at the resonance frequency (**a**) 13.78 GHz, (**b**) 15.3 GHz of proposed MM absorber. As the unit cell has another resonance at 15.3 GHz with the absorption of 99.14%, the same momentum sharing occurs here again as shown in Figure 3b and rest of the frequencies, this E-field distribution starts to scatter along the rings. Figure 4a,b shows the magnetic field distribution at the same frequency as mentioned above for the E-field distribution. For the maximum absorption, the unit cell has a few interesting properties like observed left-handed metamaterial (LHM) characteristics with values listed in Table 2. LHM has double-negative property means a metamaterial made of a repeated lattice of conducting, non-magnetic elements that exhibits effective permittivity and permeability both are simultaneously negative over a band of frequencies [40]. This type of medium has been termed 'left-handed' as the electric field, magnetic field and propagation vector (or wave number) are related by a left-hand rule. As for the EM wave shown in Equation (1), a similar expression is valid for magnetic field propagation or distribution, like:  
\[\
abla^{2}H_{m}-\gamma^{2}H_{m}=0 \tag{8}\]  
where \(H_{m}\) = H-field propagation or distribution component.