## 3 Results and Discussion
### Sensing Applications  
The absorption attributes of the designed MMA depend on impedance matching, which relies on the complex value of relative permittivity and permeability. The metamaterial property can be handled by variation of the substrate thickness and dielectric property. Hence, the absorption of MMA varies with substrate thickness and dielectric constant. MMAs can be used for sensing applications in two ways: by placing a sensor layer on top of the MMA patch [34] or by placing the sensing layer between the patch substrate and  
Figure 11: The E-field and H-field in TE mode.  
Figure 12: The E-field and H-field in TM mode.  
substrate ground [13; 30; 35]. Different mechanisms of absorption-based sensor applications have been proposed from microwave to THz frequency, such as permittivity sensors [32; 33], refractive index sensors [34], grin sensors [35], density sensors, temperature sensors [30], glucose sensor [64], etc. A permittivity sensing model using the proposed MMA is presented in Figure 13a. The relation between the dielectric constant and permittivity can be understood according to the equation \(k=\varepsilon/\varepsilon_{0}\), where \(k\) is the dielectric constant, \(\varepsilon\) is permittivity, and \(\varepsilon_{0}\) is the permittivity of the vacuum. The dielectric constant is the ratio of how fast an electric field travels through a material compared to a vacuum medium. For the investigation of permittivity sensing, an air gap of 1 mm is maintained between two FR-4 substrate materials as a sensing layer. The patch was designed on the upper surface of FR4 substrate 1, and no copper layer was used on the lower side. On the other hand, no copper was used on the upper side of substrate material 2, and full copper was used on the bottom side. Different hydrocarbons with individual dielectric constants were inserted in the air gap in the range of 1.8 to 2.2. The absorption curve of the MMA changes due to the overall thickness and variation of different dielectric constants of hydrocarbon that used in the sensing layer. As a result, the absorption of the lower two bands and the one upper band out of the quad band decreases. Only one absorption band shows near-unity absorption. The absorption plots for different hydrocarbon materials are shown in Figure 13b. Figure 13 shows a zoomed-in version of the absorption peaks zooming in to facilitate understanding of the resonant frequency shift with respect to the dielectric constant. The resonant frequency shifts towards a lower-frequency region with the increment of the dielectric constant by a measurable frequency interval, as shown in Figure 13d. Another permittivity sensor model for solid material sensing is shown in Figure 14a, where the sensing layer is placed on the MMA patch. Various Arlon substrate materials were chosen, with dielectric constants between 2.2 and 3.5. The integration of the sensing layer with the MMA results in a change in peak absorption due to the overall thickness and dielectric constant variation of the MMA. These changes shift the resonance frequency of the MMA, as shown in Figure 14c. The Arlon solid material sensing sensitivity is presented in Figure 14d.