## 3 Results and Discussion
### E-Field Distribution and EM Energy Density Analysis  
The E-Field distribution within a rectangular waveguide with the sample properties was studied. As stated earlier, the propagating mode employed in this work is the TE\({}_{10}\) mode, and as such the direction of the propagating wave will be along the z-direction of the waveguide as presented in Figure 12. The figure shows the 3D slice plot of the z-component of the E-Field within the simulated rectangular waveguide at X-band frequency for all samples at a thickness of 4.0 mm. The significant differences in the propagated E-Field intensity through mediums of different refractive index at 11.2 GHz can be seen. For M0 (Figure 12a) the maximum amplitude of the E-Field at a point within the waveguide is 149 V/m. When the EM wave was excited from port 1, large fractions of the propagated EM wave was reflected at S1, indicating large reflection coefficient at the interface. Similarly, M10 and M20 (Figure 12b,c) also displayed the same high reflectivity at the presented thickness and frequency. This could be attributed to mismatch of impedance resulting in a small fraction of the wave propagating into the sample. In contrast, a large amount of the propagated E-Field transmits through M40 (Figure 12d) from region I to region II of the waveguide. This indicates low reflectivity at the boundary, resulting from a good match of impedance between the material's interface and free space resulting in minimum RL value of \(-42\) dB. Figure 11: Attenuation constant (\(\alpha\)) of all samples. Figure 12: 3D electric field slice plot of X-band FEM simulated rectangular waveguides of all samples at 4.0 mm thickness and 11.2 GHz frequency. To further investigate the reflection coefficient at the interface (plane S1), the density of the EM energy that transmits into the sample loaded in the waveguide was studied and presented. Figure 13 shows the 3D volume plot of EM energy density of the simulated waveguide at a thickness of 3 mm and selected frequencies. For M0 and M10, the magnitude of the EM energy within the waveguide at 12.4 GHz are 129 \(\upmu\)/m\({}^{3}\) and 139 \(\upmu\)/m\({}^{3}\), respectively (Figure 13a,b). The EM energy within the region filled with samples was less dense, calculated as 73.8 \(\upmu\)/m\({}^{3}\) and 74.9 \(\upmu\)/m\({}^{3}\) (Figure 10a',b'), with poor RL value of \(-\)2.3 dB and \(-\)1.5 dB respectively. Whereas, the density of the EM energy within the waveguide loaded with M20 was 316 \(\upmu\)/m\({}^{3}\) (Figure 13c), while for M40 the density of the EM energy was 450 \(\upmu\)/m\({}^{3}\) (Figure 13d). As evident in Figure 13c',d', the total EM energy evaluated for the region filled with the samples are 317 \(\upmu\)/m\({}^{3}\) and 450 \(\upmu\)/m\({}^{3}\), respectively indicating almost zero reflection at the interface. Within this region, the samples would attenuate the EM wave and dissipate the EM energy and/or convert it to heat by their intrinsic dielectric and magnetic loss mechanism. This validates the enhanced MAP achieved with M20 and M40 with RL value of \(-\)47 dB and \(-\)41 dB, respectively which corresponds to 99.9% EM wave absorption. These findings reveal a directly dependent relationship between the density of EM energy within an absorptive material and the magnitude of the EM wave absorption. An efficient absorptive material is thus required to possess a low reflection coefficient, which requires good impedance matching characteristics and proper attenuation ability to dissipate the EM wave. The EM absorption of C-Fe\({}_{3}\)O\({}_{4}\)/PVDF reported herein can be described in terms of mutual benefits of magnetic loss from C-Fe\({}_{3}\)O\({}_{4}\) and dielectric loss from the PVDF matrix. As Fe\({}_{3}\)O\({}_{4}\) nanoparticle exists in the single domain at the nanoscale, more energy will be absorbed by the ferromagnetic resonance. Also, the great surface effect of the C-Fe\({}_{3}\)O\({}_{4}\) at the nanoscale would influence its anisotropy coefficient and damping parameters [36], thus increasing its MAP.