# Optimization of Multilayer Absorbers Using the Bald Eagle Optimization Algorithm
## 3 Results
### Oblique Incidence  
The design parameters of MAs, Design-6, Design-7, Design-8, and Design-9, for different oblique incidences of TM polarization, are given in Table 7. Each design was obtained for a single angle of incidence that varied from 30\({}^{\circ}\) to 75\({}^{\circ}\), with 15\({}^{\circ}\) angle increments. All designs had the least total thickness and reflectivity (\(<\)\(-\)20 dB) when compared to similar designs in the literature. The overall thickness and the maximum RC are \(-\)3.401 mm and 20.8919 dB for Design-6, 3.84 mm and \(-\)26.5667 dB for Design-7, 3.966 mm and \(-\)32.7952 dB for Design-8 and 3.125 mm and \(-\)26.3625 dB for Design-9. The obtained results show that the method allows the realization of broadband/wide angle MMA designs. Figure 10 illustrates the comparison of RL versus the required FR.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**BESOA**} & \multicolumn{2}{c}{**DE**} \\ \hline \multirow{3}{*}{**LAYER**} & \multicolumn{2}{c}{**Design-5**} & \multicolumn{2}{c}{[16]} \\ \cline{2-5}  & **Material** & **d** & **Material** & **d** \\ \hline
1 & 16 & 0.2377 & 16 & 0.2064 \\ \hline
2 & 6 & 1.7999 & 6 & 1.8762 \\ \hline
3 & 15 & 0.6948 & 14 & 0.5391 \\ \hline
4 & 1 & 0.4975 & 6 & 0.9499 \\ \hline
5 & 3 & 1.7415 & 5 & 1.9596 \\ \hline
6 & 4 & 0.8813 & 4 & 0.7817 \\ \hline
7 & 1 & 0.6472 & 5 & 0.4864 \\ \hline
**Max. RC [dB]** & \(-\)18.4311 & & \(-\)17.9 \\ \hline
**Total thick. [mm]** & 6.5 & & 6.8 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Design parameters of 7-layer MA for normal incidence for 1–18 GHz FR.  
Figure 9: RC versus frequency of 7-layer MA for 1–18 GHz FR (Design-5).  
Three different MAs, Design-10, Design-11, and Design-12, were designed for the applications in the frequency bands 2-8 GHz, 8-12 GHz, and 12-18 GHz, respectively (Figure 11). The design parameters for 45\({}^{\circ}\) oblique incidences for TM polarization are shown in Table 8. For Design-10, the maximum RC and total thickness are obtained as \(-\)35.1971 dB and 3.90 mm, respectively. These values are \(-\)42.2578 dB and 2.47 mm for  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**2-18 GHz**} \\ \cline{2-9}  & \multicolumn{2}{c}{**TM 30\({}^{\circ}\)/BESOA**} & \multicolumn{2}{c}{**TM 45\({}^{\circ}\)/BESOA**} & \multicolumn{2}{c}{**TM 60\({}^{\circ}\)/BESOA**} & \multicolumn{2}{c}{**TM 75\({}^{\circ}\)/BESOA**} \\ \cline{2-9}  & \multicolumn{2}{c}{**Design-6**} & \multicolumn{2}{c}{**Design-7**} & \multicolumn{2}{c}{**Design-8**} & \multicolumn{2}{c}{**Design-9**} \\ \cline{2-9}  & \multicolumn{2}{c}{**Material**} & \multicolumn{1}{c}{**d**} & \multicolumn{1}{c}{**Material**} & \multicolumn{1}{c}{**d**} & \multicolumn{1}{c}{**Material**} & \multicolumn{1}{c}{**d**} \\ \hline
1 & 16 & 0.18967 & 16 & 0.11355 & 8 & 1.14129 & 1 & 0.26282 \\ \hline
2 & 6 & 1.57262 & 7 & 1.46401 & 16 & 0.09877 & 4 & 0.32928 \\ \hline
3 & 16 & 0.23265 & 14 & 0.45781 & 8 & 1.22881 & 6 & 0.09134 \\ \hline
4 & 11 & 1.39604 & 2 & 0.30846 & 9 & 0.09967 & 2 & 2.00000 \\ \hline
5 & 4 & 0.01003 & 10 & 1.49616 & 4 & 1.39751 & 4 & 0.44156 \\ \hline
**Max. RC [dB]** & \(-\)20.8919 & \(-\)26.5667 & \(-\)32.7952 & \(-\)26.3625 \\ \hline
**Total thick. [mm]** & 3.401 & 3.840 & 3.966 & 3.125 \\ \hline  & \multicolumn{4}{c}{**PSO [13]**} \\ \hline
**Max. RC [dB]** & \(-\)19.3096 & \(-\)26.5192 & \(-\)29.1497 & \(-\)25.3794 \\ \hline
**Total thick. [mm]** & 3.4144 & 3.8420 & 4.0354 & 3.1351 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Design parameters for 5-layer absorbers optimized for a 2-18 GHz FR for TM polarization for the single angle of incidence (Design-6, Design-7, Design-8, and Design-9).  
Figure 10: RC of 5-layer MAs optimized for 2-18 GHz FR for TM polarization for (**a**) 30\({}^{\circ}\) (Design-6), (**b**) 45\({}^{\circ}\) (Design-7), (**c**) 60\({}^{\circ}\) (Design-8), and (**d**) 75\({}^{\circ}\) (Design-9) angles of incidence.