## 4 Absorbing Array Design and Discussion  
An array of the lossy dielectric bar is expected to absorb the scattered microwave power in the wind tunnel. The theoretical analysis in previous sections helps us to understand and explain the beat wave phenomenon; however, the theoretical method loses accuracy because the material is lossy, the wavelength becomes smaller relative to the edge length of the bar [18] and mutual coupling between bars may occur. To investigate the absorbing properties of the array for the application, FDTD simulation is again applied. It is assumed that the array is infinite and periodic in both transverse directions. Periodic boundary conditions are applied in the following simulations. The incident wave can be regarded as a plane wave because the distance between the target model and the absorbing array is quite long. Figure 9 shows the absorbed microwave power as a function of the periodic length in both transverse directions at different frequencies. The coupling effect helps increase the power loss when the space length increases. However, the power loss will not increase further after the space length becomes larger than 1.5\(\lambda\) because of the decay of the mutual coupling. On the other hand, the ratio between the area of the cross-plane of the bar and that of a cell of the absorbing array should be \(\sim\)2% for the steady operation of the wind tunnel. When the edge length of bar is half a lamda, smaller in fact, the corresponding period length is \(\sim\)3.5\(\lambda\) and the space length for simulation is \(\sim\)1.75\(\lambda\). Therefore, the reasonable choice of the period length is between 3\(\lambda\)-3.5\(\lambda\). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Frequency** & **Theoretical Value** & **Eigenmode Simulation** & **FDTD Simulation** \\
**(GHz)** & **(mm)** & **(mm)** & **(mm)** \\ \hline
10 & 48.9 & 43.8 & 43.9 \\
10.2 & 46.3 & 42.1 & 42.1 \\
10.4 & 43.9 & 40.5 & 40.4 \\
10.6 & 41.9 & 39.1 & 39.2 \\
10.8 & 39.4 & 37.7 & 37.7 \\
11 & 37.6 & 36.4 & 36.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Period lengths of the axial field distribution obtained by theoretical calculation, eigenmode simulation and FDTD simulation. Figure 9: Power losses as a function of frequency under different space length. The period length of the array is twice the space length, which is the distance between the simulation boundary and the model. Figures 10 and 11 shows the absorbed power as a function of the longitudinal distance. Let the longitudinal distance be denoted as \(x\) in mm; then, in Figure 10, the power loss at \(x\) mm represents the total absorbed power in the longitudinal section of the array from \(x\) mm to \((x+60)\) mm. For example, the power loss at \(x=200\) mm means the total absorbed power in the region from \(x=200\) mm to \(x=260\) mm. Figure 11 shows the absorbed power in the region from 0 to \((x+60)\) mm. It can be observed from Figure 10 that the absorbed power also has a periodicity that is naturally equal to the period length in the field distribution of the beat wave. When a is 7.2 mm, the wave numbers of the leaky and guided modes are 0.2126 rad/mm and 0.1993 rad/mm, simulated with CST Eigenmode Solver. The distance between the two adjacent amplitude peaks is \(2\pi/(0.2126\)-0.1993) = 472 mm, which is quite close to the simulated value of 453 mm with CST FDTD Solver. In Figure 10, the power loss for \(a=7.2\) mm is apparently larger than that for other larger values of \(a\). This is caused by the higher-order field distribution inside the dielectric bar as shown in Figure 12, noting that the edge length of 14.4 mm is close to half an equivalent wavelength inside the bar (\(\varepsilon_{\rm r}=4.3\)). At 10 GHz, the reasonable edge length of each bar in the array is 7.2 mm; the reasonable choice of the period length is between 3.5\(\lambda\) and the longitudinal length of each bar is suggested to be \(\sim\)300 mm for better efficiency.