## 4 Discussion  
Using the 2D model described in Section 2.1, the attenuation coefficient \(\alpha\) is calculated for _fd_ ranging from 0.5 to 1.5 MHz\(\cdot\)mm. The attenuation coefficient \(\alpha\) is defined as \(Z_{1}=Z_{0}\cdot e^{-\alpha\cdot\Delta x}\), where \(\Delta x=x_{1}-x_{0}\), \(x_{i}\) (\(i\) = 0,1) is the position of the two detection points, \(Z_{i}\) (\(i\) = 0,1) is the out-of-plane displacement of the Lamb wave propagating in the plate. Figure 7a shows the normalized attenuation coefficients \(\alpha\cdot d\) of both S\({}_{0}\) and A\({}_{0}\) modes in the aluminum plate fully immersed in water. These calculated attenuation curves show good agreement with the results calculated by SAFE [31; 36]. Figure 6: (**a**) B-scan image at the defect with scanning step of 0.05 mm; (**b**) Amplitude at the corresponding position. In the low-_fd_ range from 0.5 to 1.5 MHz-mm, the attenuation of the A\({}_{0}\) mode is much higher than that of the S\({}_{0}\) mode. The attenuation of the S\({}_{0}\) mode rises slowly at a quite low rate throughout the whole range; the coefficient of the A\({}_{0}\) mode diminishes significantly before 0.8 MHz-mm and stabilizes at \(\sim\)0.035. When _fd_ = 1 MHz-mm, the attenuation of the A\({}_{0}\) mode is about 15 times higher than that of the S\({}_{0}\) mode. Figure 7b shows the signals at different positions in the underwater plate using the top generation configuration. The experimental attenuation coefficient _a-d_ is \(\sim\)0.0365 based on the fitted curve, which has good agreement with the simulation result. According to Figure 5b,c, the S\({}_{0}\) mode generated by lateral generation configuration has a narrow wave packet due to its low dispersion. Therefore, experiments are performed in an underwater plate with multiple defects, where the defects are very close to each other. The experiments are carried out using the lateral generation configuration, and the samples with multiple defects are shown in Figure 8. Figure 8a shows a plate with two artificial notches, and the interval between them is 10 mm. Figure 8b shows a plate with three artificial notches, with a 5 mm spatial interval between adjacent notches, as illustrated in the inset of Figure 8b. The notches are similar in size, with a width of \(\sim\)0.5 mm on the _x_-axis and \(\sim\)20 mm on the _y_-axis. The probe laser scans near the center of the notch, with a scanning step of 0.5 mm. Figure 9a shows the B-scan image obtained in the plate with two notches. The reflection of S\({}_{0}\) mode is too weak to be observed, but the mode-converted A\({}_{0}\) mode is easily identified. The reflected and the transmitted mode-converted A\({}_{0}\) at two notches are marked as 'S\({}_{0}\)-r\({}_{1}\)A\({}_{0}\)' and 'S\({}_{0}\)-t\({}_{1}\)A\({}_{0}\)' (\(i\) = 1,2), respectively. The resonance at the defect is also observed, as shown in the dotted frame in Figure 9a, which helps to locate the second notch. Figure 8: Configuration of the aluminum plate, the blue stripe indicates the position of probe laser on the _y_-axis: (**a**) two artificial notches with an interval of 10 mm; (**b**) three artificial notches with an interval of 5 mm (the inset is the enlargement of the notches in the x-z plane). Figure 7: (**a**) Normalized attenuation curves for A\({}_{0}\) and S\({}_{0}\) modes in the underwater aluminum plate; (**b**) Time domain signal at different positions using the top generation configuration. In Figure 9a, due to the lager velocity difference between the \(S_{0}\) mode and the A\({}_{0}\) mode, the transmitted S\({}_{0}\) mode and 'S\({}_{0}\)-r\({}_{1}\)A\({}_{0}\)' mode can be separated by a propagating distance of \(\sim\)2 mm after interaction with the first notch. It is straightforward to extend the utilization of this technique to detect multiple defects with spatial intervals larger than \(\sim\)2 mm, by identifying mode-conversions at each defect caused by the transmitted S\({}_{0}\) mode.