## 3 Signal Enhancement of Cylindrical Surface Waves  
In this section, the signal enhancement of surface waves is investigated based on the numerical model described above. A Cartesian coordinate system is set up on a cylinder that has a diameter of 20 mm, as shown in Figure 3. Point D represents the detection position. The angle between D and the center of the laser line source on the surface of the cylinder is \(\theta\) (\(0\leq\theta\leq 180^{\circ}\)). \(\alpha\) is the angle between the negative direction of the x-axis and the artificial rectangular crack with a depth of 1.0 mm and width of 0.2 mm. The incident direction of the laser beam is defined as the y-axis. In order to ensure the accuracy of detection and facilitate the laser ultrasonic detection of the cylinders, the position of excitation and detection are fixed, and laser ultrasonic scanning detection of the cylinder is achieved by rotating the cylinder clockwise. For the sake of convenience, we assume that the initial position of \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(\rho\) (kg/m\({}^{3}\)) & \(E\) (GPa) & \(v\) & \(\mathbf{f_{T}}\) (K\({}^{-1}\)) & \(k\) (W/(m k)) & \(C_{p}\) (J/(kg K)) & \(Rc\) & \(d\) (mm) \\ \hline
2700 & 70 & 0.33 & 2.2 \(\times\) 10\({}^{-5}\) & 160 & 900 & 0.91 & 4.12, 20 \\ \hline \hline \(\rho\)—density; \(E\)—Young’s modulus; \(\
u\)—Poisson’s ratio; \(x_{T}\)—coefficient of thermal expansion; \(k\)—thermal conductivity; \(C_{p}\)—heat capacity at constant pressure; \(Rc\)—reflection coefficient; \(d\)—diameter of the solid cylinder. & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Properties of the aluminum cylinder used in numerical simulations. Figure 1: Simplification of the simulated model cylinder from 3D to 2D. the cylinder is \(\alpha=0\). During the clockwise rotation of the cylinder, the crack first passes through the laser excitation beam and then passes through detection point D, as shown in Figure 3.  
The ultrasonic surface waves excited by a pulsed laser propagate simultaneously clockwise and counterclockwise on the surface of the cylinder. When the surface waves meet the crack, the parts of the surface waves with a wavelength greater than the crack depth will continue to propagate across the crack, while the surface waves with a wavelength smaller than the crack depth will act on the edge of the crack. Figure 4 presents the B-scan image of the out-of-plane velocity of the scattered surface waves at a surface crack that is 1.0 mm deep when the crack position is \(\alpha=150^{\circ}\) and the detection position is \(\theta=10^{\circ}\)-\(90^{\circ}\). The most dominant features that corresponded to the various wave modes are labeled and their propagation paths are shown at Position  
Figure 3: Schematic diagram of the cross section of the half cylinder (L—the surface skimming longitudinal wave; R—the surface wave; Lr—the reflected surface skimming longitudinal wave; LTR—the mode-converted longitudinal-to-Rayleigh wave; RT—the mode-converted Rayleigh-to-longitudinal wave; Rr—the reflected Rayleigh wave; RTS—the mode-converted Rayleigh-to-shear wave; \(\copyright\), \(\copyright\)—the positions of surface cracks; RTL, RTS are not marked at Position \(\copyright\); \(w\)—the rotation direction of the cylinder; D—the detection point; \(a\)—the angle between the negative direction of the x-axis and the artificial rectangular crack; \(\theta\)—the angle between D and the center of the laser line source. Figure 2: (**a**) Normal displacements at the observation angle of 180\({}^{\circ}\) relative to the center of the laser line source on the surface of a cylinder with a diameter of 4.12 mm (LL: the reflected longitudinal wave; LT: the converted waves of the longitudinal and transverse wave; R1, R2, R3: the first, second, and third roundtrips of the cylindrical surface waves).