## 3 Numerical Simulations and Experiment Validation
### Simulation Results and Analysis  
To provide an intuitive understanding of wave propagation behavior in the presence of void defects, the transient acoustic fields generated by the grating-patterned laser source were analyzed for both defect-free and porous models, as illustrated in Figure 3. The pulsed laser induces a spatially periodic thermal stress distribution, which simultaneously generates narrowband SAWs and bulk waves, including longitudinal waves (L waves) and shear waves (S waves). Among these, the SAWs propagate bidirectionally along the specimen surface, with their energy highly confined within approximately one wavelength of the surface, making them particularly sensitive to both surface and near-surface discontinuities. This confinement renders SAWs especially suitable for detecting small defects located at or near the surface. In the absence of defects (Figure 3a), the SAWs propagate symmetrically along the surface with smooth, undisturbed wavefronts and no significant scattering or reflection, indicating stable wave transmission. In contrast, the porous model (Figure 3b) reveals clear evidence of wave-defect interactions. At 1.2 us, interactions between the SAWs and internal voids become evident, as local disruptions in the wavefront can be observed near the defect regions. By 3.0 us, secondary wavefronts emerge behind the primary SAW packet, indicating the presence of reflected waves resulting from scattering at the void boundaries. Figure 4 further investigates the influence of porosity on SAW propagation through a time and frequency domain analysis of the simulated signals at porosity levels of 0.00%, 2.17%, 4.04%, and 6.00%. In the time domain results, the introduction of porosity leads to the appearance of reflected waves following the primary SAW packet. As porosity increases, the amplitude of the main wave packet gradually decreases, and the waveform becomes progressively more distorted. These trends indicate increased scattering and energy attenuation due to the presence of internal voids, which disrupt the coherent propagation of the surface waves. In the frequency domain, although the individual spectra in Figure 4 do not clearly show a consistent shift in the central frequency with increasing porosity, they reveal a general reduction in overall amplitude and a slight enhancement of high-frequency components. These spectral changes suggest that porosity not only affects wave attenuation but also modifies the dispersion behavior of the propagating wavefield. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Density** & **Specific Heat** & **Thermal Conductivity** & **Thermal (K-1)** & **Elastic** (K-1)** & **Moulus (Pa)** & **Poisson’s Ratio** \\ \hline \(4.35\times 10^{3}\) & 540 & 7.0 & \(8.8\times 10^{-5}\) & \(1.1\times 10^{11}\) & 0.34 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Thermal and physical parameters used for numerical simulation. Figure 4: _Cont_. Figure 3: Transient acoustic fields generated by grating laser excitation: (**a**) defect-free model; (**b**) porous model. To better quantify the influence of porosity on wave velocity, Figure 5a provides a direct comparison of the frequency domain spectra across all porosity levels. As porosity increases, the spectral peak progressively shifts toward lower frequencies, indicating greater dispersion and energy loss--trends that are consistent with the expected interaction between SAWs and internal voids. Figure 5b further demonstrates the quantitative relationship between porosity and SAW velocity. Using the central frequency values extracted from the spectra and the known excitation wavelength (\(\lambda_{s}=0.5\) mm), the SAW velocity at each porosity level was calculated according to Equation (6). As predicted by theoretical analysis, the velocity decreases monotonically with increasing porosity due to the reduction in the effective elastic modulus and in the mass density introduced by the voids.