A Review of Finite Element Studies on Laser-Based Acoustic Applications in Solid Media

Abstract

The integration of Finite Element Method (FEM) simulations with laser-based techniques has significantly advanced acoustic research by enhancing wave measurement, analysis, and prediction in complex solid media. This review examines the role of the FEM in laser-based acoustics for wave propagation, defect detection, biomedical diagnostics, and engineering applications. FEM models simulate ultrasonic wave generation and propagation in single-layer and multilayered structures, while laser-based experimental techniques provide high-resolution validation, improving modeling accuracy. The synergy between laser-generated ultrasonic waves and FEM simulations enhances defect detection and material integrity assessment, making them invaluable for non-destructive evaluation. In biomedical applications, the FEM aids in tissue characterization and disease detection, while in engineering, its integration with laser-based methods contributes to noise reduction and vibration control. Furthermore, this review provides a comprehensive synthesis of FEM simulations and experimental validation while also highlighting the emerging role of artificial intelligence and machine learning in optimizing FEM models and improving computational efficiency, which has not been addressed in previous studies. Key advancements, challenges, and future research directions in laser-based acoustic applications are discussed.

1. Introduction

The combination of numerical simulation methods, particularly the Finite Element Method (FEM) [1,2], with laser-based techniques has significantly advanced the field of acoustics by improving the accuracy and efficiency of measuring, analyzing, and predicting acoustic wave behavior in complex media. This synergy has enabled researchers to address challenges across various disciplines, from non-destructive testing (NDT) [3] and material characterization to biomedical diagnostics and structural health monitoring (SHM) [4]. Laser-based methods provide non-contact high-resolution measurements, making them particularly useful in environments where conventional acoustic sensors are impractical. Meanwhile, the FEM offers a powerful computational framework for simulating complex acoustic wave interactions in both single-layered and multilayered media. This combination enables researchers to predict wave behavior, refine experimental setups, and extract deeper insights from data. By combining the high spatial and temporal resolution of laser-based acoustic methods with the high predictive capabilities of FEM simulations, scientists and engineers can explore intricate wave propagation phenomena and optimize system designs.

FEM simulations facilitate the study of ultrasonic wave generation and propagation in both isotropic and anisotropic media, while laser-based techniques provide high-resolution experimental validation, improving model accuracy. The combination of laser-generated acoustic waves and FEM simulations enhances structural defect detection and material integrity assessment. In biomedical diagnostics, FEM-assisted laser-induced acoustic methods are increasingly applied to skin, soft tissues [5], and hard tissues, offering novel tools for early disease detection and treatment. In engineering applications, particularly in the aerospace and automotive industries, this integration contributes to noise reduction, vibration control, and structural optimization. Additionally, this review uniquely emphasizes the role of the FEM and laser vibrometry [6] in real-time SHM, enabling early detection of structural damage and failure prediction.

Despite these advancements, challenges persist, particularly in modeling complex materials with high accuracy, improving computational efficiency, and effectively integrating experimental and numerical approaches. Unlike previous studies that focused separately on the FEM or laser-based methods, this review provides a comprehensive synthesis of their combined use. It examines their integration across wave propagation, defect detection, biomedical diagnostics, and engineering applications. A key contribution is the analysis of how experimental laser techniques and FEM simulations enhance accuracy, enable real-time assessment, and improve predictive capabilities for material and structural analysis. Furthermore, this review highlights the emerging role of artificial intelligence (AI) and machine learning (ML) [7,8] in bridging computational and experimental approaches, enhancing material modeling accuracy, and optimizing computational processes—an aspect largely unexplored in prior works.

This review is structured as follows: Section 2 examines ultrasonic wave propagation in solids and multilayered structures. Section 3 discusses FEM simulations and experimental techniques for defect detection. Section 4 explores biomedical diagnostics, particularly the latest applications of laser-induced acoustic waves and FEM simulations in tissue characterization and disease detection. Section 5 evaluates engineering applications, including recent advancements in SHM, aerospace, and automotive engineering, where the FEM and laser-based acoustics contribute to real-time assessment, vibration mitigation, and noise control. Section 6 summarizes key advancements, addresses current challenges, and suggests future research directions.

This review was conducted through a comprehensive literature search across multiple research platforms, including Scopus and Google Scholar, to ensure a broad coverage of relevant studies. The search focused on the FEM and laser-based acoustic techniques, using keywords such as laser acoustics, ultrasonics, finite element, guided waves, non-destructive testing, biomedical acoustics, and structural health monitoring. Over 150 articles were identified, with selection based on relevance, novelty, and methodological rigor. The selected studies followed two main methodological approaches. The first approach included numerical FEM simulations, which used computational models to predict ultrasonic wave behavior, defect interactions, material responses, and vibrational behavior. The second approach consisted of hybrid methods that integrated FEM simulations with experimental validation, such as laser ultrasonics and laser vibrometry, to enhance accuracy and predictive capabilities. Additionally, emerging trends, such as AI-assisted FEM modeling, were analyzed for their potential to improve computational efficiency and model accuracy.

2. Guided Ultrasonic Waves in Solid Media

Ultrasonic waves play a crucial role in various scientific and engineering applications, enabling the characterization of material properties, NDT, and medical imaging. These acoustic waves, with frequencies above the human hearing range (greater than 20 kHz), can propagate through bulk materials or along surfaces and interfaces, exhibiting different modes depending on the medium and boundary conditions. The study of ultrasonic wave propagation involves understanding their generation, transmission, and interaction with different materials, which is essential for applications in NDT, biomedical diagnostics, and SHM. Guided ultrasonic waves are waves that are confined to specific geometries, such as plates, pipes, or layers, and are guided by the boundaries of the material.

Among the various types of guided ultrasonic waves, some of the most extensively studied include Rayleigh waves (surface acoustic waves, SAWs), Lamb waves, Shear Horizontal (SH) waves, and Love waves [9,10]. Each of these wave types has unique characteristics and applications, making them valuable tools in acoustic research and engineering. SAWs propagate along the surface of a solid, exhibiting an elliptical particle motion that decays exponentially with depth. They are highly sensitive to surface defects and are widely used in material characterization, surface inspection, and sensor technology, such as SAW sensors. Lamb waves propagate in thin plates and can travel in both symmetric and anti-symmetric modes. Their ability to cover long distances makes them ideal for long-range defect detection in thin-walled structures, such as aircraft panels and pipelines. SH waves are characterized by particle motion that is perpendicular to the direction of wave propagation. These waves are particularly useful for ultrasonic guided wave inspection of layered structures and anisotropic materials. Love waves are confined to layered structures and exhibit transverse motion. They are commonly used in acoustic wave sensors and geophysical applications, where their sensitivity to surface and interface properties is advantageous [9,10].

This section explores the generation and propagation of guided ultrasonic waves through different methods and applications. It is divided into three subsections: (a) laser ultrasonic guided waves, which explores the laser-based generation of ultrasonic waves and their use in non-contact material evaluation; (b) the characterization of acoustic and mechanical properties of materials using ultrasonic waves, discussing how these waves aid in determining the aforementioned properties; and (c) transducer-generated ultrasonic guided waves, which focuses on conventional piezoelectric transducer techniques used in various ultrasonic testing applications.

2.1. Laser Ultrasonic Guided Waves

Laser ultrasonic guided waves use laser-based excitation to generate and propagate guided acoustic waves in solid media. Laser ultrasonics offer a non-contact, broadband, and high-resolution approach for wave generation and detection. This makes it particularly advantageous for applications where traditional sensors may be impractical, such as in high-temperature environments, complex geometries, or fragile materials. When a high-energy pulsed laser interacts with a solid surface, it induces localized thermal expansion, leading to elastic or plastic deformation and generating ultrasonic waves that can propagate as guided modes, including Rayleigh waves, Lamb waves, and SH waves. At even higher energies, it can cause melting and/or ablation, along with the generation and propagation of these waves. The characteristics of these waves depend on the material properties, wave mode, and excitation conditions [11,12]. Laser-based detection methods, such as laser interferometry [13], allow for the precise and remote measurement of wave propagation.

Nanosecond (ns) pulsed lasers are commonly used to generate guided ultrasonic waves due to their ability to deliver rapid high-energy bursts of light that induce localized thermal gradients in materials. This thermal effect generates stress waves, which can propagate as guided ultrasonic waves, such as SAWs or Lamb waves, with high spatial and temporal resolution. The short pulse duration ensures that the generated waves are well-defined and suitable for high-resolution inspection [14]. The most common laser used for ultrasound generation is the solid-state pulsed Nd:YAG laser.

This subsection presents a review of studies that investigated the generation and propagation of guided ultrasonic waves using FEM thermomechanical simulations and experimental laser techniques. For the thermomechanical simulations, the thermal conduction equation and the mechanical equation for wave propagation (Navier equation for displacement) are simultaneously solved. The thermal conduction equation (neglecting convective and radiated energy transport) is as follows:

$$\rho \left(T\right)C_p\left(T\right){\displaystyle \frac{\partial T\left(x,y,z,t\right)}{\partial t}}-\nabla \left[k\left(T\right)\nabla \mathrm{T}\left(x,y,z,t\right)\right]=Q(x,y,z,t)$$

(1)

where x, y, and z are the space coordinates and ρ, C_p, k, and T are the mass density, specific heat at constant pressure, thermal conductivity of the target material, and temperature distribution, respectively. The source term Q(x,y,z,t) represents the laser-absorbed energy per volumetric unit per second and is equal to $Q\left(x,y,z,t\right)=I_{0}f\left(t\right)g\left(x,y\right)h(z)$, where I₀ is the peak laser intensity, f(t) describes the temporal profile of the laser pulse, g(x,y) is the Gaussian spatial profile for a laser with a beam radius, and h(z) is deposited heat as a function of depth z. If a laser line source is considered the spatial profile has the form g(x), the energy distribution is uniform along the length of the line (y-axis) and follows a Gaussian profile in the transverse direction (x-axis). The displacements satisfy the Navier equation:

$$\rho \left(T\right){\displaystyle \frac{{\partial }^{2}U\left(x,y,z,t\right)}{\partial t^2}}=\mu {\nabla }^{2}U\left(x,y,z,t\right)+\left(\lambda +\mu \right)\nabla [\nabla U\left(x,y,z,t\right)]-a(3\lambda +2\mu )\nabla T(x,y,z,t)$$

(2)

where U is the time-dependent displacement, λ and μ are the Lamé constants, and α is the thermoelastic expansion coefficient. The accuracy and convergence of FEM simulations are highly dependent on the time resolution and spatial resolution of the model. Therefore, choosing the appropriate meshing strategy is crucial to ensure the fidelity and reliability of the numerical results. Proper meshing balances computational efficiency with the level of detail required to accurately capture the physical phenomena being studied. To guarantee the accuracy of the solution, the integration time step, Δt, and the size of the element, Δx, are respectively chosen according to [15]:

$$\Delta t\le {\displaystyle \frac{1}{20f_{max}}}$$

(3)

$$\Delta x\le {\displaystyle \frac{{\lambda }_{min}}{20}}$$

(4)

where f_max and λ_min are the highest acoustic frequency and the shortest wavelength, respectively.

FEM simulations of laser-generated Lamb waves were analyzed in terms of temperature, displacement, frequency spectrum, and equivalent thermal forces by Lee and Burger [16]. The temperature profile showed good agreement with semi-analytical solutions. Mesh density effects were assessed, confirming no spurious wave reflections. The results indicated that the mesh quality was the dominant factor in wave accuracy, with coarse meshes producing higher-frequency waves but negligible amplitudes. The research of Xu et al. [17] and Shen et al. [18] investigated the thermoelastic generation of ultrasound in layered coating–substrate systems subjected to ns pulsed laser irradiation using 2D FEM simulations. By accounting for the temperature dependence of thermophysical properties, the study examined the transient temperature and temperature gradient fields that serve as bulk sources for ultrasound generation. The numerical analysis focused on two-layer and three-layer systems, highlighting the influence of coating thickness and propagation distance on SAWs. The key findings revealed that SAW dispersion characteristics varied depending on material configurations, with normal dispersion observed in slow-coating/fast-substrate systems and anomalous dispersion in fast-coating/slow-substrate systems. Additionally, in three-layer structures, the surface skimming longitudinal wave (SSLW) was primarily affected by the surface layer thickness, while the SAW was more sensitive to the bonding layer, offering a potential method for determining coating and bonding layer properties. A SSLW is a type of ultrasonic wave that propagates just below the surface of a solid material. These results provided valuable insights into laser-induced ultrasound propagation and its applications in material characterization and non-destructive evaluation.

Xu et al. [15] also presented a thermoelastic 2D FEM model for laser-generated ultrasound in aluminum (Al) plates, focusing on the transient response characteristics of the thermoelastic wave source. The model incorporated the effects of thermal diffusion, as well as the finite width and duration of the ns laser pulse, allowing for a more accurate representation of laser-induced wave propagation. Numerical simulations revealed that the temperature dependence of thermophysical parameters significantly influenced the behavior of SAWs, particularly at high frequencies. The results indicated that transient stress distributions involved vertical forces propagating downward and horizontal forces moving outward, with thermal effects dominating waveforms near the heated region, while Rayleigh waves prevailed in the far field. These findings enhanced the understanding of laser-generated ultrasound.

Wang et al. [19] developed an optimized 2D FEM model to investigate laser thermoelastic generation and propagation of SAWs in a transparent coating–opaque substrate system. By analyzing meshing size, time step, and solution stability, the transient temperature and temperature gradient fields were obtained, which acted as buried bulk sources for ultrasonic wave generation. The study revealed that axial temperature gradients induced longitudinal waves, while radial gradients generated shear waves and SAWs. The influence of coating thickness on SAWs and surface skimming longitudinal waves was examined, showing that multiple reflections within the coating led to oscillatory wave behavior, which enhanced the understanding of wave dispersion and propagation in layered structures. Wang et al. [20] also employed the FEM to investigate the thermoelastic generation of ultrasonic waves in non-metallic material (glass) using a ns pulsed laser. The model accounted for key factors such as thermal diffusion, optical penetration, laser pulse shape, and temperature-dependent material properties. By optimizing mesh size, time step, and solution stability, transient temperature and temperature gradient fields were obtained, serving as bulk force sources for ultrasound generation. The study examined the influence of optical penetration on heat distribution and ultrasonic waveforms, revealing that optical absorption played a dominant role in heat penetration. The numerical results showed that ultrasonic waveforms, including SAWs and longitudinal waves, are highly dependent on optical penetration depth, affecting the precursor shape of longitudinal waves (see Figure 1).

Zhao et al. [21] used the FEM to simulate the ultrasonic field induced by a pulsed laser line source on isotropic Al cylinders, accounting for the temperature dependence of thermal parameters. The simulation modeled SAWs, including cylindrical Rayleigh and Whispering Gallery modes, which closely matched experimental and previously reported waveforms. The dispersion properties of cylindrical Rayleigh waves were analyzed using phase spectral analysis, revealing that as frequency increased, the phase velocity rapidly increased to a maximum value before decreasing to that of the plane Rayleigh wave. Additionally, as the cylinder diameter decreased, both the maximum phase velocity and the corresponding frequency increased. This approach offered significant advantages in modeling complex geometries and obtaining full-field solutions, providing insights into the dispersion behavior of cylindrical Rayleigh waves.

Xu et al. [22] investigated the effect of anisotropy and temperature on the generation and propagation of dispersive Lamb waves in a transversely isotropic thin plate using the FEM. The 3D model incorporated various factors, such as the spatial and temporal distributions of the incident ns laser beam, optical penetration, thermal diffusivity, plate thickness, and source–receiver distance. The results revealed that under strong optical absorption, a subsurface thermal source leads to both vertical and lateral shear tensions, with the lateral shear tension acting as a shear dipole at the top face. The amplitude of the dipole depended on material symmetry, and the character and strength of the surface stress varied with the propagation direction. The study presented detailed results for lower anti-symmetric and symmetric mode propagation in all planar directions, analyzing both spatial and frequency dispersion. Xu et al. [23] also investigated the effect of anisotropy on ultrasound wave generation and propagation in a unidirectional fiber-reinforced composite plate using FEM thermoelastic simulations. The model accounted for various factors, such as laser beam distribution, optical penetration, and thermal diffusivity. The results showed that the size of the laser volume source influenced the amplitude and directivity of longitudinal waves, producing strong bipolar waves. For ultrasonic propagation along the fiber direction, material inhomogeneity introduced dispersion, affecting the waveforms, while increasing the laser pulse dimensions resulted in broader displacement waveforms with decreased magnitude.

Tang et al. [24] investigated the anti-symmetric flexural (ASF) modes, a type of guided wave propagating along the tip of wedge-shaped waveguides, with a focus on their dispersion behavior when a coating layer was applied. Using a combined numerical and experimental approach, the effects of coatings on ASF modes were examined for brass wedges with Al coatings (slow matrix/fast coating) and Al wedges with copper (Cu) coatings (fast matrix/slow coating). The results revealed that ASF modes exhibited loaded and stiffened phenomena similar to surface acoustic waves on flat coated surfaces, with the wedge tip geometry enhancing these effects. The numerical simulations showed good agreement with the experimental findings, while a laser-generation/laser-detection ultrasound technique was used for the measurements. Cerniglia et al. [25] examined how laser beam profile and size influenced ultrasonic wave generation in metallic materials using experiments and FEM simulations. A Gaussian beam created a hoop-wrapping effect, where lower-temperature outer regions constrained inner deformation, altering wave propagation. Increasing the beam size shifted the maximum angular directivity of longitudinal waves from ~65° to smaller angles, although this effect was negligible for diameters under 3 mm. Feng et al. [26] developed a FEM-based numerical model to analyze the ultrasonic displacement field induced by a pulsed laser in an Al film within a diamond anvil cell. The results showed that the diamond window significantly influenced the thermoelastic force source and ultrasonic wave directivity. Longitudinal waves were concentrated near the laser incident direction, while shear waves were deflected between 30° and 60°. These characteristics differ from those observed on a free surface in the thermoelastic regime but resemble those in the ablation regime.

In a study by Dixon et al. [27], a pulsed Nd:YAG laser was focused into a sharp ring on an Al sample in the thermoelastic regime, using a combination of a bi-convex lens and an axicon lens to enhance focus. This ring-shaped acoustic source generated both surface Rayleigh waves and bulk waves on thick samples. The surface waves traveled outward and focused inward at the center, producing large-amplitude Rayleigh waves. Out-of-plane displacements caused by these waves were measured with a Michelson interferometer. The experimental results showed good agreement with the numerical results. Soltani et al. [28] examined the effects of laser parameters on laser-generated ultrasonic waves in an Al plate using the FEM. The numerical results indicated that surface conditions and pulse duration significantly influenced ultrasound waves, helping optimize experimental laser settings. While thermal diffusion was highly localized, it had minimal impact on wave generation. Increasing the line source width or pulse duration broadened the displacement waveform, reduced its magnitude, and delayed its arrival.

The 3D spatiotemporal response of thin metal films excited by nanosecond laser pulses was studied in the thermoelastic, melting, and ablation regimes by Dimitriou et al. [29]. A combination of an experimental laser interferometric technique and 3D FEM simulations was used to model the laser–surface interaction and predict key thermomechanical responses. The integrated approach successfully described the generation and evolution of SAWs and transient surface deformation. The model provided detailed insights into material behavior under varying laser fluences, with excellent agreement between experimental and numerical results, offering a powerful tool for studying material dynamics under extreme conditions. The same team [30] investigated the interaction dynamics between ns laser pulses and thin metal films on dielectric substrates, focusing on the melting and ablation regimes. High-resolution experimental techniques, including interferometry, were combined with a 3D FE model to investigate the thermomechanical behavior of the material during phase transitions from solid to liquid and liquid to vapor. The FEM model accurately predicted the observed deformations, phase changes, and material dynamics, providing insights into the topology of the melted and ablated mass (see Figure 2).

Kaselouris et al. [31] investigated the elastoplastic dynamic behavior of thin metallic films under ns laser pulse excitation using a coupled thermal–structural transient 3D finite element model. The model incorporated temperature-dependent stress–strain curves, thermal properties, and phase changes, capturing the material’s elastoplastic response. The simulations provided detailed spatiotemporal descriptions of elastic and plastic deformations during laser interaction. Gold (Au), Cu, and Al films were used as test cases, validating the model’s effectiveness in predicting and diagnosing the material’s dynamic mechanical response. Abdullaev et al. [32] developed a laser-based technique using ns pulses to measure melting thresholds in refractory metals (Nb, Mo, Ta, and W) by detecting laser-generated shear waves. The melting thresholds were found to scale with the materials’ melting points, exhibiting different shearing behaviors. High-accuracy measurements were achieved through motorized laser energy control and real-time acoustic waveform monitoring. Numerical finite element modeling confirmed the experimental results by incorporating elastodynamic and thermal conduction equations. Melting was linked to shear modulus disappearance and rapid molten pool expansion, delaying shear wave transit. This technique enabled the remote examination of rapid melting in extreme environments with high spatiotemporal resolution.

Guan et al. [33] developed a FEM model to study laser-generated SAWs in composite plates, considering near-surface viscosity variations. The model analyzed the effects of viscous modulus, thickness, and Lamé constants on wave attenuation. The results showed that viscosity influenced attenuation but not propagation velocity, with shear modulus playing a key role. Grabec et al. [34] presented a method to create a statistical digital twin of a polycrystalline Al sample, matching its spatial two-point correlation function to real-world data. A 3D FEM model was developed to simulate SAW attenuation and phase velocity, aligning with previous experimental results. The study confirmed a different scattering behavior for SAWs compared to bulk waves. Discrepancies at higher frequencies highlighted the need for improved spatial averaging and suggested improvement strategies for future experimental studies and advanced analytical models. Liang et al. [35] investigated the impact of surface roughness on the dispersion and attenuation of laser-induced SAWs using FEM modeling based on measured surface profiles of C45E steel. The results showed that SAW dispersion and attenuation increased with roughness, with dispersion changes being relatively uniform while attenuation varied unpredictably. The influence of roughness on SAW velocity and attenuation became more significant as roughness increased. The study confirmed that SAW dispersion was approximately linear with frequency, aligning with perturbation theory predictions. The FEM provided a feasible approach for evaluating roughness effects, particularly for high-roughness surfaces.

Huang et al. [36] employed non-contact laser-induced ultrasonic technology to analyze the effect of top-coat thickness on SAWs in thermal barrier coatings (TBCs) using FEM simulations and experiments. The results showed that SAW amplitude, spectral amplitude, and dispersion behavior were influenced by coating thickness. Thicker coatings led to higher ultrasonic wave amplitude and greater dispersion, with SAW velocity decreasing as thickness increased. The study established a correlation between SAW properties and top-coat thickness, providing a foundation for the inverse characterization of TBC thickness using laser-induced SAWs. Papadaki et al. [37] performed 3D FEM simulations to analyze the dynamic behavior of solid silicon (Si) targets irradiated by ns laser pulses. The simulations revealed that due to Si’s low thermal expansion and high penetration depth, the generated SAW had a small amplitude and required more time and distance to form compared to metals like Au, Cu, and Al. Also in the melting regime, nonlinear thermal stresses created an irregular bulge and a secondary bulge, generating an irregular and nonlinear ultrasound. The developed high-resolution model enabled further analysis of asymmetric features and multiscale studies, offering valuable insights for experimental diagnostics.

When studying laser-guided ultrasonic waves using picosecond (ps) and femtosecond (fs) laser pulses, the time evolution of the lattice and electron temperatures, T_l and T_e, is described by two coupled nonlinear differential equations:

$$C_e\left(T_e\right){\displaystyle \frac{\partial T_e\left(x,y,z,t\right)}{\partial t}}-\nabla \left[k_e\left(T\right)\nabla T_e\left(x,y,z,t\right)\right]=Q\left(x,y,z,t\right)-G(T_e-T_l)$$

(5)

$$C_l\left(T_l\right){\displaystyle \frac{\partial T_l\left(x,y,z,t\right)}{\partial t}}=G(T_e-T_l)$$

(6)

where C, K, and T are the heat capacities, thermal conductivities, and temperatures of the electrons and lattice as denoted by subscripts e and l, respectively, the source term Q represents the laser-absorbed energy per volumetric unit per second, and G is the electron–phonon coupling constant. In pure metals, energy transport by free electrons is much greater than that by lattice vibrations. Therefore, heat conductivity by the lattice is neglected.

Giannetti et al. [38] investigated the ultrafast thermal and mechanical dynamics of a 2D lattice of metallic nanodisks using near-infrared pump–probe diffraction measurements and finite element analysis (FEA). The experiments revealed that SAWs, with a wave vector matching the lattice periodicity, are excited by 120 fs Ti: Sapphire laser pulses. Numerical simulations of elastic eigenmodes and thermal dynamics clarified the interaction between the nanodisks and the substrate. The findings revealed that the observed SAW velocity shift arose from mechanical interactions between the SAWs and nanodisks, while SAW damping was caused by energy radiation into the substrate. These findings provided insights into the coupling mechanisms in nanoscale systems. Nakamura et al. [39] investigated fs-optical-pulse-induced strain dynamics in thin (100 nm) and thick (10,000 nm) Si plates using FEM simulations. In the thin sample, the pulse created a standing wave in the out-of-plane direction, along with plate waves that propagated laterally. Fourier analysis showed these waves are mainly symmetric Lamb waves. In the thick sample, the pulse excited only the near-surface region, generating out-of-plane strain and lateral strain pulses composed of multiple Lamb wave modes. The study provided a detailed understanding of photoinduced strain dynamics based on material properties like thickness and sound velocity.

Kosma et al. [40] investigated the generation of acoustic strains in thin ZnO layers using ultrashort laser pulses and an Au thin-film transducer. A pump–probe transient reflectivity setup at 800 nm was employed to monitor the acoustic strain propagation. The results were supported by a FEM model combining the two-temperature model and elasticity theory, considering the anisotropic properties of the ZnO film. A good agreement was found between experimental and simulation results, demonstrating a novel method for characterizing acoustic strain in layered structures. Kaleris et al. [41] explored nano-acoustic strain generation in thin metallic films using ultrafast laser excitation, highlighting tantalum as a superior material for photoacoustic transduction compared to titanium and noble metals like silver. Experiments on tantalum films deposited on silicon substrates, measured via pump–probe transient reflectivity, revealed strong Brillouin oscillations due to efficient photon–phonon interactions. These results, supported by two-temperature model simulations and thermomechanical FEA, demonstrated tantalum’s enhanced photoacoustic efficiency (see Figure 3). The findings offered insights into optimizing thin-film systems for acoustic wave generation.

Wang et al. [42] presented a physical model for pump–probe fs photoacoustic NDT in metal nanofilms. The model simulated laser–matter interaction, heat distribution, strain pulse generation, and surface reflectivity changes. It provided insights into key parameters, such as temperature distribution, strain pulse, and acoustic wave magnitude. The model also investigated the damage threshold in 500 nm AlCu nanofilms and the influence of laser parameters on the photoacoustic signal. Simulations showed good agreement with experimental data, offering optimization recommendations for laser sources in NDT applications.

2.2. Laser Ultrasonic Guided Waves for Solid Material Characterization

Laser-generated ultrasonic waves provide a non-contact and high-precision method for quantifying the mechanical properties of a solid, enabling its characterization. By analyzing the resulting wave behavior, key material properties can be determined. Elastic properties such as Young’s modulus, shear modulus, and Poisson’s ratio can be extracted by measuring the phase velocity of different ultrasonic waves, including Rayleigh, longitudinal, transverse, and Lamb waves, and applying appropriate dispersion relations. Wave dispersion can indicate variations in material composition or anisotropy, while the relationship between sound velocity and density allows for density estimation when elastic properties are known. The characterization of thin films and coatings can also be achieved through the interaction of SAWs with coatings, providing information on film thickness, adhesion quality, and mechanical integrity. Dispersion curves of SAWs offer a means to determine the elastic moduli of coatings. Additionally, temperature and stress evaluation is possible as changes in ultrasonic velocity and attenuation with temperature reveal thermal properties and stress states. Real-time monitoring of stress relaxation and thermal expansion is also feasible using laser ultrasonics [9,11].

Xu et al. [43] introduced an inverse method using artificial neural networks (ANNs) to determine the elastic properties of thin films from laser-generated surface waves. The input data were the transient surface displacement of a film–substrate system, measured using conventional experimental techniques. The samples for training ANNs were obtained from FEM simulations. The ANN model provided material parameters like Young’s modulus, density, Poisson’s ratio, and film thickness as outputs. The Levenberg–Marquardt algorithm optimized ANN training. This approach directly extracted material properties from transient surface waveforms without relying on dispersion curves or least-square fitting. Yuan et al. [44] used the FEM to investigate thermoelastic ultrasound generation in systems with multiple gradient layers on a substrate. The near-surface elastic properties, particularly Young’s modulus, were modeled by discretizing the affected layer into homogeneous, isotropic, and linearly elastic layers. Different acoustic wave modes were observed, and their phase velocities were analyzed using 2D fast Fourier transformation. The results showed that phase velocity was sensitive to layer thickness and elastic modulus changes. By measuring these modes and their phase velocities, material properties like density, Young’s modulus, and layer thickness could be determined.

Dong et al. [45] investigated residual stresses in laser-welded Al alloy plates using both numerical simulation and laser ultrasonics. A 3D FEM model was developed to predict temperature distribution and thermo-structural response during welding. SAWs generated by a pulsed laser were experimentally analyzed to determine velocity distributions, from which residual stresses were calculated using acoustoelastic theory. A comparison between simulation and experimental results showed good agreement. Sherman et al. [46] explored the use of high-amplitude SAWs for investigating interfacial stresses and potential thin-film delamination in thin film–substrate systems. A FEM model was used to simulate the mechanical loading from a strongly ablative laser source, treating it as an equivalent compressive surface load. The model calculated resulting stresses and particle velocities, examining how interface tractions depended on the ratio of film thickness to SAW wavelength. By matching numerical results with experimental data, the study predicted dynamic interfacial stresses in a Cu film on a fused silica substrate. The findings highlighted the potential of SAWs for characterizing interfacial failure in thin-film systems.

Knapp et al. [47] investigated the mechanical properties of SiO₂ thin films deposited on LiNbO₃ substrates using plasma-enhanced chemical vapor deposition and physical vapor deposition. The phase velocity dispersion was measured using differential delay lines and laser ultrasonic methods. By fitting finite element simulations to the phase velocities, the density (ρ) and elastic constants (c₁₁, c₄₄) were determined with an accuracy of at least ±4%. These findings enhanced the characterization of SiO₂ thin films for acoustic applications. Zhan et al. [48] determined the elastic constants of Al plates by measuring ultrasonic wave velocities induced by a pulsed laser. A dual-channel non-contact method captured surface wave data, while FEA simulated the laser-induced ultrasonic process using a Gaussian-distributed pulse load. A thermal coupling model validated the simulation, and wave velocities were used to calculate elastic constants via acoustic elastic equations. Numerical results matched theoretical values, confirming the model’s accuracy for studying material properties using laser ultrasonics.

Ye et al. [49] presented an ultrasonic method to evaluate surface and subsurface longitudinal residual stresses induced by gas metal arc welding. The method relied on acoustoelastic effects, where velocity variations in Rayleigh waves were linked to stress states. A Q-switched Nd:YAG laser generated broadband ultrasonic waves, while an electromagnetic acoustic transducer (EMAT) measured the time of flight of Rayleigh waves traveling parallel to the welding seam. By varying the wave path distance from the weld center, velocity variations were experimentally determined. A 3D thermomechanical FEM model was developed to validate the technique, showing a strong correlation between measured velocity variations and simulated residual stresses. Zhang et al. [50] performed FEM simulations to analyze laser-generated SAWs for the NDT of thin films. A layered structure with SiO₂ and low-dielectric-constant Black Diamond films was modeled, and the effects of laser pulse rising time and source linewidth on SAW frequency and amplitude were investigated. The results showed that the frequency range decreased with increasing pulse rising time and linewidth, while the amplitude peaked at a linewidth of 5 μm. The experimental results confirmed the accuracy of the simulations, and dispersion curves were used to measure Young’s modulus of the films.

Qian et al. [51] proposed a non-contact method using grating laser ultrasonic acoustic spectra to measure the thickness of top coatings in thermal barrier coatings (TBCs), addressing the limitations of conventional ultrasonic methods. The dispersion curve of SAWs in TBCs was obtained, and a three-layer media model was simulated using the FEM. Experiments on TBC specimens with varying top-coat thicknesses were conducted, and the results were corrected using ultrasound attenuation theory. The corrected experimental data aligned well with the theoretical and numerical results, demonstrating the method’s accuracy and potential for the thickness measurement of TBC top coatings (see Figure 4). Meng et al. [52] presented an improved laser ultrasonic method for high-temperature NDT of mechanical properties. By analyzing surface and longitudinal wave velocities, the method avoided challenges in detecting shear waves. Two detection schemes were designed and tested on an Inconel 600 from 25 to 1000 °C, showing that an increase in temperature leads to decreasing wave velocities, elastic modulus, and shear modulus but increases Poisson’s ratio. The mechanical properties of materials at different temperatures were successfully calculated, and the experimental results were in accordance with the reference values.

Burger et al. [53] presented an imaging method for gigahertz SAWs in transparent layers using infrared subpicosecond laser pulses and an optical pump–probe technique. By capturing reflectivity modulations caused by the photoelastic effect with an sCMOS camera, wave field propagation was imaged over time. Experiments on fused silica and x-cut quartz revealed Rayleigh and high-velocity pseudo-surface acoustic wave modes, with velocity profiles extracted from circular grids. FEM simulations agreed with the experimental results, with a relative error of 2–5%. This method enabled fast full-field imaging for characterizing thin transparent materials in the gigahertz range.

2.3. Transducer-Generated Ultrasonic Guided Waves

Transducer-generated ultrasonic guided waves, produced using conventional piezoelectric transducer techniques, are widely used in ultrasonic testing applications for material evaluation and SHM. Piezoelectric transducers efficiently excite guided wave modes, such as Lamb waves and SH waves, enabling long-range inspection with high sensitivity to defects. For precise and non-contact detection, laser vibrometers and laser velocimeters are utilized to measure wave propagation by detecting surface vibrations and velocity changes with high spatial and temporal resolution. This combination of piezoelectric excitation with laser-based detection enhances the applicability of ultrasonic guided wave inspection across various materials and structures. To model these phenomena, FEM simulations were performed, considering either a force load or a displacement function that the transducer uses for excitation.

Morvan et al. [54] investigated the reflection and mode conversion of Lamb waves at the free end of a plate across a wide frequency range. Energy conversion coefficients were determined theoretically, numerically using the FEM, and experimentally via laser interferometry. A piezo-composite transducer generated Lamb waves using the wedge method, and a Polytec laser vibrometer measured surface displacements. The results showed good agreement across methods, providing insights into energy balance in Lamb wave reflection. In [55], Dutton et al. introduced an enhanced in-plane EMAT for detecting generated ultrasound via pulsed ns laser. A new EMAT design increased magnetic flux density by a factor of 1.8, validated via 3D finite element modeling and experiments. The improved design increased in-plane sensitivity by a factor of 2.0, enhancing the detection of Rayleigh waves for laser ultrasound applications.

Fromme et al. [56] investigated the impact of material anisotropy on guided ultrasonic wave propagation in monocrystalline Si wafers used in solar panels. Phase slowness and beam skewing of the fundamental Lamb wave modes (A0 and S0) were analyzed through experiments and FEM simulations. The results showed significant wave skew and beam widening, particularly for the S0 mode, due to anisotropy. While experimental and theoretical results aligned well for the A0 mode, discrepancies were observed for the S0 mode. These findings highlighted the need to account for anisotropy in the NDT of Si wafers using guided waves.

Weser et al. [57] examined SAWs on a piezoelectric substrate generated by interdigital transducers. Mechanical displacements were measured via laser Doppler vibrometry and simulated using FEA, with results showing strong agreement, enabling SAW beam shape and displacement amplitude estimation. Park et al. [58] explored the selective generation of specific Lamb wave modes in finite-width plates using a commercial piezoelectric transducer and an angle-beam excitation technique with especially designed acoustic insulation wedges. Unlike infinitely wide plates, finite-width plates exhibited both thickness and width modes with distinct cutoff frequencies and wave velocities. Two wedge designs, groove-based and patch-based, were tested through FEM simulations (see Figure 5) and experiments using a laser scanning vibrometer. The results confirmed the method’s effectiveness, with the dual-wedge technique offering superior mode selection.

In [59], a novel directional transducer was introduced using guided waves for SHM and acoustic data communication. The transducer employed frequency steerable acoustic transducers to address guided wave dispersion and multipath interference, enabling frequency-dependent directional control. Designed to actuate/sense A0 Lamb waves in three orientations (50–450 kHz), its performance was validated via FEM simulations and laser Doppler vibrometry. The transducer’s capabilities and frequency directivity showed excellent agreement with simulations, offering the potential for robust communication in harsh environments. Jiang et al. [60] investigated quasistatic pulse (QSP) generation in CFRP composite pipes through numerical simulations and experiments. Theoretical aspects of QSP generation in anisotropic materials were analyzed, focusing on waveform characteristics, cumulative effects, generation efficiency, and duration. Finite element modeling and experimental measurements using a piezoceramic transducer array and a 3D laser vibrometer confirmed that QSP amplitude is proportional to excitation magnitude and frequency. Bouzzit et al. [61] explored an ultrasonic method for assessing the integrity of ball bearings without disassembly. By analyzing the interaction of Rayleigh SAWs with a spherical ball on a plane, both experimentally and numerically, resonance frequencies and wave dispersion were extracted. Using shear wave transducers and laser vibrometry, the study demonstrated how back-generated waves retain SAW characteristics, enabling material characterization.

3. Guided Ultrasonic Waves in Defect Identification

Guided ultrasonic waves are widely used in defect identification due to their ability to propagate over long distances while interacting with material discontinuities. These waves, confined to specific geometries such as plates, pipes, or layered structures, provide valuable insights into the presence, location, and severity of defects in solid media. Their sensitivity to structural anomalies makes them essential tools in NDT and SHM. Various guided ultrasonic waves—SAWs, Lamb waves, SH waves, and Love waves—are used for defect detection, each responding uniquely based on wave mode, frequency, and material properties. Rayleigh waves, with elliptical surface motion, are ideal for detecting surface cracks and corrosion. Lamb waves, propagating in thin plates, enable long-range defect detection in aircraft, pipelines, and composites. SH waves, with perpendicular particle motion, are ideal for inspecting layered structures and anisotropic materials and identifying delaminations and bonding defects. Love waves, which are confined to layered media, are effective for detecting surface and interface defects in coatings and layered materials. The interaction of guided waves with defects results in scattering, mode conversion, and changes in wave amplitude and velocity. These effects can be analyzed using advanced signal processing techniques, such as time–frequency analysis, dispersion curve analysis, and machine learning algorithms, to enhance defect identification accuracy [9,62,63,64].

This section explores the propagation of guided ultrasonic waves in solid media for defect identification. It is divided into two subsections: (a) laser-generated guided waves, which examines the use of laser-based techniques to generate ultrasonic waves for non-contact defect detection, and (b) transducer-generated guided waves, which discusses conventional piezoelectric transducer techniques for generating ultrasonic waves and their application in various NDT methods.

3.1. Laser Ultrasonic Guided Waves

Laser-generated guided waves provide a highly effective non-contact method for defect identification in solid materials, including the detection of surface defects, subsurface defects, surface-breaking notches, and cracks. Pulsed laser line sources are mainly utilized for defect identification by generating ultrasonic waves that interact with material imperfections, enabling the precise detection and characterization of surface and subsurface defects. Nanosecond pulsed lasers are commonly used for their ability to generate well-defined high-resolution stress waves suitable for detecting small and hidden defects. This subsection explores the literature on laser-guided waves for defect identification, including FEM thermomechanical simulations and experimental investigations focusing on detecting cracks, surface-breaking notches, and other structural defects.

Sato et al. [65] developed the phase velocity scanning (PVS) method, a novel laser ultrasonic technique for the non-destructive evaluation of defects in MEMS components. The method enabled the selective generation of single-mode acoustic waves in multimode media by scanning a laser beam at the phase velocity of a specific mode [66]. A feasibility study was conducted on Si wafers with micro-slits of varying depths and widths, successfully detecting scattered waves from a 6.8 mm-deep slit using 60 MHz surface acoustic waves. Two- and three-dimensional FEM simulations confirmed the generation and scattering behavior of waves from defects, demonstrating that the PVS method offered improved directivity and reduced interference compared to conventional laser ultrasonics. The FEM was used to simulate laser-generated ultrasound propagation and its interaction with surface-breaking cracks by Jeong [67]. A thermoelastic laser line source was modeled as a shear dipole and applied as nodal forces in a plane strain FEM model. The model successfully generated Rayleigh surface waves on an intact surface and was then extended to study wave interaction with cracks of varying depths. The crack-scattered waves were analyzed for crack sizing, accurately reproducing experimentally observed features for characterizing surface-breaking defects.

Guan et al. [68] performed FEM simulations to analyze the interaction of laser-generated surface acoustic waves with a surface crack, modeled as a rectangular notch. A 2D plane strain analysis was considered for the thermoelastic problem, as well as laser line source illumination. The captured waveforms revealed four distinct reflected components: a direct reflection of a compressive pulse, Rayleigh wave conversion upon impact with the notch, a reflection of the initial Rayleigh wave from the near side of the notch, and a mode-converted wave originating from the notch base. The arrival time of the fourth component indicated a dependence on notch depth, highlighting its potential for crack depth assessment. The same team [69] employed FEM modeling to simulate the acoustic field generated by a laser line source near a surface defect, represented as a rectangular notch. The analysis examined the transient displacement distributions and identified the ultrasonic wave modes, including longitudinal waves, transverse waves, and SAWs. As notch depth increased, notable effects were observed: changes in bulk wave directivity, increased amplitude of reflected SAWs, and a time lag in transmitted SAW pulses. The simulation results confirmed the experimental findings in [70].

Jian et al. [71] investigated crack depth measurement using wideband Rayleigh waves generated by a pulsed laser line source in the thermoelastic regime. The FEM was employed to analyze wave scattering, revealing that reflected and transmitted Rayleigh waves exhibited distinct propagation paths and frequency spectra. The arrival times of these waves correlated with crack depth and enabled accurate depth estimation. The experimental results aligned with the 2D FEM predictions, validating the effectiveness of this method for non-destructive crack evaluation. The same team [72] used a pulsed laser combined with an EMAT for rapid online inspection of steel billets. FEM simulations helped to explain the laser-generated ultrasonic field and its consistency with EMAT-detected signals. By optimizing the separation between the laser and EMAT, bulk waves were used for internal defect detection, while Rayleigh waves enabled surface defect inspection. This dual-mode capability enhanced the efficiency and accuracy of non-destructive steel inspection.

Wang et al. [73] examined the propagation of laser-generated SAWs on samples with surface defects. Numerical modeling revealed that surface defects acted as low-pass filters, with the cutoff frequency decreasing as the defect depth increased. Additionally, wider defects caused significant wave attenuation. Ni et al. [74] investigated the propagation and scattering of ultrasound in a cracked Al specimen using a dual-laser source and the FEM. Various ultrasonic modes were analyzed (see Figure 6), and a method for determining crack orientation angles was proposed based on the arrival times of scattered waves. Experimental measurements validated the numerical simulations, demonstrating strong agreement between theoretical predictions and observed results. The findings confirmed that specific ultrasonic wave arrivals can be used to accurately calculate crack orientation, offering a reliable approach for crack assessment. The same team [75] examined the interaction of a laser line source with a crack modeled as a slot, a key process in the scanning laser line source technique. Using the FEM, the scattering of ultrasonic waves was simulated and wave propagation paths were analyzed. Displacements for different slot orientations were calculated, revealing that the arrival times of specific ultrasonic wave modes can determine slot orientation. The study clarified the relationship between slot orientation and ultrasound diffraction patterns, aiding crack detection and characterization.

A FEM model was developed by Dai et al. [76] to investigate the interaction of generated SAWs by pulsed laser line source with surface notches of varying depths and orientations. The study examined signal enhancement mechanisms, notch position evaluation using reflected Rayleigh waves, and depth/orientation determination via shear waves generated by mode conversion. The results aligned with experimental findings, demonstrating the model’s effectiveness in optimizing SAW-based surface crack detection. Guan [77] performed FEM simulations to analyze the scattering of laser-generated SAWs from surface cracks of varying depths and widths. The study captured bipolar Rayleigh waves and identified oscillation signals following the reflected waves, with their temporal characteristics linked to notch depth and width. Based on these findings, a new crack evaluation method was proposed, offering an accurate approach for measuring surface crack depth.

Dong et al. [78] proposed a new technique, using multiple-pulse narrow-band ultrasound generated by laser arrays, to improve the sensitivity and efficiency of laser-based ultrasonic methods for detecting surface-breaking cracks. FEM simulations based on thermoelastic theory were used to analyze the interaction of these narrow-band ultrasonic waves with cracks. The study compared the frequency spectra of reflected and transmitted waves, showing that variations in multiple-frequency components correspond significantly to crack depth. Pei et al. [79] investigated the detection and evaluation of internal volume defects in metals using laser-generated ultrasonic waves and EMAT detection. A FEM model was developed to simulate wave interactions with defects, revealing both directly scattered shear waves and mode-converted creeping waves along the defect surface. Experimental validation using a non-contact laser-EMAT system confirmed these findings. A new defect evaluation method was introduced based on the time-of-flight analysis of scattered and mode-converted waves, demonstrating accurate defect size estimation for artificial holes.

Burrows et al. [80] modeled the propagation of laser-generated Lamb waves in an Al sheet using FEA and investigated their interaction with defects. Experimental validation was conducted using an EMAT for wave detection. The results showed that the frequency content of the received wave was enhanced when the laser generation point was directly over a defect. Time–frequency analysis using a Wigner transform successfully identified individual wave modes, demonstrating the method’s effectiveness for defect detection. Zeng et al. [81] performed FEM simulations to investigate the interaction of SAWs with near-surface defects in an Al plate. The results showed that as SAWs propagated through defects of varying depths, an oscillation effect occurred, followed by gradual attenuation. The simulation data indicated that the center frequency of the oscillation signal shifts with defect depth, ranging from 0.4 to 0.76 MHz for depths between 0.1 and 0.5 mm. Additionally, increasing defect width led to significant signal attenuation. Zhou et al. [82] investigated the interaction of laser-generated Rayleigh waves with surface-breaking cracks using FEM simulations and experimental validation. The results showed that Rayleigh waves in the 3–5 MHz frequency range were highly sensitive to surface-breaking cracks. As the crack depth increased, transmission coefficients decreased almost linearly, while reflection coefficients initially decreased and then increased. The correlation between transmission coefficients and crack depth enabled quantitative defect characterization.

Ni et al. [83] explored the generation and propagation of laser-generated ultrasound using a laser array source in a thermoelastic regime, modeled through FEM simulations. By adjusting the trigger delay between laser sources, giant bulk acoustic waves with enhanced amplitudes and specific wavefronts were produced. These waves exhibited significantly improved defect detection capabilities compared to single-pulse laser-generated waves. The findings suggested that laser array sources can enhance non-destructive testing methods. The same team [84] investigated the generation of ultrasound using a laser array source in a thermoelastic regime and its interaction with surface-breaking cracks through FEM simulations. By adjusting the spatial distribution of the laser array, narrow-band acoustic waves were generated and analyzed in the frequency domain. The study compared these waves with wideband reflections from a single laser source to understand their interaction with cracks. The results indicated that narrow-band acoustic waves were sensitive to crack depth variations.

Chen et al. [85] investigated the propagation of anti-symmetric flexural (ASF) wedge waves along wedge tips with perfect and imperfect rectangular defects using FEM simulations and laser ultrasound measurements. The research revealed complex interactions, including direct reflections, transmissions, and newly discovered mode conversions. It was found that ASF modes can convert to higher-order modes upon encountering defects, with reflection and transmission coefficients varying based on defect depth. Additionally, scattered Rayleigh waves carried significant energy during defect interactions. Imperfect defects showed lower reflection and higher transmission compared to perfect ones. These findings are useful for SHM of wedge-like structures, such as machine tool edges. Sun et al. [86] investigated the non-contact characterization of debonding defects in lead-alloy steel bonding structures using laser-generated and detected ultrasonic waves. FEM simulations modeled thermoelastic excitation and wave propagation, clarifying the effects of defects on the wave field. Experimental validation extracted key signal features, optimizing wave frequency and probe position. Laser ultrasonic C-scan imaging successfully detected circular debonding defects larger than 4 mm.

Orphanos et al. [87] presented an integrated pump–probe experimental setup combining fs and ns laser pulses for the excitation and high-resolution imaging of SAWs in gold thin films on glass substrates. The method enabled full-field dynamic interferometric imaging without time-delay restrictions. Numerical simulations, combining a finite-difference two-temperature model with a FEM model, supported the experimental findings. The results demonstrated the advantages of fs-laser-generated SAWs for surface defect detection, achieving ultrahigh spatial resolution and precise metrology. Additionally, the coupling depth of the fs-laser-generated SAWs in multilayered materials was found to be less than 15 µm. In [88], a 3D multiphysics thermo-structural FEM model was developed to investigate the generation and propagation of ultrasonic waves in metallic films. The model provided detailed insights into the spatiotemporal evolution of acoustic waves and the effects of geometric characteristics and temperature on their behavior. The study extended to analyzing the impact of surface and solid volume defects on wave propagation. The results indicated that surface gaps within the metallic film did not affect Rayleigh wave propagation, whereas defects extending to the substrate caused partial transmission and reflection of the waves.

Hao et al. [89] investigated the influence of ultrasonic waves excited by laser point and line sources on detecting rail surface defects. Using the FEM, the sound fields and acoustic signals for both excitation modes were compared, and the detection of horizontal, vertical, and 45° oblique defects was simulated. Experimental tests validated the simulations, showing that laser line source excitation produced SAWs with strong directionality and high signal amplitude, making it more effective for detecting various rail surface defects. Jiang et al. [90] presented a quantitative method for detecting internal defects in rail heads using laser-generated ultrasonic bulk waves. FEM simulations modeled wave interactions with defects to analyze mode conversion. An optimized variational modal decomposition technique improved the signal-to-noise ratio and enabled defect signal extraction. The experimental validation of artificial defects confirmed the method’s accuracy, achieving location errors within 3% and size estimation errors within 7%. Zeng and Yao [91] explored the non-destructive detection of surface defects in cylindrical pipes using laser-generated ultrasonic waves. FEM simulations analyzed wave propagation, showing that surface waves and shear waves converted to surface waves were effective for defect detection. The maximum negative peak of reflected waves increased with defect depth, and B-scan imaging enabled defect localization.

Zeng et al. [92] investigated the characteristics of laser-generated ultrasonic waves interacting with subsurface defects using the FEM. A rectangular subsurface hollow was modeled to represent defects, and the resulting diffracted bulk modes and oscillation effects were analyzed. The study revealed that the amplitude of echo waves and oscillating waves varied with defect depth, showing distinct oscillation characteristics in frequency ranges of 1–2 MHz, 2–3 MHz, and 3–4 MHz. These frequency-dependent amplitude variations can be used to detect the size and location of subsurface defects. The findings provided a potential method for detecting various subsurface structures and measuring surface slot angles. Zeng et al. [93] also proposed a physical model of a phased-array laser source for detecting surface defects, which contained five pulsed laser sources. FEM simulations were used to optimize the system by analyzing the amplitude and spectrum characteristics of ultrasonic waves generated with different element spacings (see Figure 7). The results showed that when the element spacing was 0.1–0.2 mm, the transmitted wave amplitude was at its highest, while for larger spacings (0.3–0.6 mm), the amplitude gradually decreased. Additionally, as the surface defect depth increased from 0.5 mm to 2.5 mm, the reflected wave amplitude increased, while the transmitted wave amplitude decreased, and its peak time shifted. Kou et al. [94] presented a non-contact nonlinear ultrasonic testing method using laser ultrasonics for detecting closed surface cracks. A pulsed laser grating source generated narrow-band SAWs, and a nonlinear numerical simulation based on the FEM modeled the generation of higher harmonics caused by crack interactions. The results showed that the acoustic nonlinearity parameter increased with crack length but decreased with crack depth. Experimental validation using a wideband laser interferometer confirmed the method’s effectiveness.

Zeng et al. [95] explored the use of a laser ultrasonic system for non-contact inspection of defects in Wire + Arc Additive Manufactured (WAAM) components, which are challenging to assess using conventional ultrasonic methods due to rough surfaces and high temperatures. A pulsed laser and laser interferometer were used to detect artificial defects (cracks, flat-bottom holes, and through-holes) without surface machining. FEM simulations modeled the interaction of laser-generated ultrasonic waves with defects, and experimental laser ultrasonic inspections provided A- and B-scan plots for quantitative defect analysis. The results confirmed the feasibility of laser ultrasonics for inspecting WAAM components. The same team [96] investigated the influence of surface profiles on laser ultrasonic inspection. FEM simulations and experiments showed that surface roughness affected the signal-to-noise ratio for internal defects, while surface waviness impacted superficial crack detection sensitivity. A robotic laser ultrasonic inspection system was developed, demonstrating the potential for online WAAM process monitoring.

Lin et al. [97] investigated the use of a backpropagation neural network (BPNN) combined with laser-generated SAWs to detect and measure subsurface crack depth and length. FEM simulations were used to study SAW interactions with cracks, and the reflected and transmitted waves were analyzed using Fourier and wavelet transforms. Selected wave parameters were used to train and test the BPNN, achieving an estimation error below 4%. The results demonstrated the method’s high accuracy and potential for quantitative subsurface crack measurement using laser ultrasonics. Ding et al. [7] employed a NDT technique using laser ultrasonics and a ResNet-based deep learning approach to detect and quantify surface and subsurface defects. Unlike conventional methods that required manual feature extraction, the ResNet model automatically learned informative features from SAW signals obtained via the transient thermal grating method. The FEM was used to generate training data, which were verified through experiments (see Figure 8). The ResNet model achieved a 96.21% classification accuracy and outperformed VGG16, BP, and SVM algorithms. The regression results confirmed high prediction accuracy for unknown defect depths, demonstrating the method’s reliability for inspecting metal, ceramic, and semiconductor materials. Zhang et al. [8] integrated laser ultrasonic testing with deep learning for intelligent defect detection. FEM models and experiments on surface and subsurface defects analyzed their impact on SAW propagation. To enhance data diversity, Gaussian white noise was added to both simulation and experimental signals. Wavelet transform images of reflected and transmitted signals were used to train a convolutional neural network (CNN). A dataset of 40,000 surface defect signals and 21,000 subsurface defect signals was created and split for training, testing, and validation. The CNN achieved a 94.13% classification accuracy for surface defect depth and a minimum error of 5.6% for subsurface defect width detection. The study demonstrated the feasibility of combining laser ultrasonics with deep learning for accurate defect characterization, although further research is needed to determine subsurface defect depth.

3.2. Transducer-Generated Ultrasonic Guided Waves

Transducer-generated ultrasonic guided waves are widely used to identify defects in structures such as pipelines, plates, and composite materials. These waves propagate along the structure, interacting with defects like cracks, corrosion, or delaminations, which alter their amplitude, phase, or mode. By analyzing the reflected or transmitted wave signals, defects can be detected and characterized with high sensitivity. Guided waves, such as Lamb waves or SH waves, are particularly effective for long-range inspection, making them valuable in NDT and SHM applications. For accurate and non-contact detection, laser vibrometers and laser velocimeters are employed to measure wave propagation by capturing surface vibrations and velocity variations with high spatial and temporal resolution. FEM simulations are conducted to model these phenomena, using either a force load or a displacement function to simulate the excitation applied by the transducer.

Hosten et al. [98] explored ultrasound-stimulated thermography for defect detection in viscoelastic anisotropic materials like polymers and fiber-reinforced polymers. Unlike traditional methods that relied on heat generated by defect friction or plastic deformation, this approach detected defects by analyzing modifications in the ultrasonic field and resulting temperature distribution. A FEM model was used to compute stress, displacement, and heat generation due to wave attenuation. Experimental validation was conducted using a sonotrode, based on an actuator, to excite a PVC plate, with ultrasonic displacement measured via a laser velocimeter. The model’s predictions were compared to infrared camera images, demonstrating its effectiveness in defect detection. Thring et al. [99] introduced a high-resolution NDT method using a focused EMAT optimized for generating 2 MHz Rayleigh waves. This high frequency enabled the detection of millimeter-depth defects, while the focus improved the sizing of shorter defects compared to standard EMATs. Laser vibrometry and finite element modeling were used to analyze the focusing behavior and aperture angle effects, showing that a reduced aperture shifted the focal point and increased focal depth. The dual-EMAT system demonstrated an excellent signal-to-noise ratio (up to 30 dB) and successfully imaged surface-breaking defects, including a 2 mm-long, 0.2 mm-wide, and 1.5 mm-deep defect in aluminum billets. These findings supported the design of optimized EMATs for enhanced defect detection.

Sato et al. [100] developed a manufacturing and inspection system for miniaturized bearing rollers using directed energy deposition for fabrication and laser ultrasonics for crack detection. To detect the acoustic waves, a laser Doppler interferometer was used. Thin jigs with a 0.4 × 0.6 mm² cross-section were fabricated and inspected non-destructively. Challenges in laser ultrasonics inspection, such as beam overlap, complex wave interactions, and acoustic field complexity, were addressed using FEM modeling and complex discrete wavelet transform. The results successfully detected spontaneous cracks. Peyton et al. [101] investigated the use of SH waves for detecting defects in laser-welded thin titanium sheets. The potential use of EMATs, in both generation and detection, for the inspection of titanium samples was investigated. FEM simulations and experiments revealed that defect geometry, particularly width and length, significantly influenced wave reflection. Phase differences between reflections from the defect’s front and back faces caused shifts in peak positions. The findings confirmed the effectiveness of SH waves in defect detection and highlighted the potential of EMATs for inspecting titanium components.

4. Laser Ultrasonic Guided Waves in Biomedical Diagnostics

FEM simulations play an important role in analyzing the behavior of skin, soft tissues, and hard tissues, particularly in biomedical applications involving laser-induced acoustic methods. By modeling how laser-generated acoustic waves interact with different tissue types, these simulations provide valuable insights into tissue properties and disease detection. In dermatology, FEM helps to evaluate the skin’s response to laser waves, aiding in the detection of abnormalities like melanoma (Section 4.1). Similarly, in dentistry, FEM simulations assist in understanding the interactions between acoustic waves and dental hard tissues, facilitating the early detection of dental caries, cracks, and other oral health issues (Section 4.2). These thermomechanical simulations (see Equations (1) and (2)) enhance the precision and effectiveness of non-invasive diagnostic methods.

4.1. Laser Ultrasonic Guided Waves in Human Skin

L’Etang and Huang [102] explored the use of laser-generated SAWs for characterizing skin properties through a multilayered FEM model. A coupled thermal and mechanical analysis simulated the propagation of SAWs in a three-layer skin model, ensuring that laser energy remained within the thermoelastic regime, preventing thermal damage. The study examined how variations in dermis layer thickness affected wave propagation and deformation responses. The results indicated that SAW waveforms contained valuable information about skin layer properties, highlighting the potential of laser ultrasonics for non-invasive skin characterization in medical applications. Li et al. [103] investigated the generation and propagation of laser-generated ultrasound in human skin using FEM modeling. A two-layer isotropic biomaterial model simulated the thermoelastic response of skin to a high-power laser pulse, analyzing transient temperature distribution and ultrasonic wave propagation. The results showed that the laser beam radius and pulse width significantly affected wave characteristics while keeping the heat-affected zone localized. These findings provided a foundation for using laser-generated ultrasound as a non-contact and non-destructive method for evaluating human skin properties.

Li et al. [104] explored laser-generated SAWs in soft tissue-mimicking agar-agar phantoms using FEM modeling and low-coherence interferometry. A Nd:YAG laser line source generated SAWs, which were detected by a time-domain interferometry system. The source term for the deposited laser energy per unit volume per second was considered, along with the absorption coefficient and the scattering coefficient. Both FEM simulations and experiments produced SAW phase velocity dispersion curves, showing strong agreement. This was the first application of laser-generated SAW dispersion techniques to soft materials, offering the potential for the non-invasive measurement of soft tissue mechanical properties. Humphries et al. [105] performed FEA to simulate the fragmentation of ink granules during Q-switched Nd:YAG laser tattoo removal, considering both thermal and acoustic mechanisms. The results aligned closely with clinical observations, showing that thermal fragmentation is the primary mechanism at a 6 ns pulse and 1064 nm wavelength. The study suggested that increasing fluence levels in later treatments and using larger spot diameters can enhance pigment clearance while minimizing tissue damage. These findings provided insights into optimizing laser settings for more effective tattoo removal.

Chen et al. [106] explored the use of laser-generated SAWs and thermomechanical FEM simulations to detect and characterize melanoma in human skin. A three-layer skin model was developed, showing that melanoma presence altered the dispersion curve of SAW phase velocity. The study demonstrated that the minimum detectable melanoma size was influenced by FEM meshing resolution, with a current detection limit of 0.03 mm. The simulated dispersion curve had a clear upward pattern, presenting a dramatic increase and decrease in the curve when the melanoma existed. The findings highlighted the potential of LSAW spectroscopy for early melanoma diagnosis. An et al. [107] performed FEM simulations to investigate laser-induced ultrasonic waves in soft tissues, considering factors like thermal diffusion, optical penetration, tumor elasticity, and laser pulse duration. The model calculated transient temperature distributions and thermoelastic stress fields, revealing that larger tumors produced stronger ultrasound peaks and earlier longitudinal wave arrivals, while smaller tumors resulted in shorter signal durations and larger high-frequency components. The experimental results validated these findings, demonstrating the potential for laser ultrasonics in detecting and characterizing tumors in soft tissues.

Li et al. [108] explored the use of laser-induced SAW technology for the non-invasive and accurate detection of melanoma in human skin. FEM simulations were conducted to determine optimal pulse laser parameters for generating surface waves, including irradiance (0.1–10 mJ/mm²), rise time (≥20 ns), beam radius (≥1 mm), and wavelengths (900–1600 nm). The study identified a working bandwidth of 0.2–2 MHz and a minimum detectable melanoma size of 0.03 mm. The results showed that SAW dispersion curves were highly sensitive to melanoma-induced changes (see Figure 9).

Zeng et al. [109] explored laser-generated ultrasound as a non-invasive method for detecting and characterizing melanoma in human skin. FEM simulations analyzed the interaction between SAWs and skin tissue, with a focus on tumor size evaluation. The correlation coefficient method was introduced as a tool to quantify tumor size, showing that as the tumor was enlarged, the correlation coefficient decreased. Future research aims to develop a 3D model for visualizing tumor size, providing theoretical guidance for laser ultrasonics-based skin cancer detection. Zeng et al. [110] also proposed a laser ultrasonic detection method using a PSO-SVM (Particle Swarm Optimization–Support Vector Machine) algorithm to identify and classify skin tumors. A FEM model of laser-generated ultrasound in human skin tumors was developed to analyze ultrasonic waves at different tumor locations (epidermis, dermis, and between layers). Key features, such as entropy values and time-domain characteristics, were extracted, and the SVM algorithm, optimized with PSO, was used for tumor classification. The simulation results confirmed the effectiveness of this approach, offering a promising method for non-invasive skin tumor detection.

4.2. Laser Ultrasonic Guided Waves in Dental Applications

Sun et al. [111] explored a non-destructive laser ultrasonic technique to generate and detect broadband SAWs in human teeth with varying degrees of demineralization. Using a scanning laser line source method and a two-dimensional fast Fourier transform, the dispersion spectrum of SAWs was analyzed to evaluate the elastic properties of healthy and carious teeth. FEM simulations were used to study SAW propagation and dispersion, with the results being comparable to the experimental findings. The findings confirmed that laser ultrasonic techniques were highly sensitive in assessing dental enamel properties and can be applied to study different tooth conditions non-invasively. The same team [112] presented the first application of a remote non-destructive laser ultrasonic system for detecting cracks in human teeth. Using a scanning laser line source technique and a laser Doppler vibrometer, ultrasonic waves were generated and detected on extracted teeth with different types of cracks. B-scan images and peak-to-peak amplitude variation curves of SAWs were analyzed to determine crack position and depth. FEM simulations validated the experimental results, demonstrating the laser ultrasonics system’s accuracy. This technique showed great potential for the early non-invasive clinical diagnosis of cracked teeth.

Yuan et al. [113] investigated laser-induced SAW propagation in human teeth using the FEM and Laguerre polynomial expansion method (LPEM). The FEM provided full-field temperature and SAW displacement data, while LPEM calculated SAW phase velocity in healthy and carious teeth. The results demonstrated that enamel inhomogeneity, thickness variations, and caries significantly affected SAW characteristics. These methods offered a theoretical basis for the non-destructive evaluation of teeth, enabling the extraction of structural parameters and detection of caries. Sun et al. [114] investigated the use of laser-generated SAWs to evaluate the elastic properties of early caries in human teeth. FEM simulations analyzed the effects of enamel thickness and tooth curvature on SAW dispersion spectra. Experiments on extracted incisors and molars with different demineralization conditions demonstrated that using a reference tooth with similar geometry helped minimize interference, enabling accurate detection of caries. The findings confirmed the sensitivity of laser ultrasonics for the evaluation of early caries, with plans to adapt the technique for in vivo clinical measurements using optical fiber lasers.

Hériveaux et al. [115] studied the interaction between ultrasonic waves and the dental implant–bone interface using both experimental and numerical approaches. A 10 MHz ultrasonic transducer was used to generate waves, and laser interferometry was used to measure displacement amplitudes along the implant axis, ranging from 3.2 to 8.9 nm. The results confirmed guided wave propagation with a velocity of 2110 m/s and frequency components below 1 MHz, aligning with numerical simulations. Understanding guided wave behavior in dental implants could enhance techniques for assessing and stimulating osseointegration.

5. FEM and Laser-Based Acoustics in Engineering Applications

In engineering applications such as aerospace and automotive industries, the integration of the FEM and laser-based acoustics plays a crucial role in enhancing performance, safety, and efficiency. By accurately simulating and analyzing sound wave propagation, these technologies contribute to noise reduction, vibration control, and structural optimization, leading to quieter and more durable designs. FEM modal analysis further refines this process by identifying the natural frequencies, mode shapes, and dynamic behavior of structures, helping engineers design components that minimize resonance and unwanted vibrations. Additionally, the combination of laser vibrometry and the FEM allows for real-time infrastructure assessment, enabling the precise monitoring of mechanical components and the detection of structural weaknesses before they escalate into critical failures. These techniques are particularly useful for evaluating the behavior of plates, which are common in many structural applications. Through laser-based acoustics and FEM modal analysis, engineers can assess the vibrational modes, stiffness, and stress distributions in plates, optimizing their design for maximum strength and efficiency. Techniques such as electronic speckle pattern interferometry (ESPI) further enhance these capabilities by providing high-resolution full-field vibration measurements, allowing engineers to monitor surface deformations and frequency responses with exceptional accuracy. This approach is especially valuable in SHM, where early damage detection and failure prediction in plates and other components can prevent costly repairs and extend the lifespan of engineering systems.

Buehrle et al. [116] explored extending the frequency range of FEM models for dynamic predictions in stiffened aircraft fuselage structures, aiming for mid-frequency noise control. Various models (beam, plate, and solid elements) were used to analyze stiffener components and attachment interfaces. Validation with experimental modal analysis, scanning laser Doppler velocimetry, and electro-optic holography showed that plate element models were needed at higher assembly levels. The results indicated that attachment models with constraints over the entire contact surface were too stiff, with better agreement found using rivet-line attachment models. The study also addressed challenges in increasing modal density and spatial resolution at higher frequencies, requiring further refinement in FE modeling. Auweraer et al. [117] presented a vibration testing system using pulsed laser holographic ESPI, which provided time-triggered vibration images instead of time-averaged ones. The integration of this system into a modal testing and analysis procedure was reviewed, and the accumulation of results at multiple excitation frequencies allowed the construction of frequency response functions. A novel parameter extraction method, utilizing spline-based data reduction and maximum-likelihood parameter estimation, was developed. The approach was extended for industrial applications, including the integration of geometry, response information, and FEM data, as well as the identification of critical panels and modes. This global procedure was applied to several industrial case studies, including car panels, light truck panels, a full vehicle, and household products.

Yang and Ume [118] investigated the thermomechanical reliability of flip-chip solder bumps using laser ultrasound-interferometric inspection and FEA. Key findings from the research were that laser ultrasound effectively detected solder bump fatigue cracks and tracked crack propagation through thermal cycling. It was also observed that the outermost solder bump, experiencing the highest strain, was most prone to failure. Additionally, a strong correlation was found between the inelastic strain energy density from FEA and the results from laser ultrasound testing, which helped validate the FEM simulations. The research aimed to develop a low-cost high-sensitivity inspection system for solder bump defects. Yamaguchi et al. [119] investigated the mechanical properties of complex silicon submicron structures using both experimental ultrafast spectroscopy and FEA. The research focused on periodic and random arrays of silicon submicron spirals grown via oblique angle deposition. Femtosecond laser pulses were used to excite resonant vibrational modes in the spirals, resulting in the observation of multiple harmonics. The eigenfrequencies and mode patterns of the vibrations were successfully simulated using FEA. The findings highlighted the potential of submicron spiral arrays for studying the mechanical and acoustic properties of complex structures in the low-gigahertz frequency range.

Huang and Ma [120] provided comprehensive results on the dynamic characteristics of GT-cut and SC-cut quartz plates at resonance, obtained through experimental measurements and numerical calculations. The quartz plates were excited using voltage and acoustic waves on the surfaces. The first experimental method, amplitude-fluctuation ESPI, was used to measure resonant frequencies and full-field vibration mode shapes simultaneously. The laser Doppler vibrometer was employed to verify the resonant frequency results from ESPI. The investigation focused on cantilever and free quartz plates, with the experimental results being comparable to the FEM simulations. The same authors [121] investigated 3D coupled vibrational characteristics of piezoelectric shells using experimental methods (amplitude-fluctuation ESPI, laser Doppler vibrometry, and impedance analyzer) and FEM modeling. The results demonstrated that piezoelectric shells exhibited coupled vibrations at high frequencies (lateral/angular modes) but remained uncoupled at low frequencies (radial modes). The experimental and numerical results aligned closely, validating the model. The findings highlighted the complex vibrational behavior of piezoelectric shells across a broad frequency range.

Klepka et al. [122] explored the use of nonlinear acoustics for detecting impact damage in composite laminates. Two composite plates were analyzed, with one subjected to a low-velocity impact. Ultrasonic C-scans revealed the extent of barely visible damage, while FEM modeling was used to identify vibration mode shapes and estimate the local defect resonance frequency. Nonlinear acoustics tests, guided by a delamination divergence study, were conducted to detect damage. Surface-bonded piezoceramic transducers provided high-frequency ultrasonic excitation, while low-frequency modal excitation was applied using an electromagnetic shaker. Scanning laser vibrometry was used to capture the vibro-acoustic responses. The results showed that nonlinear vibro-acoustic modulations can effectively detect impact damage. Eriksson et al. [123] developed a unimorph flexural transducer design consisting of a passive metal cap structure with a thin piezoelectric disc bonded to the inside. Extensive FEM modeling and experimental 2D time-resolved displacement measurements were conducted to analyze the transducer’s flexural properties and compare them to analytical thin plate vibration models (see Figure 10). A key focus was on understanding the influence of the passive layer before bonding the piezoelectric element. A high-power Nd:YAG laser was used for non-contact actuation, and frequency analysis identified flexural modes, including non-axisymmetric ones, which are often disregarded due to poor acoustic properties. The study found strong agreement between the experimental results and FEM simulations, with notable deviations from traditional plate vibration theory.

Galos et al. [124] studied the impact of embedding lithium-ion polymer (LiPo) batteries into carbon fiber laminates and sandwich panels on their vibration and acoustic properties. Experimental measurements using Laser Doppler vibrometry, along with FEM modal analysis, were conducted to assess modal frequencies and damping characteristics. The findings highlighted the importance of strategic battery placement as embedding LiPo batteries at nodal points significantly increased the vibration bending damping ratio—by up to 220% for mode II and 310% for mode III. Additionally, LiPo batteries enhanced acoustic performance by raising the coincidence frequency and reducing the wavenumber amplitude at higher frequencies. These results suggested that careful integration of LiPo batteries can improve the vibration and acoustic behavior of composite structures. Santos Silva et al. [125] examined the impact of high-temperature and high-frequency vibratory loads on Hastelloy-X plates. Non-contact techniques captured full-field temperature and displacement data as plates were heated and mechanically excited. Experimental modal analysis identified eleven resonant modes, validated by a FEM model with temperature-dependent material properties. The results showed that resonant frequencies depended on temperature distribution, with transverse heating increasing the frequency, while longitudinal heating had little effect. Accurate thermal loading representation in FEM models was crucial for reliable high-temperature structural behavior predictions.

6. Advances, Challenges, and Future Perspectives

Recent advances in laser-generated ultrasound have significantly improved our understanding of wave propagation, thermoelastic effects, and material interactions. Advanced FEM simulations, combined with experimental techniques such as laser interferometry and pump–probe methods, have provided detailed insights into SAW dispersion, Lamb wave behavior, and the influence of coating thickness, optical penetration, and anisotropy on ultrasonic wave characteristics. These studies have led to optimized models that account for temperature-dependent material properties, laser pulse parameters, and complex wave interactions, enabling accurate predictions of wave behavior in layered and composite structures. However, challenges remain, including the need for more precise modeling of nonlinear effects such as phase transitions, melting, ablation, and elastoplastic deformations under extreme conditions. The computational cost of large-scale 3D simulations remains high, and discrepancies between numerical and experimental results at higher frequencies highlight the need for improved spatial resolution. Additionally, the influence of surface roughness, microstructural variations, and viscoelastic effects on SAW propagation requires further investigation to enhance accuracy. Future research should focus on integrating machine learning and data-driven approaches to refine FEM models, improving computational efficiency while maintaining accuracy. The development of advanced optical detection techniques will allow for higher spatiotemporal resolution in experimental studies, enabling better characterization of transient wave phenomena.

Laser-generated ultrasonic waves have also advanced significantly as a non-contact high-precision tool for characterizing the mechanical properties of solids, with applications in thin film analysis, stress evaluation, and high-temperature material testing. Recent research uses FEM simulations, artificial neural networks, and advanced experimental techniques to extract key material parameters such as Young’s modulus, density, Poisson’s ratio, and residual stress distributions. The integration of dispersion relations, acoustoelastic theory, and machine learning approaches has enabled more accurate property estimation without reliance on conventional least-square fitting or dispersion curve analysis. However, challenges remain, including the complexity of modeling multilayered materials, the computational cost of high-precision simulations, and the influence of experimental uncertainties on measurement accuracy. The need for improved detection techniques, such as high-resolution optical pump–probe imaging and grating-based methods, is evident in enhancing ultrasonic wave analysis in complex materials. Additionally, the study of interfacial stresses, thin-film delamination, and anisotropic behavior requires further refinement in both numerical and experimental approaches. Future advancements should focus on improving the spatial and temporal resolution of laser ultrasonic methods, integrating data-driven techniques to optimize inverse problem-solving.

Laser-generated guided waves are also a powerful non-contact tool for detecting and characterizing surface and subsurface defects, with advances including phase velocity scanning, laser arrays, and hybrid techniques integrating EMATs and deep learning models. FEM simulations have provided critical insights into wave interactions with defects, enabling precise crack depth estimation, defect orientation analysis, and improved sensitivity through narrow-band ultrasound. Challenges remain in optimizing wave propagation in complex materials, mitigating interference in multimodal wave environments, and improving detection in rough or high-temperature surfaces like WAAM components. Future perspectives include using machine learning for automated defect classification, enhancing phased-array laser sources for tailored wave generation, and integrating real-time robotic laser ultrasonics for industrial-scale inspections.

Laser ultrasonic guided waves have shown significant advancements in non-invasive biomedical diagnostics, particularly in skin and dental applications. Research has demonstrated that laser-generated SAWs effectively characterize skin properties, detect melanoma, and optimize tattoo removal by leveraging FEM modeling to analyze wave dispersion and thermal effects. Similarly, laser ultrasonics has proven highly sensitive for evaluating dental conditions, including early-stage caries and crack detection, using scanning laser line source techniques and numerical modeling. Nevertheless, challenges persist, such as optimizing laser parameters to minimize tissue damage, improving detection limits for smaller anomalies, and refining FEM simulations for greater accuracy. Additionally, ensuring in vivo applicability remains a hurdle as factors like biological variability and real-time signal processing require further development. Future perspectives include integrating AI for automated diagnosis, developing real-time imaging techniques for clinical use, and enhancing laser ultrasonic systems for broader medical applications, including early-stage cancer detection and dental implant assessments.

The integration of the FEM and laser-based acoustics has led to significant advancements in engineering applications, particularly in aerospace, automotive, and SHM. These techniques enable vibration control and real-time assessment of mechanical components, leading to improved safety and durability. Laser vibrometry, ESPI, and nonlinear acoustics have provided high-resolution insights into material behavior, defect detection, and resonance characteristics across various structures, including aircraft fuselages, composite laminates, and piezoelectric shells. Challenges remain in refining FEM models for higher frequency ranges, improving accuracy in complex geometries, and addressing material property variations under extreme conditions. The development of real-time monitoring systems and the enhancement of non-contact measurement techniques represent key future directions.

The integration of the FEM, laser-based acoustics, and emerging AI technologies holds immense potential for advancing scientific research and engineering applications. As computational models become more sophisticated and experimental methods become more precise, this synergy will continue to drive innovation across multiple disciplines, offering solutions for industry and healthcare. Expanding the application of FEM and laser acoustics into emerging fields such as energy storage systems, metamaterials, and bio-inspired structures presents new opportunities for future research and development.