Numerical simulation and experimental validation of multi-pulse ultrafast laser processing of microholes in glass light guide plate

Abstract

Glass light guide plates (LGPs) are widely employed in ultrathin display applications due to their excellent optical transmittance, chemical stability, and mechanical strength. The fabrication of microholes with precisely controlled morphology on glass surfaces using ultrafast lasers is crucial for further enhancing the optical performance of LGPs. However, the interaction mechanisms between ultrafast lasers and glass have not yet been precisely described, and the insufficient consideration of inter-pulse interactions under high repetition frequency conditions leads to limited predictive accuracy for microhole morphology. Here, a rotary laser processing system is employed for the high-efficiency fabrication of glass LGPs. To address the moving multi-pulse laser irradiation scenario, an improved two-temperature model (TTM) incorporating the laser incubation effect is proposed, enabling the calculation of both the material temperature field and the evolution of microhole morphology during the moving multi-pulse laser processing. The model is experimentally validated using a rotational laser processing system, and the simulated results agree well with both single- and multi-pulse microhole ablation under various laser parameters. For LGP applications, a strategy is further proposed to obtain conical microholes suitable for LGP operation by controlling the pulse number at different processing speeds, thereby enhancing optical performance. This multi-pulse laser ablation model for glass provides important theoretical guidance for microhole fabrication in LGPs and demonstrates significant engineering application value.

Graphical abstract

Keywords

Ultrafast laser processing / Glass light guide plates / Two-temperature model / Laser incubation effect

1 Introduction

Glass light guide plates (LGPs) are key components of display devices, responsible for converting LED light sources into uniform planar illumination. Due to the limited thermal stability and yellowing susceptibility of conventional polymer materials [1], glass materials with superior optical performance and higher mechanical strength are increasingly being adopted as replacements [2]. To satisfy practical application requirements, LGPs must simultaneously achieve high luminance uniformity and efficient light utilization, typically through the construction of microhole structures on the material surface to regulate light propagation. The morphology and dimensions of these microholes strongly influence light scattering and transmission, thereby determining the final optical output and spatial distribution. Consequently, the precise and consistent fabrication of microholes on glass surfaces constitutes a critical technological foundation for high-performance glass LGPs.

Microholes in glass LGPs are typically fabricated by mechanical machining, chemical etching, electrical discharge machining, or continuous-wave laser processing [3]. However, these approaches generally suffer from severe thermal damage, edge chipping, and limited machining precision [4,5]. Ultrafast laser processing, with pulse durations in the femtosecond to picosecond range and extremely high peak power densities, enables the fabrication of submicron-scale microholes [6,7]. Ultrafast laser processing platforms currently mainly include mechanical translation stages and galvanometer scanning systems. Mechanical translation stages offer high positioning accuracy [8], whereas galvanometer scanners provide relatively high processing speed [9]. However, for the practical fabrication of large-area microhole arrays on LGPs, mechanical translation stages require reciprocating row-by-row motion, which depends on frequent start–stop operations as well as repeated acceleration and deceleration of the stage. In contrast, galvanometer scanning systems are constrained by the field of view of the f-theta lens, making large-area microhole processing challenging. The rotary laser processing system adopted in this work enables efficient fabrication of microholes on LGPs through continuous rotation of the turntable, thereby eliminating time losses caused by repeated stage start–stop motions while also providing a large effective processing area.

Nevertheless, the microhole morphology is influenced by multiple factors [10,11]. During multi-pulse cumulative irradiation, the dynamic evolution of microhole morphology and progressive heat accumulation alter the conditions experienced by subsequent pulses, making it difficult to predict final microhole morphology [12]. Accordingly, researchers have developed various models to describe ultrafast laser and material interactions, including the two-temperature model (TTM) [13,14], molecular dynamics (MD) models [15], coupled TTM-MD models [16,17], and other improved models [18], characterizing energy deposition, transport, and material response. These models are predominantly based on assumptions of static material morphology [19] or few-pulse ablation [20], limiting their ability to capture energy accumulation and morphological evolution under multi-pulse, moving-processing conditions. To overcome these limitations, some studies have examined the spatiotemporal distribution of laser energy during scanning and its effect on microhole formation [21,22], while others incorporate material removal mechanisms to reflect ablation-induced morphology changes [23]. Despite these advances, accurately describing inter-pulse interactions at high repetition frequency and predicting microhole morphology with high fidelity remain challenging.

Here, a rotary laser processing system is employed for the high-efficiency fabrication of glass LGPs. To address the moving multi-pulse laser irradiation scenario, an improved TTM incorporating the laser incubation effect is proposed, enabling the calculation of both the material temperature field and the evolution of microhole morphology during the moving multi-pulse laser processing. The evolution of microhole ablation morphology was simulated in COMSOL Multiphysics, enabling characterization of both the transient temperature field and the morphology formation process under moving multi-pulse laser irradiation. The model was validated through ablation experiments and showed good agreement with the measured hole diameter, depth, and cross-sectional profiles. To meet the application requirements of LGPs, the influence of laser parameters on the central cross-sectional morphology and symmetry of the microholes was systematically investigated, thereby providing a route to improve the optical performance of the LGPs. The proposed multi-pulse glass ablation model offers an effective theoretical basis and practical process guidance for the design and fabrication of microhole structures in LGPs, demonstrating significant engineering application potential.

2 Processing system

Conventional processing methods based on mechanical displacement platforms can increase microhole depth by applying multiple pulses at fixed positions. However, this approach relies on frequent start–stop and acceleration–deceleration motions of the platform, which substantially reduce processing efficiency and make it unsuitable for large-area, high-density microhole fabrication. In this study, a laser rotary processing system is employed, in which microholes are fabricated under continuous platform rotation. This strategy avoids frequent platform stops while achieving deep microhole structures, as illustrated in Fig. 1a.

The system primarily consists of an infrared picosecond laser source, an acousto-optic modulator (AOM), a beam expander (BE), mirrors (M), a focusing lens, and a high-speed rotary stage. The AOM functions as a high-speed optical switch by electrically controlling beam deflection. During processing, the laser beam sequentially passes through the AOM, BE, and mirrors, and then enters a rotating mirror located at the center of the rotary stage. After reflection, the beam is focused by the focusing lens onto the upper surface of the glass LGP.

The feed system consists of a rotary stage and a linear translation stage. The rotary stage continuously rotates to generate arc-shaped machining trajectories on the sample surface, while the translation stage advances the sample at a constant speed, enabling row-by-row processing. This configuration allows continuous fabrication of microholes without frequent start–stop motions. The maximum processing speed of the system can reach 10⁷ microholes per minute, representing an approximately 10-fold improvement in efficiency compared with conventional equipment [24]. A schematic of the single-pulse and multi-pulse laser processing is shown in Fig. 1b, with the corresponding ablation results presented in Figs. 1c and 1d.

3 Model

Based on the laser rotary processing system, the laser continuously moves across the glass surface, with multiple pulses accumulating to form ablation microholes. The TTM can accurately describe the evolution of the temperature field following laser energy absorption, providing a theoretical basis for analyzing material removal mechanisms. Compared with MD simulations, the TTM requires significantly less computational effort, making it well suited for simulating multi-pulse processes. Here, the TTM is employed to capture energy accumulation and material removal during moving multi-pulse laser irradiation and to predict the resulting microhole morphology.

3.1 Two-temperature model

The TTM consists of two coupled energy transport equations describing the photon–electron and electron–lattice interactions [25]. Under the operating conditions of LGPs, the central cross-section of microholes plays a dominant role in determining the optical performance, while variations along the width direction have a negligible influence. Therefore, a simplified two-dimensional central cross-sectional model based on the 2D-TTM is developed to numerically simulate the morphological evolution of the microhole profile. In this model, the lateral heat diffusion perpendicular to the scanning direction is not explicitly resolved. This approximation significantly reduces the computational cost while maintaining good agreement with the experimentally measured cross-sectional morphology evolution under the investigated processing conditions. The coupled energy equations are expressed as follows:

(1)\begin{array}{rl}{C}_{\text{e}}{\displaystyle \frac{\mathrm{\partial }{T}_{\text{e}}}{\mathrm{\partial }t}}=& {\displaystyle \frac{\mathrm{\partial }}{\mathrm{\partial }x}}\left(K_{\text{e}}{\displaystyle \frac{\mathrm{\partial }{T}_{\text{e}}}{\mathrm{\partial }x}}\right)+{\displaystyle \frac{\mathrm{\partial }}{\mathrm{\partial }y}}\left(K_{\text{e}}{\displaystyle \frac{\mathrm{\partial }{T}_{\text{e}}}{\mathrm{\partial }y}}\right)\\ & -G\left(T_{\text{e}}-T_{\text{l}}\right)+I\left(x,y,t\right)\alpha \exp \left(-\alpha y\right),\end{array}

(2)C_{\text{l}}{\displaystyle \frac{\mathrm{\partial }{T}_{\text{l}}}{\mathrm{\partial }t}}={\displaystyle \frac{\mathrm{\partial }}{\mathrm{\partial }x}}\left(K_{\text{l}}{\displaystyle \frac{\mathrm{\partial }{T}_{\text{l}}}{\mathrm{\partial }x}}\right)+{\displaystyle \frac{\mathrm{\partial }}{\mathrm{\partial }y}}\left(K_{\text{l}}{\displaystyle \frac{\mathrm{\partial }{T}_{\text{l}}}{\mathrm{\partial }y}}\right)+G\left(T_{\text{e}}-T_{\text{l}}\right),

where C_{\text{e}} and C_{\text{l}} are the heat capacities of the electron and lattice subsystems, respectively; T_{\text{e}} and T_{\text{l}} are the electron and lattice temperatures, respectively; K_{\text{e}} and K_{\text{l}} are the thermal conductivities of the electron and lattice subsystems, respectively. The term G\left(T_{\text{e}}-T_{\text{l}}\right) represents electron–lattice coupling, where G is the electron–phonon coupling coefficient. \alpha denotes the absorption coefficient, I\left(x,y,t\right)\alpha \exp \left(-\alpha y\right) represents the laser energy absorbed by the material, as described by the Beer–Lambert law. Here, the x-direction corresponds to the laser scanning direction on the material surface, while the y-direction represents the depth direction along the laser propagation axis.

3.2 Moving multi-pulse laser

The laser input term I is used to describe the spatiotemporal intensity distribution of the incident laser and can be expressed as follows:

(3)I(x,y,t)=(1-R){\displaystyle \frac{F}{\tau }}A[I_{\text{space}}(x)][I_{\text{time}}(t)],

where R is the laser reflectivity of the material, F is the laser fluence, \tau is the laser pulse duration, and A is the laser absorption coefficient of the material. I_{\text{space}}\left(x\right) and I_{\text{time}}\left(t\right) represent the Gaussian spatial and temporal distributions of the incident laser, respectively.

To account for laser motion across the material surface, some studies incorporate focal point movement into the propagation equation [26], describing the spatial distribution of successive pulses. As ablation progresses, the evolving microhole morphology alters the laser–material interaction boundary conditions. While some works approximate multi-pulse ablation as a superposition of single-pulse events [27], interactions between successive pulses remain insufficiently captured.

The conventional Gaussian pulse model is extended to account for the focal motion along the processing direction with velocity v and the pulse repetition frequency f_{\text{rep}}. The laser incidence is modeled using Dirichlet boundary conditions, and the spatiotemporal intensity distribution of the pulsed laser can be expressed as:

(4)I_{\text{space}}\left(x\right)\text{=exp}\left(-2{\displaystyle \frac{{(x-vt)}^2}{r_0^2}}\right),

(5)I_{\text{time}}\left(t\right)\text{=exp}\left(\text{4ln2}\left({\displaystyle \frac{{\left(t-N/f_{\text{rep}}\right)}^2}{{\tau }^2}}\right)\right),

where r_0 is the laser spot radius, N is the number of laser pulses, and \alpha is the material absorption coefficient. A represents the effective surface absorptivity after accounting for reflection losses. Within the high-repetition-rate picosecond laser processing conditions investigated in this work, the optical properties of the glass are not expected to vary significantly. Therefore, both A and \alpha were treated as constant parameters in the present model.

3.3 Material removal

The temperature field obtained from the TTM can be coupled with a material removal method to predict post-ablation microhole morphology. Some studies define the ablation region using the isothermal surface at the vaporization temperature [28], neglecting material removal and often causing overheating. Many works also assume full thermal recovery between pulses [29]. However, at high repetition frequency, heat accumulation [30] and the laser incubation effect [31,32] markedly influence energy absorption and material response.

The laser incubation effect refers to the gradual accumulation of structural defects within the material and changes in its electronic absorption properties induced by repeated laser irradiation, which consequently reduces the material’s ablation threshold. Based on this mechanism, a deformable geometry module was incorporated into the model to simulate material removal. The latent heat of vaporization during material removal was also considered in the temperature field calculation. Moreover, due to the laser incubation effect, the energy absorption capability of the material under laser pulses is enhanced, making material removal more efficient under the same incident laser energy. Although transient melting may occur during laser irradiation, its characteristic timescale is extremely short, and heat transfer is predominantly governed by thermal conduction. In addition, the high viscosity of molten glass strongly restricts fluid motion; therefore, the influence of convective effects can be reasonably neglected under the present processing conditions. During material removal, the ablation velocity v_{\text{a}} is introduced to describe the mesh movement velocity at the material surface and is expressed as follows:

(6)v_{\text{a}}={\displaystyle \frac{Q_{\text{a}}}{\rho H_{\text{evap}}}}\times {\displaystyle \frac{F_{\text{th}}(1)}{F_{\text{th}}\left(N\right)}},

where \rho is the material density, H_{\text{evap}} is the latent heat of evaporation, and Q_{\text{a}} is the energy absorbed during the ablation process. F_{\text{th}}\left(1\right) and F_{\text{th}}\left(N\right) are the ablation thresholds corresponding to a single pulse and N pulses, respectively. The terms Q_{\text{a}} and F_{\text{th}}\left(N\right) can be expressed as follows:

(7)Q_{\text{a}}=h_{\text{a}}\left(T_{\text{l}}-T_{\text{evap}}\right),

(8)F_{\text{th}}\left(N\right)=F_{\text{th}}\left(\mathrm{\infty }\right)+\left[F_{\text{th}}\left(1\right)-F_{\text{th}}\left(\mathrm{\infty }\right)\right]\exp \left[-k(N-1)\right],

where T_{\text{evap}} is the evaporation temperature, and h_{\text{a}}\left(T\right) is the heat transfer coefficient defined in the form of a ramp function. Q_{\text{a}}>0 only when the lattice temperature T_{\text{l}}>T_{\text{evap}}. k is the incubation factor. The parameters F_{\text{th}}\left(1\right) and F_{\text{th}}\left(\mathrm{\infty }\right) are determined by measuring the minimum laser fluence required to generate ablation pits on the surface of the glass material under single-pulse irradiation and effectively infinite-pulse irradiation, respectively, at different energy levels. In this work, the experimentally obtained values are F_{\text{th}}\left(1\right)=15.6 J/cm² and F_{\text{th}}\left(\mathrm{\infty }\right)=3.85 J/cm². In addition, F_{\text{th}}\left(10\right)=5.9 J/cm² is obtained under a 10-pulse irradiation condition and is used as an intermediate constraint. Based on the experimental data of F_{\text{th}}\left(1\right), F_{\text{th}}\left(10\right) and F_{\text{th}}\left(\mathrm{\infty }\right), nonlinear fitting is performed according to Eq. (8) to extract the incubation factor k.

The laser ablation process is schematically illustrated in Fig. 2a, and the moving multi-pulse TTM coupled with material removal is illustrated in Fig. 2b. Successive laser pulses induce transient evolution and accumulation of electron–lattice temperatures, which drive material removal. The laser incubation effect lowers the ablation threshold, enhancing material removal for the same pulse energy. Notably, energy deposition and material removal occur simultaneously, and the evolving microhole profile continuously modifies the boundary conditions for subsequent pulses.

For the picosecond multi-pulse laser ablation model of glass, the numerical parameters used in the simulations are summarized in Table 1. All simulations are conducted in COMSOL Multiphysics.

4 Results and discussion

Experiments were performed using the laser rotary processing system, with a 1064 nm central wavelength, 8.2 ps pulse duration, linearly polarized, and a focused spot diameter of 16 μm defined at the 1/e² intensity level of the Gaussian beam profile. The three-dimensional morphology of the ablated microholes was measured using a VK-X150 laser microscope (KEYENCE, Japan). Iris glass (Corning Inc.) was used as the substrate material, with a chemical composition of SiO₂ 75.23 wt.%, Na₂O 11.79 wt.%, Al₂O₃ 8.43 wt.%, MgO 4.41 wt.%, and others 0.14 wt.%. Numerical simulations were conducted under identical laser parameters to enable direct comparison with experimental results.

4.1 Single-pulse ablation

Laser ablation of glass under different laser fluences was numerically simulated. Figure 3a shows the temporal evolution of the maximum electron and lattice temperatures on the glass surface at a laser fluence of 24 J/cm². Upon laser irradiation, the electron subsystem rapidly absorbs energy, reaching a peak temperature of approximately 11900 K at 23 ps. Energy is then transferred to the lattice through electron–lattice coupling. Because the electron relaxation time in glass is much shorter than the laser pulse duration [39], the lattice temperature rises nearly synchronously with the electron temperature and reaches the ablation threshold at 27 ps. Subsequently, SiO₂ undergoes phase transition and vaporization, and continuous heat removal by evaporation maintains the temperature near the ablation point during material removal. After ablation, thermal equilibrium is reached at 30 ns, followed by gradual cooling to room temperature. During ablation, the material removal rate greatly exceeds lattice thermal diffusion, indicating that the deposited laser energy is highly localized, which effectively suppresses macroscopic thermal damage. The simulated temperature field distributions immediately before and after ablation are shown in Fig. 3b.

Figure 3c shows the variation of microhole depth and diameter with laser fluence. The three-dimensional microhole morphology was measured using a microscope, and the corresponding central cross-sectional profiles from simulations and experiments are shown in Fig. 3d, with depth and diameter values presented in Figs. 3e and 3f. As the laser fluence increases from 16.8 J/cm² to 24 J/cm², the microhole depth rises from 0.13 μm to 0.37 μm and the diameter from 9.2 μm to 11.4 μm, exhibiting a clear linear trend. This behavior is attributed to the Gaussian laser beam profile, higher fluence enlarges the area exceeding the ablation threshold, producing deeper and wider microholes.

4.2 Multiple-pulse ablation

Multi-pulse laser ablation of glass was further investigated with a repetition frequency of 10 MHz, a maximum single-pulse laser fluence of 5.5 J/cm², and a scanning speed of 5 m/s, yielding a center-to-center pulse spacing of 0.5 μm. Figure 4a shows the temporal evolution of the maximum electron and lattice temperatures. After the first pulse, the electron temperature rapidly rises to 4896 K within 21 ps, while the lattice temperature reaches 2468 K at 70 ps, remaining below the ablation threshold and insufficient for material removal.

By the arrival of the second pulse, the electron and lattice temperatures have not fully returned to room temperature, decreasing instead to 1500 K, while the material’s ablation threshold is simultaneously reduced. Significant material removal occurs only after the fourth pulse. Figure 4b shows the evolution of microhole depth with pulse number, which rises rapidly at first and then gradually plateaus. This behavior reflects the laser incubation effect, where the material’s energy absorption increases with successive pulses, leading to progressively greater material removal per pulse.

Figure 4d shows the microhole morphology and temperature field evolution at different time points, while Fig. 4c depicts the left and right taper angles as a function of pulse number. Both angles increase rapidly at first and then gradually plateau. Notably, although the early growth rates are similar, the right taper angle eventually exceeds the left, causing the microhole to evolve from an initially symmetric shape to an asymmetric one.

Multi-pulse laser ablation of glass was further investigated under varying pulse numbers, fluences, and scanning speeds, with the corresponding simulation and experimental results shown in Fig. 5. Different laser parameters produced distinct microhole morphologies, and simulations closely matched the experimental trends. Although picosecond laser ablation can induce violent evaporation and phase explosion, causing partial molten material to resolidify as granular residues around the microholes, the developed numerical model reliably captures the evolution of microhole cross-sectional profiles, demonstrating strong predictive capability.

5 High-performance LGP

Microhole structures in LGPs disrupt total internal reflection, enabling the conversion of LED point or line sources into uniform planar illumination. Numerical simulations in Section 4.2 reveal that, during moving multi-pulse laser ablation, the microhole cross-sectional profile progressively evolves from a symmetric conical shape to an asymmetric morphology with a gentler slope on the left side. Such asymmetric microholes induces directional disparities in light scattering within the LGP, resulting in luminance non-uniformity and degraded optical performance. Based on the improved model proposed in this work, the critical transition point from symmetric to asymmetric microhole morphology can be accurately predicted, enabling the fabrication of relatively deep microholes while preserving a symmetric conical profile.

We investigated the critical pulse numbers for microhole morphology transition at two different processing speeds of 2.5 and 5 m/s, which were determined to be 37 and 24 pulses, respectively. Furthermore, a backlight module was established in LightTools to evaluate the practical optical performance of these four representative microhole morphologies. The backlight model mainly consists of the LGP, LED light sources, and a receiving screen. The LGP has dimensions of 330 mm × 190 mm × 2 mm, and the arrangement of microholes on its bottom surface can be characterized by the dot filling ratio f(x) [40], the dot distribution is shown in Fig. 6a:

(9)f\left(x\right)={\displaystyle \frac{a}{1-bx}},

where f(x) describes the spatial variation of the dot filling ratio along the light propagation direction inside the LGP. Here, the dot filling ratio represents the ratio of the total microhole area to the local unit area. The coefficients a and b are determined according to the optical design requirements for luminance uniformity.

Figure 6b shows a glass LGP fabricated using 37 laser pulses at a processing speed of 5 m/s. The measured luminance values at nine points are 11050, 11310, 11000, 9875, 10510, 9956, 9859, 10420, and 10400 cd/m², respectively. The corresponding luminance uniformity is 87.2%, which exceeds the international illumination standard of 80%. Figures 6c–6f present the morphologies of microholes fabricated at a scanning speed of 2.5 m/s with 50 and 37 pulses, and at 10 m/s with 50 and 24 pulses, together with the corresponding simulated irradiance distributions of the LGP. The luminance uniformity values calculated using the 9-point measurement method are 90.6%, 92.5%, 89.4%, and 93.6%, respectively. It can be observed that the symmetric conical microholes formed under 37 pulses and 24 pulses exhibit higher luminance uniformity compared to those produced with a larger number of pulses. Furthermore, the simulated irradiance maps indicate that symmetric conical holes yield a more uniform overall brightness distribution, whereas asymmetric microholes tend to produce a stronger intensity concentration on the right side of the LGP. Based on the proposed theoretical model, the processing parameters of the rotary laser system can be effectively optimized to achieve symmetric conical microhole geometries while maintaining high processing efficiency. These results demonstrate that the improved model provides effective guidance for optimizing laser processing parameters in LGP fabrication.

6 Conclusion

This study systematically investigates multi-pulse picosecond laser ablation of microholes in glass LGPs through numerical modeling, experimental validation, and optical performance analysis. To overcome the limitations of the conventional TTM in capturing material removal and microhole morphology evolution under high repetition frequency multi-pulse conditions, an improved TTM incorporating the laser incubation effect is proposed. This approach enables dynamic prediction of temperature field evolution, material removal, and microhole cross-sectional profiles, accurately forecasting depth, diameter, and shape. In LGP fabrication, adjusting laser parameters enables the creation of depth-controllable, symmetric conical microholes, which enhances optical performance. The developed multi-pulse ablation model and associated process strategies provide a robust theoretical foundation for high-precision microhole fabrication in LGPs, demonstrating significant engineering potential.

References

[1] Min , I. , Lee , S. , Lee , S. , Kim , J. , Yoon , K. : An experimental study of yellow shift in injection-molded light guide plate. Korea-Australia Rheol. J 28(3), 187–196(2016)

[2] Quesada , M. , Senaratne , W. , Li , S. , Sullivan , A. : All-glass micro-groove light guide plate by mask and etch. Opt. Mater. Express 11(2), 497–508(2021)

[3] Hof , L.A. , Abou Ziki, J. : Micro-hole drilling on glass substrates—a review. Micromachines (Basel) 8(2), 53(2017)

[4] Mamedov , A. : Machining of brittle materials: micro milling of glass. J. Mech. Sci. Technol 35(9), 4143–4148(2021)

[5] Jahan , M.P. , Perveen , A. , Rumsey , A.M. : A review on the conventional, non-conventional, and hybrid micromachining of glass. Mach. Sci. Technol 23(2), 264–338(2019)

[6] Ahsan , M.S. , Sohn , I.B. , Choi , H.K. : Gorilla glass cutting using femtosecond laser pulse filaments. Appl. Sci. (Basel) 14(1), 312(2024)

[7] Zhang , J. , Cheng , W. , Wang , J. , Ku , D. , Huang , W. , Li , J. : Numerical simulation and experimental investigation of laser pulse duration effects on Ni/SiC ohmic contacts during ultraviolet laser annealing. Opt. Laser Technol 192, 113499(2025)

[8] Wang , Z. , Wang , Y. , He , H. , Chen , F. , Shi , J. , Peng , Y. , Zhang , T. , Zhu , R. : Nanosecond laser irradiation assisted chemical mechanical polishing (CMP) process for promoting material removal of single crystal 4H–SiC. Ceram. Int. 50(19 19, Part A), 34702–34709(2024)

[9] Zhang , T. , Lei , P. , Huang , Y. , Rong , Y. : Opto-mechanical error analysis and compensation method for multi-axis laser galvanometer scanning systems. Measurement 244, 116508(2025)

[10] Balage , P. , Lopez , J. , Bonamis , G. , Hönninger , C. , Manek-Hönninger , I. : Crack-free high-aspect ratio holes in glasses by top–down percussion drilling with infrared femtosecond laser GHz-bursts. Int. J. Extreme Manuf 5(1), 015002(2023)

[11] Xu , S. , Yao , C. , Dou , H. , Liao , W. , Li , X. , Ding , R. , Zhang , L. , Liu , H. , Yuan , X. , Zu , X. : An investigation on 800nm femtosecond laser ablation of K9 glass in air and vacuum. Appl. Surf. Sci 406, 91–98(2017)

[12] Teng , T. , Chang , T. , Tsai , H. : Optical characteristics on practical verification for pico-laser-engraved glass light guide plate with concave microstructures. Int. J. Adv. Manuf. Technol 118(9), 3375–3387(2022)

[13] Alexopoulou , V.E. , Markopoulos , A.P. : A critical assessment regarding two-temperature models: an investigation of the different forms of two-temperature models, the various ultrashort pulsed laser models and computational methods. Arch. Comput. Methods Eng 31(1), 93–123(2024)

[14] Chen , L. , Chen , Z. , Shimada , K. , Mizutani , M. , Kuriyagawa , T. : Electric field analysis coupled with the two-temperature model to elucidate the generation process of laser-induced periodic surface structure. J. Mater. Process. Technol 305, 117601(2022)

[15] Yang , H. , Shen , H. : Combined two-temperature method and coarse-grained molecular dynamic model in femtosecond laser ablation at large spatiotemporal scale. J. Manuf. Process 150, 191–202(2025)

[16] Liu , J. , Wu , M. , Sun , Z. , Zhang , Q. , Zhu , Y. , Fu , Y. : The picosecond laser ablation mechanism of monocrystalline silicon by coupling two-temperature model (TTM)-Molecular dynamic (MD). Appl. Surf. Sci 661, 160022(2024)

[17] Yang , D. , Zhang , M. , He , Z. , Liu , Y. , Li , L. : Ultrafast heat transfer and microstructural evolution of Inconel 718 alloy under femtosecond laser processing. Int. J. Heat Mass Transf 256, 128016(2026)

[18] Das , M. , Bhattacharya , C. : Sub-picosecond laser absorption and ablation in aluminum: role of collision frequency. J. Appl. Phys 138(17), 175901(2025)

[19] Li , T. , Yin , Z. , Chen , M. , Cheng , J. , Zhao , L. , Zhang , T. : Ablation profile prediction of hard brittle fused silica optics irradiated by single-pulse femtosecond laser. Appl. Surf. Sci 688, 162319(2025)

[20] He , K. , Ren , Y. , Dai , Z. , Zhang , J. , Tu , X. , Cheng , L. , Xin , Z. , Cai , L. , Ye , Y. : Theoretical and experimental study of ablation of fused silica by femtosecond laser bursts. Opt. Commun 537, 129440(2023)

[21] Zhu , H. , Zhang , Z. , Xu , J. , Ren , Y. , Zhu , Z. , Xu , K. , Wang , Z. , Wang , C. : A numerical study of picosecond laser micro-grooving of single crystalline germanium: mechanism discussion and process simulation. J. Manuf. Process 69, 351–367(2021)

[22] Zhu , H. , Zhang , Z. , Zhou , J. , Xu , K. , Zhao , D. , Tangwarodomnukun , V. : A computational study of heat transfer and material removal in picosecond laser micro-grooving of copper. Opt. Laser Technol 137, 106792(2021)

[23] Peng , L. , Li , M. , Wang , P. , Li , X. , Zhang , Y. , He , M. , Zhou , C. , Zhang , H. , Chen , S. : Numerical simulation and investigation of ultra-short pulse laser ablation on Ti6Al4V and stainless steel. AIP Adv 13(6), 065018(2023)

[24] Marks , M.R. , Cheong , K.Y. , Hassan , Z. : A review of laser ablation and dicing of Si wafers. Precis. Eng 73, 377–408(2022)

[25] Anisimov , S. , Kapeliovich , B. , Perel’man , T. : Electron emission from metal surfaces exposed to ultrashort laser pulses. Sov. Phys. JETP 39, 375–377(1974)

[26] Dong , Y. , Wu , Z. , You , Y. , Yin , C. , Qu , W. , Li , X. : Numerical simulation of multi-pulsed femtosecond laser ablation: effect of a moving laser focus. Opt. Mater. Express 9(11), 4194–4208(2019)

[27] Xu , Z. , Zhao , N. , Zhang , C. , Cai , S. , Wang , K. , Wang , K. , Li , J. , Zhang , Q. , Yan , X. , Zhu , K. : Accurate two-dimensional simulation model and experimental demonstration in ultraviolet picosecond laser scribing ablation. Opt. Express 32(14), 24041–24057(2024)

[28] Chen , C. , Zhang , F. , Zhang , Y. , Xiong , X. , Ju , B.F. , Cui , H. , Chen , Y.L. : Single-pulse femtosecond laser ablation of monocrystalline silicon: A modeling and experimental study. Appl. Surf. Sci 576, 151722(2022)

[29] Wang , X. , Huang , Y. , Li , C. , Xu , B. : Numerical simulation and experimental study on picosecond laser ablation of stainless steel. Opt. Laser Technol 127, 106150(2020)

[30] Tang , E. , Lin , X. , Han , Y. , Chen , C. : Experimental research on thermal-dynamic damage effect of K9 optical lens irradiated by femtosecond laser. Int. J. Appl. Glass Sci 11(2), 277–284(2020)

[31] Liu , H. , Lin , W. , Lin , Z. , Ji , L. , Hong , M. : Self-organized periodic microholes array formation on aluminum surface via femtosecond laser ablation induced incubation effect. Adv. Funct. Mater 29(42), 1903576(2019)

[32] Guinea , A. , Aginagalde , A. , Mendiguren , J. , Saenz de Argandoña, E. , Llavori , I. , Zabala , A. : Dimple prediction modelling in ultrashort laser processing: A benchmark study on ablation threshold determination methods and incubation models. Surf. Coat. Tech 497, 131712(2025)

[33] Chimier , B. , Utéza , O. , Sanner , N. , Sentis , M. , Itina , T. , Lassonde , P. , Légaré , F. , Vidal , F. , Kieffer , J.C. : Damage and ablation thresholds of fused-silica in femtosecond regime. Phys. Rev. B Condens. Matter Mater. Phys 84(9), 094104(2011)

[34] Kitamura , R. , Pilon , L. , Jonasz , M. : Optical constants of silica glass from extreme ultraviolet to far infrared at near room temperature. Appl. Opt 46(33), 8118–8133(2007)

[35] Imgrunt , J. , Chakanga , K. , von Maydell, K. , Teubner , U. : Femtosecond laser texturing of glass substrates for improved light in-coupling in thin-film photovoltaics. Appl. Phys., A Mater. Sci. Process 123(12), 776(2017)

[36] Vaghasiya , H. , Krause , S. , Miclea , P.T. : Thermal and non-thermal ablation mechanisms in crystalline silicon by femtosecond laser pulses: classical approach of the carrier density two temperature model. J. Phys. D Appl. Phys 55(17), 175109(2022)

[37] Elhadj , S. , Matthews , M. , Yang , S. , Cooke , D. , Stölken , J. , Feit , M. : Evaporation kinetics of CO₂ laser heated fused silica. J. Opt. Soc. Am 20, 1575–1587(2011)

[38] Xu , S. , Yao , C. , Dou , H. , Liao , W. , Li , X.y. , Ding , R. , Zhang , L. , Liu , H. , Yuan , X. , Zu , X. : An investigation on 800nm femtosecond laser ablation of K9 glass in air and vacuum. Appl. Surf. Sci 406, 91–98(2017)

[39] Bian , H.D. , Dai , Y. , Ye , J.Y. , Song , J. , Yan , X.N. , Ma , G.H. : Analysis of electron momentum relaxation time in fused silica using a tightly focused femtosecond laser pulse. Acta Physica Sinica 63(7), 074209(2014)

[40] Wang , J. , Sun , S. , Liu , Q. , Shao , J. , Zhang , F. , Zhang , Q. : Effects of laser processing parameters on glass light guide plate scattering dot performance. Opt. Laser Technol 115, 90–96(2019)

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