# Compact 15 mJ Fiber-Solid Hybrid Hundred-Picosecond Laser Source for Laser Ablation on Copper
## 3 Experimental Results and Discussion
### The Theoretical Simulation of Hundred-Picosecond Laser Ablation
The simulated ablation morphologies are shown in Figure 11. In the initial stage, the laser only melts the surface depth of the material, as shown in Figure 11a (t = 0.22 ns). As the irradiation time increases (Figure 11a,b), the material at the center of the focused spot begins to vaporize, and the vaporized splitting mixture is ejected from the surface. The material is gradually vaporized and removed accompanied by the ejection of splitting matter, resulting in the formation of a micropore. A micron-sized hole was formed when the irradiation time increased to 0.46 ns, as illustrated in Figure 11c. Subsequently, the ablation depth varied with increasing irradiation time, but not linearly (Figure 11d-h). The micropore was close to the final etched morphology when the irradiation time increased to 0.82 ns, as shown in Figure 11f. The final etched depth of copper was approximately 7.86 \(\upmu\)m. The simulationresults adequately demonstrate the rapid temperature change of the copper material under the action of the hundred-picosecond laser. This means that the etching process of the material was basically finished within a very short time after the action of the 228 ps pulse laser. It is evident that the etch formation time was longer than the pulse duration. The possible reason for this is the heat conduction losses of the material. In our theoretical simulations, the power density of the pulsed laser source was 72.8 \(\times\) 10\({}^{5}\) W\(\cdot\)cm\({}^{-2}\). When the power density of the incident light is below 10\({}^{6}\)-10\({}^{8}\) W\(\cdot\)cm\({}^{-2}\), most of the energy is needed to heat the whole material; thus, most of the energy will be lost in this process. In addition, the thermal conductivity of copper at 300 K is 4.01 W\(\cdot\)cm\({}^{-1.\circ}\) C\({}^{-1}\), which is higher than that of other metallic materials. This means that only a small portion of the energy is used to evaporate the copper [41]. Therefore, this etching process requires a longer irradiation time. Figure 10: Simulation results of the temperature field distribution at an irradiation time of 1 ns. Figure 9: Variation of electron and lattice temperatures in the time domain; the inset shows a local enlarged view. In the early stages of the micro-hole formation process, the ablation depth is usually increasing rapidly. However, the hole depth is not changed in the later stages (after \(\sim\)0.82 ns, as shown in Figure 11g-h). This can be explained by two factors. First, the focused high-peak-power-density laser beam is initially capable of removing large amounts of material. However, as the depth of ablation increases, the peak power density of the laser beam decreases due to the defocused beam, thus reducing the rate of material removal. Second, a large number of free electrons are generated due to multiphoton ionization and avalanche ionization effects under the hundred-picosecond laser irradiation, resulting in the formation of a dense plasma on the target surface. In general, the formed plasma can further absorb the energy of the incident laser via the inverse Bremsstrahlung (IB) effect, thereby reducing the energy of the laser beam delivered to the target [42]. To further corroborate the plasma generation under this hundred-picosecond laser irradiation, in accordance with the hydrodynamic theory, three first-order quasi-linear partial differential equations were solved separately using the finite element method [43; 44]. Accordingly, we obtained the two-dimensional spatial distribution of the free electron concentration within the 100 ps time range, as demonstrated in Figure 12. In Figure 12, the color legend on the right represents the relative intensity of the free electron concentration. The \(z\)-axis and the \(r\)-axis represent the distance perpendicular to the target surface and the distance from the laser beam axis, respectively.