# 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  
Here, to test this hundred-picosecond laser source, we carried out a theoretical numerical simulation of picosecond single-pulse laser ablation of metallic copper material. First, a geometric model was created using Comsol software, which was simplified to a 2D axisymmetric form for computational processing. Then, the mapping mesh was divided into appropriate densities to improve the computational accuracy and reduce the computational time. Finally, the simulation of the physical field was completed by solving the partial differential equations. For the interaction of picosecond pulsed laser with metallic copper, the ablation mechanism was a nonthermal equilibrium ablation process. To characterize this nonequilibrium process, the time for the electrons to interact with the lattice and, thus, complete the electron-lattice energy transfer could not be neglected. This means that the time required for the electron-lattice relaxation process needed to be taken into account. In this case, the electron temperature (\(T_{e}\)) and lattice temperature (\(T_{l}\)) were not equal since the pulse duration was on the same timescale as the relaxation time [39]. From this, we established a two-temperature diffusion model to describe the one-dimensional heat transfer in the electron system and the lattice system. We set the initial conditions (\(T_{e}=T_{l}=300\) K) and boundary conditions. The two-temperature equations were solved using the finite element method, thereby obtaining the variation law of the electron and lattice temperatures in the time domain. Figure 9 plots the temporal evolution of electron and lattice temperatures at the front surface of metallic copper heated by the 228 ps laser pulse with a pulse energy of 14.58 mJ. In spite of the relatively flat intensity distribution at the center of the laser beam from this hundred-picosecond laser source, it still exhibited Gaussian beam characteristics when converging on the surface of a metallic copper target via a lens with a focal length of 100 mm. The spatial profile of the Gaussian beam output from this laser source was measured using a beam quality analyzer, and the focal spot diameter of \(\sim\)35.72 \(\upmu\)m was determined by the transformation relationship of the Gaussian beam waist. The inset of Figure 9 illustrates a local enlarged view of the electron and lattice temporal evolution. As depicted in the inset, the electron temperature increased sharply to \(\sim\)11,499 K under this hundred-picosecond laser irradiation. Simultaneously, the lattice temperature also increased during the electron-lattice energy transfer. At the end of a laser pulse, the electron temperature stopped growing. Moreover, the energy transfer induced a decrease in the electron temperature and a continued increase in the lattice temperature. Correspondingly, the maximum temperature of the lattice reached \(\sim\)11,496 K (\(t=0.78\) ns). Eventually, the temperatures of the electron and the lattice reached equilibrium. Figure 10 displays the final temperature field distribution of the copper target, thus clearly observing that the temperature was higher at the center of the laser focus and lower near the laser edge. The main reason for this was the Gaussian distribution of the picosecond laser power density in the spatial domain. The color legends on the left and right represent the temperatures of the isopleths and isosurfaces, respectively. It can be seen that the temperature at the laser focus was up to \(\sim\)1.15 \(\times\) 10\({}^{4}\) K when the laser irradiation time was 1 ns. Moreover, the temperature of the isopleths was accompanied by a significant variation. The simulation results prove that the ablation temperature was much higher than the evaporation temperature of copper, 2840 K [40]. Therefore, the homemade millijoule-level hundred-picosecond laser is able to meet the material removal requirements for copper.