## 3 Results
### Effect of the Focused Spot's Energy\(-\)Flux Density on the Face of Material Removal  
For etching of the nano-crystalline diamond coatings, energy\(-\)flux densities of \(14.2\) J/cm\({}^{2}\), \(19.8\) J/cm\({}^{2}\), \(22.7\) J/cm\({}^{2}\), \(28.3\) J/cm\({}^{2}\), \(34.0\) J/cm\({}^{2}\), and \(42.5\) J/cm\({}^{2}\) were chosen when the laser repetition frequency was \(1\) kHz and the scanning speed was \(1\) mm/s. From Equation (3), the relationship between the focused spot energy\(-\)flux density and the laser output power can be calculated, and the results are shown in Table 2.  
Figure 8: Ablation widths and depths under different repetition rates: (**a**) widths and (**b**) depths. Figure 9: Material removal rates under different repetition rates. Figure 10 depicts the morphology of the white\(-\)light interferometer scan made possible by the femtosecond laser etching of diamond coatings with various energy\(-\)flux densities. Figure 11 displays the appropriate etches' widths and depths. As demonstrated in Figure 10, the area of the etched area grows as the energy\(-\)flux density rises, and the border between the etched area and the surrounding area becomes increasingly evident, exhibiting deeper and deeper ablation holes. Figure 11 displays the etching. With a rise in energy density, the etching's width and depth considerably increase. When the energy\(-\)flux density reaches 42.5 J/cm\({}^{2}\), the material's etching width and depth considerably increase. The material has an etching breadth and depth of 128.2 \(\upmu\)m and 4.32 \(\upmu\)m, respectively. These values are considerably higher than those of the other energy densities. The amount of material accumulating in the laser scanning path is minimal when the concentrated spot energy\(-\)flux density (14.2-22.7 J/cm\({}^{2}\)) is low. The material removal mechanism at this point is primarily a Coulomb explosion [42]; when the focused spot energy\(-\)flux density is low (14.2-22.7 J/cm\({}^{2}\)), the material accumulates less energy in the laser scanning path, resulting in a smaller volume of diamond reaching the ablation threshold per unit time and, therefore, a smaller etch width and depth. The electrostatic field on the coated surface becomes unstable as a result of femtosecond excitation, and a Coulomb explosion happens if the electric field strength is greater than the binding energy of the target atoms. Electron-hole pair excitation trajectories with a charge imbalance are also produced. The mass is only slightly reduced by the typical melting and vaporization of the etched area. As the energy\(-\)flux density rises, the laser power density rises, the etching intensity rises, and the etching depth and etching width rise significantly. The role of phase explosion and vaporization predominates at greater energy\(-\)flux densities [43]. The laser-irradiated region enters the phase diagram sub\(-\)stable region when the critical temperature is approached and the thermodynamic stability limit is met. The superheated liquid changes into a mixture of liquid and vapor and evaporates pretty quickly when the liquid temperature reaches a critical threshold. After evaporation removes a small amount of material, the phase explosion continues with thermal evaporation, leading to significant material removal and disruption of the nanoscale structure. \begin{table}
\begin{tabular}{c c c c c c c} \hline Power (mW) & 50 & 70 & 80 & 100 & 120 & 150 \\ \hline Energy\(-\)flux density (J\(\cdot\)cm\({}^{-2}\)) & 14.2 & 19.8 & 22.7 & 28.3 & 34.0 & 42.5 \\ \hline \end{tabular}
\end{table} 
Table 2: Laser output powers under different energy\(-\)flux densities of focusing spot. Figure 10: Cross\(-\)sectional coating ablation morphologies under different energy\(-\)flux densities of the focusing spot.