## 2 Experimental Methods
### Determination of Focus and Processing Parameters of Nanosecond Fiber Laser System for PCD Material
\begin{table}
\begin{tabular}{c c} \hline \hline
**Brand** & **IPG** \\ \hline Model & YLPN-1-4x200-30-M \\ Wavelength & 1064 nm \\ Average power & 30 W \\ Pulse width & 4,8,14,20,30,50,100,200 ns \\ Pulse repetition rate & 1.6 \(\sim\) 2000 kHz \\ Output beam diameter & 7 mm \\ Beam quality M\({}^{2}\) & 1.5 \\ Maximum peak power & 15 kW \\ Maximum pulse energy & 1 mJ \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Specifications of nanosecond fiber laser system. To obtain better laser cutting efficiency, this study first investigated the cutting depth of PCDs based on different operating parameters of the nanosecond fiber laser, such as the scan rate and number of processing passes. For measuring the cutting depth of PCDs, the laser cutting was proceeded over the workpiece edge, and a Nikon Eclipse ME600 optical microscope was used to investigate the edge surface. The processing parameters that yielded the best processing efficiency were selected and used in the subsequent experiments. The selected parameters are listed in Table 3. A slower scan rate was selected for the testing to reflect the physical properties of good thermal conductivity and higher reflectivity of the PCD bulk, and the other laser processing parameters and number of processing passes were fixed. The following tests were performed at the scan rates of 1, 3, 5, 7, and 9 mm/s. The laser machining parameters and scan rates were fixed, and the number of processing passes was set at 1, 3, 5, 7, and 9 passes per path in this study. The laser power can be divided into peak power and average power. The peak power is the highest power of each laser pulse. The average power is the total power output of the laser beam in a unit of time and is affected by the peak power, pulse repetition rate, and pulse width. Equations (3)-(5) express the relationships between them [25]. \[P_{a}=E_{p}\times f \tag{3}\]  
\[E_{p}=P_{p}\times\tau \tag{4}\]  
\[P_{a}=P_{p}\times\tau\times f \tag{5}\]  
where \(P_{a}\) is the average power (W), \(P_{p}\) is the peak power (W), \(E_{p}\) is the pulse energy (J),\(f\) is the pulse repetition rate (Hz), and \(\tau\) is the pulse width (s). The average power directly affects the results of material processing. The main reason is that the processing energy of the laser beam is proportional to the average power. Increasing the laser average power increases the laser output energy. In addition, the magnitude of laser energy, which is higher than the material ablation threshold, is increased. This also increases the amount of material that is removed. When the average power is fixed, the pulse width is inversely proportional to the peak power, and when the peak power is fixed, the pulse width is proportional to the average power. Therefore, processing the workpiece with different pulse widths under a fixed average power causes variation in the peak pulse power. In addition, the pulse repetition rate affects the pulse overlap rate during the processing. If the rate is very low, the cutting edge becomes very  
Figure 1: Schematic of pulse overlap at different laser scan rates and pulse repetition rates: (**a**) at a high scan rate or low pulse repetition rate, the pulse overlap area is small; (**b**) at a low scan rate or high pulse repetition rate, the pulse overlap area is significant. \begin{table}
\begin{tabular}{c c c c} \hline
**Fixed Parameter** & **Parameter Setting** & **Variable Parameter** & **Parameter Setting** \\ \hline Average power (W) & 25.5 & Number of passes per path & 1, 3, 5, 7, 9 \\ Pulse width (ns) & 200 & Scan rate (mm/s) & 1, 3, 5, 7, 9 \\ Pulse repetition rate (kHz) & 17 & & \\ \hline \end{tabular}
\end{table} 
Table 3: Operating parameters for testing the effects of number of passes per path and scan rate on the PCD kerf depth. rough, and the processing quality is affected. When the average power is fixed, processing the workpiece with different pulse repetition rates will cause variation in the peak power.