## 2 Material, Experiment, and Measurement  
Single-mode Quasi-CW Ytterbium Fiber Laser (IPG YLM-200/2000-QCW) was used with CW mode. The \(M^{2}\) value was 1.05. The wavelength was 1070 nm and the maximum average output power was 250 W. The vertical distance from the F-theta lens to the surface was set to be 100 mm. The laser spot size at focus was 23 \(\upmu\)m. The width of the cathode sample was 30 mm, and the cutting distance was 20 mm horizontally so that even though the laser cut sample was completely separated, the rest of the sample remains attached. Both ends of the specimen were held by clamps so that the space was formed between the specimen and the table to prevent any possible effects such as heat conduction and material attachment from the table, as shown in Figure 1. The laser output power used for the experiments were varied from 50 W to 250 W at intervals of 50 W and the laser scanning speed was varied from 500 mm/s to 5000 mm/s at an interval of 500 mm/s. These are shown in Table 1. The volume energy depending on the output power and scanning speed is shown in Figure 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline \# & **Power (W)** & **Speed (mm/s)** & **Volume Energy (J/m\({}^{3}\))** \\ \hline \multirow{2}{*}{50, 100, 150, 200, 250} & 500, 1000, 1500, 2000, 2500, 3000, 3500, 4000, & 4.348 \(\times\) 10\({}^{5}\)–2.174 \(\times\) 10\({}^{7}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Laser power, speed, and volume energy used for the experiments. Figure 1: Cathode sample and Experimental set-up. Compressed and uncompressed cathode samples were used. The compressed cathode was coated with a 76 \(\upmu\)m-thick active electrode material on a 20 \(\upmu\)m-thick current collector and then was compressed from 76 \(\upmu\)m to 56 \(\upmu\)m, as shown in Figure 1. The uncompressed sample was coated with a 70 \(\upmu\)m-thick active electrode material on a 20 \(\upmu\)m-thick current collector. The detailed information of the materials was summarized in Table 2. It should be noted that the total thickness of this cathode was relatively thin for high power applications. The active electrode material consists of 90% of LiFePO4, 5% SuperC65 (Conducting agent), and 5% of polyvinylidene fluoride (binder). The current collector is aluminum. The working electrode was formulated by the mixing of active materials, conductive carbon materials and PVDF binder with a controlled amount of NMP solvent. After slurry coating on Al current collector, the electrode was dried at 120 \({}^{\circ}\)C in a convection oven for 6h and then dried at 90 \({}^{\circ}\)C in a vacuum oven for 24 h before use. A Scanning Electron Microscope (SEM, VEGA3, TESCAN, Brno, Czech Republic) was utilized to observe the cut surface and cross-section of the laser cut sample. After the laser cutting, the sample is cut into 2 \(\times\) 2 cm size for SEM analysis. Energy-dispersive X-ray spectroscopy (EDX) analysis was conducted to measure the composition variation. Furthermore, the absorption rates were measured by UV-VIS spectroscopy (SolidSpec-3700, Shimadzu, Kyoto, Japan). The kerf, top, and melting widths were measured based on the previously published papers [12; 13; 14]. The energy used in cutting to melt and evaporate the cathode can be derived from the measured widths and shown in Figure 2. Since the melting width rarely occurred, the melting width is set equal to the kerf width. The volume removed by melting and evaporation are expressed by  
\[\mathbf{V_{melt_{AE}}}=\mathbf{V_{evap_{AE}}}=\mathbf{l_{g}d_{AE}W_{top}} \tag{1}\]  
\[\mathbf{V_{melt_{CC}}}=\mathbf{V_{evap_{CC}}}=\mathbf{l_{g}d_{CC}W_{kref}} \tag{2}\]  
where \(d_{AE}\) is the thickness of an active electrode (AE) material, and \(d_{CC}\) is the thickness of a current collector (CC). The energy required to evaporate the given volume is expressed by  
\[