## 2 Materials and Methods  
The experimental set-up is schematically shown in Figure 1. The laser used in the following experiments was a neodymium-doped yttrium aluminium garnet (Nd:YAG) laser pumped by a laser diode, LR-SHG (low-repetition second harmonic generation), from MegaOpto Co., Ltd (Saitama, Japan). It has a maximum power output of \(>\)1 W, a wavelength of 532 nm and a spot diameter of 85 \(\upmu\)m. The laser output energy has an approximate Gaussian distribution. The laser beam was controlled using a galvanometer scanner system with a Miramo controller GMP-507005 made by Y-E Data Inc. (Saitama, Japan). Laser motion programs were created using GmcLib.DLL 2.0 software provided by Y-E Data Inc., and FFFTP (file transfer protocol) software developed by Sota & cooperators (Izumo, Japan) was used to download these programs to the galvanometer scanner system. The laser beam was focused onto a workpiece stage using an f-theta lens. The diamond sample was placed on a base with an opening so that the lower surface of the diamond was not in contact with the stage surface. The laser parameters used are shown in Table 1.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Wavelength (nm) & 532 \\ Pulse width (ns) & 15.6 \\ Repetition frequency (kHz) & 1 \\ Power (mW) & 450, 515, 560, 590, 625 \\ Fluence on upper surface (J/cm\({}^{2}\)) & 7.8, 9.1, 9.9, 10.3, 11.0 \\ Scanning speed (mm/s) & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Experimental laser parameters.  
The CVD diamond was a rectangular sample with dimensions of 4 \(\times\) 3.5 \(\times\) 1.10 \(\pm\) 0.02 mm. The HPHT diamond was also a rectangle, sized 3 \(\times\) 3 \(\times\) 1.10 \(\pm\) 0.02 mm. Both had flat, polished surfaces and the irradiated surface was the (100) Miller surface (all the other faces also had an equivalent crystal orientation). The surface roughness of these samples was Ra = 1.8 \(\pm\) 0.6 nm for the CVD sample and Ra = 0.4 \(\pm\) 0.1 nm for the HPHT sample.  
As the transparency of these materials is very important for laser processing, we measured the transmission rate of each sample. Measurements were performed at four different locations on the sample to ensure that they were similar and so that local disparities would not affect the results. The transmission rate was obtained by measuring the raw laser power by a 3-sigma single-channel laser power meter produced by Coherent Inc. (Santa Clara, CA, USA) followed by another measurement with the diamond sample above the power meter, then taking the ratio of the two.  
To detect the laser-induced phase transformation of diamond, Raman spectroscopy of the samples before/after laser processing was performed by a laser micro-Raman spectroscopy NRS-3100 (JASCO Corporation, Tokyo, Japan). To remove the laser-induced debris, the samples were then cleaned using a chemical cleaning process. The samples were placed in a solution of nitric, sulphuric and perchloric acid (in a volume ratio of roughly 1:5:3) and heated to \(\sim\)200 \({}^{\circ}\)C. After cleaning, they were observed using the VHX-1000 optical digital microscope (Osaka, Japan) made by KEYENCE, the Inspect S50 Scanning Electron Microscope (SEM) (Hillsboro, OR, USA) made by FEI Company for higher magnifications, and the MP-3 laser probe made by Mitaka Kohki Co., Ltd. (Mitaka, Japan) to measure groove depth.