# Gorilla Glass Cutting Using Femtosecond Laser Pulse Filaments
## 4 Results and Discussion
### Characterization of Femtosecond Laser Filaments Fabrication Using a 100\(\times\) Objective Lens  
We also investigated the femtosecond laser pulse filaments in the Gorilla glass sample by means of a 100\(\times\) objective lens. We varied the laser energy from 25 \(\upmu\)J to 37 \(\upmu\)J and focused the femtosecond laser beam in different layers beneath the sample surface (50 \(\upmu\)m to 470 \(\upmu\)m). The femtosecond laser beam was scanned at a velocity of 10 mm/s and, consequently, the period of the filaments (i.e., micro-voids) was 10 \(\upmu\)m. The images of the filament arrays formed in different layers of the Gorilla glass at laser energy of 25 \(\upmu\)J are presented in Figure 6a-d. The filament length varied from 62 \(\upmu\)m to 123 \(\upmu\)m for \(f\) varying from 100 \(\upmu\)m to 400 \(\upmu\)m, respectively. The filament length showed an increasing trend with the increase in \(f\). We did not observe any filaments when the value of \(f\) was 50 \(\upmu\)m and 470 \(\upmu\)m.  
To increase the filament length, we increased the laser energy to 37 \(\upmu\)J. Figure 6e-j show the optical microscope images of the filament array, fabricated inside different layers of the Gorilla glasses at laser energy of 37 \(\upmu\)J. The filament length ranged between 45 \(\upmu\)m and 146 \(\upmu\)m when the \(f\) varied from 50 \(\upmu\)m to 470 \(\upmu\)m. Compared to the filament length formed under 25 \(\upmu\)J, the filament length was higher for 37 \(\upmu\)J in most of the cases. For both energies, no filaments were evident when the value of \(f\) was below 50 \(\upmu\)m and beyond 470 \(\upmu\)m. For the formation of filaments, the Kerr medium thickness should have a minimum value, which is dependent on the numerical aperture and magnification of the objective lens, and the type of Kerr medium. From the experimental results, we can infer that 50 \(\upmu\)m thick Kerr medium might not be enough for the formation of filaments in Gorilla glass using a 100\(\times\) objective lens (NA: 0.7) when the laser energy was equal to or below 37 \(\upmu\)J. In contrast, beyond \(f\) = 470 \(\upmu\)m, the laser energy was reduced down to a value which was lower than the critical energy suitable for self-focusing required to form filaments. These facts are also appropriate for the absence of filaments when the value of \(f\) was 50 \(\upmu\)m and 470 \(\upmu\)m at the laser energy of 25 \(\upmu\)J. Like the results obtained by 50\(\times\) objective lens, the filament position was different than the focus position in all cases for 100\(\times\) lens. When the laser energy was 25 \(\upmu\)J, the filament position was in the range between 153 \(\upmu\)m and 617 \(\upmu\)m for \(f\) varying from 100 \(\upmu\)m to  
Figure 5: Filament position and length under variable laser energy for 50\(\times\) objective lens. 400 \(\upmu\)m, respectively. On the contrary, when the laser energy was 37 \(\upmu\)J, the filament position varied between 82 \(\upmu\)m to 720 \(\upmu\)m for \(f\) varying from 50 \(\upmu\)m to 470 \(\upmu\)m, respectively. The filament position and length under variable laser energy and focus position for 100\(\times\) lens are summarized in Table 2. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Focus Position (\(f\))**} & \multicolumn{2}{c}{**Filament Position (\(P\))**} & \multicolumn{2}{c}{**Filament Length (\(L\))**} \\ \multicolumn{2}{c}{**(\(\upmu\)m)**} & \multicolumn{2}{c}{**(\(\upmu\)m)**} & \multicolumn{2}{c}{**(\(\upmu\)m)**} \\ \hline \(E\) = 25 \(\upmu\)J & \(E\) = 37 \(\upmu\)J & \(E\) = 25 \(\upmu\)J & \(E\) = 37 \(\upmu\)J & \(E\) = 25 \(\upmu\)J & \(E\) = 37 \(\upmu\)J \\ \hline
50 & 50 & No Filaments & 82 & No Filaments & 45 \(\pm\) 2 \\
100 & 100 & 153 & 154 & 62 \(\pm\) 4 & 66 \(\pm\) 3 \\
200 & 200 & 319 & 309 & 75 \(\pm\) 5 & 85 \(\pm\) 5 \\
300 & 300 & 471 & 460 & 95 \(\pm\) 5 & 105 \(\pm\) 5 \\
400 & 400 & 617 & 615 & 123 \(\pm\) 6 & 110 \(\pm\) 6 \\
470 & 470 & No Filaments & 720 & No Filaments & 146 \(\pm\) 7 \\ \hline \hline \end{tabular}
\end{table}