# Gorilla Glass Cutting Using Femtosecond Laser Pulse Filaments
## 4 Results and Discussion
### Characterization of Femtosecond Laser Filaments Fabrication Using a 50\(\times\) Objective Lens  
To characterize femtosecond laser pulse filaments in Gorilla glass using a 50\(\times\) objective lens, the focus position of the laser beam from the top surface of the glass was varied from 100 um to 600 um. Filament-assisted micro-voids were fabricated with variable laser energy at a scanning speed of 10 mm/s: 25 uJ and 50 uJ. The period of the micro-voids was 10 um. The optical microscope images of the filament array, formed inside different layers of the Gorilla glass under laser energy of 25 uJ, are illustrated in Figure 4a-f. When the value of \(f\) was 100 um to 600 um, the filament length ranged from 43 um to 58 um. The variation of filament length with the variation in \(f\) was too small.  
Figure 4g-l show the optical microscope images of the filament array, fabricated in different layers of the Gorilla glass under 50 uJ laser energy. The filament length ranged from 50 um to 65 um for the \(f\) varying from 100 um to 600 um. The variation in filament length with the change in\(f\) was also small. However, overall the filament length was higher for the laser energy of 50 uJ as compared to 25 uJ. In both cases, we did not detect any filaments when the \(f\) was lower than 100 um and higher than 600 um. For \(f\) = 100 um, the  
glass thickness might not be enough to prolong the focal point required for the formation of filaments. On the contrary, when \(f=600\) um, the laser energy was sufficiently attenuated to cross the critical energy required for self-focusing to form filaments.  
As expected, the filament position (i.e., starting point of filaments from the top surface of the sample glass) was different than the value of \(f\) in all cases. For 25 um laser energy, the filament position ranged between 138 um and 897 um when the value of \(f\) varied from 100 um to 600 um, respectively. Similarly, for the laser energy of 50 uJ, the filament position varied from 150 um to 910 um when the value of \(f\) was 100 um to 600 um, respectively. The self-focusing property of femtosecond lasers along with spherical aberrations play significant role in the change in the filament position from the focus position [40]. Table 1 summarizes the filament position and length for different laser irradiation conditions when 50\(\times\) objective lens has been used.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Focus Position (\(f\))**} & \multicolumn{2}{c}{**Filament Position (\(P\))**} & \multicolumn{2}{c}{**Filament Length (\(L\))**} \\ \cline{2-5}  & \multicolumn{2}{c}{**(\(\mu\)m)**} & \multicolumn{2}{c}{**(\(\mu\)m)**} \\ \cline{2-5}  & \(E\) = 25 uJ & \(E\) = 50 uJ & \(E\) = 25 uJ & \(E\) = 50 uJ \\ \hline
100 & 138 & 150 & \(43\pm 2\) & \(50\pm 3\) \\
200 & 280 & 300 & \(49\pm 2\) & \(52\pm 3\) \\
300 & 435 & 450 & \(52\pm 3\) & \(55\pm 3\) \\
400 & 588 & 600 & \(57\pm 3\) & \(62\pm 4\) \\
500 & 744 & 755 & \(56\pm 3\) & \(64\pm 4\) \\
600 & 897 & 910 & \(58\pm 4\) & \(65\pm 4\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Filament position and length under variable laser irradiation conditions for 50\(\times\) objective lens.  
Figure 4: Optical microscope images of the filament array fabricated inside different layers of the Gorilla glasses using 50\(\times\) objective lens under variable laser energies. (**a–f**) \(E\) = 25 uJ; (**g–f**) \(E\) = 50 uJ.  
Figure 5 plots the filament position and length with respect to focus position under 25 \(\upmu\)J and 50 \(\upmu\)J laser energies. Experimental results confirm a linear increase in the filament position relating to focal position of the laser beam. In contrast, a slight increase in the filament lengths was evident with an increase in the focal length.