## 3 Results and Discussion
### Self-Focusing in the Fluoride Crystals  
The critical energy was determined for a UV laser beam propagating in each of the four fluoride laser host materials. The propagating laser beam is the emission from the laser material rather than the excitation beam used to achieve lasing. The laser beam is assumed to have a Gaussian shape, a pulse width of 100 fs, and a wavelength tuning range from 200 nm to 400 nm. Figure 3 shows that the critical energy of each laser host material is higher when the wavelength of the laser beam is longer. As mentioned earlier, self-focusing \begin{table}
\begin{tabular}{c c c} \hline \hline
**Material** & \
\begin{tabular}{c} **Wavelength** \\ **(nm)** \\ \end{tabular} &
\begin{tabular}{c} **Nonlinear Refractive Index** \\ \(\times\)**10\({}^{-7}\) (cm\({}^{2}\)/W)** \\ \end{tabular} \\ \hline LiCAF & 290 & 8.02 \\ LiSAF & 290 & 9.41 \\ LaF & 290 & 34.42 \\ YLF & 308 & 11.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Peak laser emission wavelength and nonlinear refractive index (\(n_{2}\)) of the fluoride laser materials at their respective peak laser emission wavelength. Figure 2: Nonlinear refractive index (\(n_{2}\)) of the fluoride laser materials. will occur when the energy of the laser beam is greater than the critical energy. Table 5 summarizes the critical energy of the laser host materials at their respective peak laser emission wavelengths. Looking at the respective peak laser emission wavelengths of each of the laser host materials, LiCAF has the highest critical energy. This means that LiCAF would be able to tolerate higher laser beam energies before self-focusing sets in. The trend in critical energy for the four laser host materials is consistent with the trend observed for \(n_{2}\) where LiCAF also exhibited the smallest \(n_{2}\). It follows that, among the four fluoride laser host materials studied here, LiCAF has the best potential for high-power UV laser generation. On the other hand, LaF could be limited by self-focusing when higher UV laser output energies are elicited either through direct lasing or amplification. Figure 4 shows the variation in the nonlinear refractive index \(n_{2}\) for a Gaussian laser pulse with 1 mJ energy, 100 fs pulse duration, and 0.5 mm beam radius. The calculations were performed at the peak laser emission wavelength of each of the laser materials. For a Gaussian laser beam, the intensity distribution is not uniform, and therefore \(n_{2}\) also varies according to the beam's Gaussian intensity distribution. It follows that the value of \(n_{2}\) is highest at the center of the beam, and it tapers off at the edge of the beam. More interestingly, the variation in \(n_{2}\) is smallest for LiCAF, which means that nonlinear effects would be more homogeneous throughout the material's volume. Consequently, higher excitation energies can be used to elicit higher laser emission energies. Furthermore, laser emission would be more uniformly distributed throughout the laser material's volume as the laser threshold is achieved almost uniformly. For LaF, on the other hand, self-focusing  
Figure 3: Critical energy, which defines the energy limit before self-focusing occurs, as a function of wavelength. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Material** & **Wavelength (nm)** & **Critical Energy \(\times\)10\({}^{-7}\) (f)** \\ \hline LiCAF & 290 & 1.20 \\ LiSAF & 290 & 1.01 \\ LaF & 290 & 0.24 \\ YLF & 308 & 0.93 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Peak laser emission wavelength and critical energy of the fluoride laser materials at their respective peak laser emission wavelength. could set in at areas around the peak of the Gaussian beam leading to very high intensities that could potentially damage the laser material, while the areas surrounding the peak would have lower intensities. Consequently, the energy distribution will be less uniform.