## 4 Results and Discussion
Figure 2: Variation of the SC induced by the filamentation of (**a**) LG and (**b**) BG beams with D in the case of \(l\) = 0. The incident pulse energy of LG and BG beams are 104 \(\upmu\)J and 188 \(\upmu\)J, respectively. In the process of moving the cuvette, both the focal regions of LG and BG beams pass through the cuvette wall; however, the spatial distribution of the transmitted spectrum only shows a 'dip' in the case of LG beams (at D = 40 mm). This is caused by the different spatial distribution of the laser intensity of the two beams. The focus region of LG beams is very small, which results in higher intensity of LG beams in the focal region. In contrast, due to the existence of the Bessel region, the focal region of BG beams is very long, resulting in a lower intensity of BG beams in the focal region, which is lower than the damage threshold of the cuvette wall. As a result, the laser pulse energy will not be absorbed by the cuvette wall when the focal region of BG beams covers the cuvette wall, and the transmitted spectrum is similar to that measured when the focal region is located in the air, as shown in Figure 2b. It should be noted that the thickness of the cuvette wall is 1 mm, which is comparable with the length of the LG beam filament in water. Since the focal length of the focusing lens is \(f\) = 75 mm, at D = 40 mm, the focal region of LG beams covers the front wall of the cuvette (see Figure 4c). The laser intensity of the focal region of LG beams is higher than the damage threshold of the cuvette wall, resulting in the ablation of the cuvette wall. As a result, part of the laser signal is reflected, and part of the laser energy is absorbed by the cuvette wall, resulting in a weak transmitted spectrum. Figure 2 show the SC induced by filamentation of LG and BG beams only in the case of \(l\) = 0. In the following part, we will study the SC produced by higher-order LG and BG beams (i.e., \(l\) > 0). Table 2 show the pulse energy and TC value of these vortex beams selected in our experiment. The laser pulse energy also affects SC generation. By changing the pulse energy (10, 52 and 104 uJ), we study the variation of the SC induced by filamentation of LG beams with D in the case of \(l\) = 0 and \(l\) = 2, as shown in Figure 5. It can be seen from Figure 5a,d that when the pulse energy is 10 uJ, the transmitted laser spectrum shows no obvious broadening, indicating that no filament is formed, for the SC generation is an obvious feature of femtosecond filamentation. It should be noted that due to the low pulse energy (10 uJ), the laser intensity in the focal region is relatively low, which is lower than the damage threshold of the cuvette wall, and thus little energy is absorbed or reflected by the cuvette wall. As a result, though the focal region of LG beams covers the cuvette wall at D = 40 mm, the transmitted spectrum changes little, which confirms the previous speculation of spectral 'dip'. As the pulse energy is 52 and 104 uJ, filaments can be formed \begin{table}
\begin{tabular}{c c c} \hline \hline
**Vortex Beam** & **Pulse Energy (μ)** & **TC Value** \\ \hline  & 10 & \(l\) = 0–5 \\ LG & 52 & \(l\) = 0–5 \\  & 104 & \(l\) = 0–5 \\ \hline BG & 188 & \(l\) = 0–5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the LG and BG beams used in our experiment. Figure 4: Spatial relationship between the focal region of (**a–d**) LG, (**e–h**) BG beams and cuvette. The red areas denote the focal region, and light blue rectangles denote the cuvette filled with water. by LG beams, and the transmitted spectrum shows obvious broadening. Due to the high laser intensity in the focal region, as the cuvette wall overlaps with the focal region, it is ablated, part of the laser energy is absorbed or reflected, and thus the spatial distribution of transmitted spectrum shows a 'dip', as shown by Figure 5b,c,e,f. Figure 6 show the variation of the SC generated by LG beams with D when the value of TC is 0, 1, 2, 3, 4 and 5.