## 4 Results and Discussion  
First of all, by measuring the transmitted spectrum, we obtain the SC induced by the filamentation of 0-order LG and BG beams (i.e., \(l=0\)) at different locations in water, as shown in Figure 2. It should be noted that the intensity of the transmitted spectrum around 800 nm (central wavelength) is beyond the measuring range of the spectrometer and the dark red area indicates that the spectral intensity is saturated. In the paper, we mainly focus on the degree of spectral broadening, and thus we do not discuss the saturation of the spectral signal. To facilitate the discussion of the experimental results, we define the position where the front wall of the cuvette is 3 mm (35 mm) away from the axicon lens (focusing lens) as the 'zero position', i.e., D = 0 mm, as shown in Figure 3a,b. It can be clearly seen from Figure 2 that the variation of the SC induced by the filamentation of 0-order LG and BG beams in water with D shows different tendencies. As the filament formed by LG beams gradually moves toward the front wall of the cuvette, it could be seen that when D is between 0 mm and 35 mm, the degree of spectral broadening remains almost unchanged, and thus the transmitted spectrum exhibits a plateau, as shown in Figure 2a. As we further increase D, the degree of spectral broadening becomes smaller, and the transmitted spectrum becomes very weak at D = 40 mm, showing a 'dip'. As D is larger than 40 mm, the transmitted spectrum remains almost unchanged. In contrast, the SC generated by the filamentation of BG beams shows entirely different behaviors: as D increases, the degree of spectral broadening firstly becomes larger, reaches its maximum at a certain position and gradually becomes smaller, as shown in Figure 2b. Figure 1: Schematic diagram of the experimental setup to explore the SC induced by the filamentation of BG and LG beams at different locations in water. M1, M2: plane mirror, H: half-wave plate, G: Glan prism, SLM: spatial light modulator, A: axicon lens, the dashed rectangle indicates it can be replaced by a focusing (plano-convex) lens, C: cuvette filled with water, IS: integrating sphere. The black and blue lines are the optical fiber and data cable, respectively. Usually, Bessel beams are produced by an axicon lens whose focus is linear, resulting in a longer focal region (see Figure 3d), and it has non-diffraction property in the Bessel region; therefore, the filament generated by Bessel beams is longer than that generated by Gaussian beams with the same energy. In the process of changing the distance between the cuvette and the axicon lens, the length of the Bessel beam filament located in water firstly increases and then decreases, as schematically shown in Figure 4e-h. Consequently, the degree of spectral broadening induced by the BG beams firstly becomes larger, reaches its maximum at a certain position and becomes smaller gradually. In contrast, the filament generated by LG beams is relatively short, which is much shorter than the length of the cuvette. As we move the cuvette, the filament is almost located in water (see Figure 4a,b). Consequently, when D is between 0 mm and 35 mm, the SC changes little in both intensity and the degree of spectral broadening. As D is between 35 mm and 40 mm, part of the filament enters into the back wall of the cuvette, leading to the decrease in the length of filament in water, and thus the degree of spectral broadening becomes smaller. As D is larger than 40 mm, the focal region of LG beams moves out of the cuvette and enters the air (see Figure 4d). Since the critical power of self-focusing \(P_{\rm cr}\) in the air [40] is much higher than that in water [39], no filament is formed, and the spectrum is hardly broadened. Figure 3: Definition of the ‘zero position’ in the experiment (i.e., D = 0 mm) in the case of using the (**a**) focusing and (**b**) axicon lenses. Schematic diagram for Gaussian beam which passes the (**c**) focusing and (**d**) axicon lenses. The red areas in (**c**,**d**) denote the focal region.