Fig. 1. Schematic diagram of experimental setup

Fig. 2. Evolution of laser filamentation in fused silica when a tilted angle θ=0°. (a) m=4 and incident laser energy is 30 μJ; (b) m=6 and incident laser energy is 35 μJ; (c) m=8 and incident laser energy is 40 μJ

Fig. 3. Side fluorescence images of filamentation of different vortex laser beams in fused silica with a tilted angle θ=0°

Fig. 4. Cross sectional intensity distributions of vortex beam with topological charge m=4 after passing through focusing lenses with tilted angles of (a1), (a2) 17°; (b1), (b2) 20°; (c1), (c2) 23°. Beam propagates (a1)‒(c1) linearly in air with laser energy of 8 μJ and (a2)‒(c2) nonlinearly in fused silica with laser energies of 16, 21, and 36 μJ, respectively

Fig. 5. Cross sectional distributions of filamentation in fused silica of femtosecond vortex beams with different topological charges after passing through lens with a tilted angle θ=20°, where laser energies used are 30 μJ and 49 μJ, respectively. (a) Topological charge is 6; (b) topological charge is 8