Fig. 1. (a) Simulated intensity pattern and SoP distribution of the focused AV-HP-VF with m=2 and φ0=0, and 10% amplitude random noise. (b) Simulated filamentation pattern of the AV-HP-VF shown in (a) under the conditions of P=12PC, ζ=1.6, ε′=0.33, and ε′′=10−4. (c)–(e) Simulated on-axis accumulated phases for three filaments labeled H1, H2, and H3 under the same conditions as (b). (f) Simulated relative phases between H1 and H2 as well as H1 and H3. For comparison, the simulated on-axis phases of the perfect AV-HP-VF with m=2 and φ0=0 are given in (c)–(f).

Fig. 2. Simulated evolution of the peak intensity of filament with the propagation distance for AV-HP-VF with m=2 and φ0=0, under the conditions of ε′=0.33 and ε′′=10−4 (a) at different random noise levels of no noise, 5% noise, and 10% noise at P=12PC and (b) at different input powers of P=10PC, 11PC, and 12PC without random noise.

Fig. 3. Simulated collapsing evolution and multiple filamentation of the AV-HP-VFs by Eq. (3) under the conditions of ε′=0.33, ε′′=10−4, and P=12PC with 10% amplitude random noise. (a) AV-HP-VF with m=1 and φ0=0. (b) AV-HP-VF with m=2 and φ0=0.

Fig. 4. Measured six consecutive, 10-shot average CCD images of filamentation of AV-HP-VFs at 2.0 μJ pulse energy for two AV-HP-VFs with (a) m=1 and (b) m=2.