Fig. 1. Distribution of vortex models with fractional topological charge γ when l0 changes. Every subplot has a peak at the nearest integer to γ. When γ=3.5 (half-integer), this results in two peaks of equal height at the two neighboring integers. The spread in the distribution is determined by the fractional value γ.

Fig. 2. Average mode probability Dl(r,z) of FoBG beam along the direction of the beam radius r for different values of Δl.

Fig. 3. Average probability densities Dl(r,z) of vortex modes for fractional FoBG beam along the direction of the beam radius r with different values of γ. (a) Δl=0, mode probability; (b) Δl=1, crosstalk probability.

Fig. 4. Average probability densities Dl(r,z) of vortex modes for fractional FoBG beam along the direction of the beam radius r with different values of α. (a) Δl=0, mode probability; (b) Δl=1, crosstalk probability.

Fig. 5. Average probability densities Dl(r,z) of vortex modes for fractional FoBG beam along the direction of the beam radius r with different values of Cn2. (a) Δl=0, mode probability; (b) Δl=1, crosstalk probability.

Fig. 6. Average probability densities Dl(r,z) of vortex modes for fractional FoBG beam along the direction of the beam radius r with different values of beam waist w0. (a) Δl=0, mode probability; (b) Δl=1, crosstalk probability.

Fig. 7. Normalized powers Lz(l) of fractional vortex modes for FoBG beam along the direction of the transmission distance z with different values of Δl.

Fig. 8. Normalized powers Lz(l) of fractional vortex modes for FoBG beam along coherence radius r with different values of beam waist w0. (a) Δl=0, signal normalized powers; (b) Δl=1, crosstalk normalized powers.