Fig. 1. Iso-intensity of simulated partially coherent tilted vortices in (a) x-t view and (b) y-t view. The coherence time, τ_c = 186 fs, is overlaid in one section to highlight the typical length of the intensity fluctuations and vortices. (c) A small region of the same realization shown to highlight the random vortex tilt path.

Fig. 2. (a) Magnitude of mean OAM vector and mean OAM vector components for decreasing coherence; (b) x-component OAM histogram for ${\sigma }_{\omega }=\frac{\pi }{8}$ and σ_ω = π; (c) mean OAM angles; and (d) variance of OAM angles for decreasing coherence.

Fig. 3. |L(t₀)|, θ(t₀) and ϕ(t₀) plotted together for each time instance for different levels of randomness. OAM magnitude, polar angle, and azimuthal angle randomness increase with source randomness as shown by high-density areas broadening.

Fig. 4. (a), (b) Simulated interference pattern at two reference delays of 30 µm separation; (c) 3D trace of the singularity.

Fig. 5. (a) Experimental setup. BS, beam splitter; CL, cylindrical lenses with focal length f₁ = 100 mm; SLM, spatial light modulator; M, mirror; SL, spherical lens with focal length f = 300 mm; distances z₁ = 200 mm and z₂ = 200 mm. (b) Spectrum of ASE light source coming from Yb-fiber ring cavity; (c) phase map of the pulse shaper SLM, which applies an x−ω spatiotemporal spiral phase; (d) same phase map, including random phase expected with ASE.

Fig. 6. (a), (b) Experimental interference patterns at two reference delays showing moving singularity indicated by arrows. The coloring minimum value is limited to 0.3 of the normalized intensity to improve the fringe contrast. Insets show enlarged areas containing the singularity interference fork. (c) Plot of vortex singularity points position versus delay.