Fig. 1. Flow branching as an intense laser propagates through an uneven plasma along the x direction. (a) Initial distribution of electron density, with contour plots (in blue) of the uneven plasma background. (b) Distribution of the laser intensity at t = 1095 fs as it propagates in the uneven plasma. (c) Corresponding distribution in a homogeneous plasma at the same average density as the uneven one, for comparison. The initial laser intensity is 10¹⁴ W/cm². (d) Autocorrelation function of the initial electron density distribution shown in (a). (e) Spatial evolution of the scintillation index Σ = (⟨I²⟩/⟨I⟩²) − 1 of a reference plane wave with identical interaction parameters propagating through the same plasma with randomly uneven (in red) and homogeneous (in blue) density distribution. The black dotted line in (b) and black arrow in (e) mark the first caustics, or branching point.

Fig. 2. Evolution of the laser light spectrum. (a) and (b) (k_x, k_y) spectrum of the laser field E_z at t = 1095 fs as it propagates in uneven and homogeneous plasmas, respectively. (c) Time Fourier transform of E_z in the uneven plasma. The black, red, and blue curves are recorded at x = 5, 15, and 150 µm, respectively.

Fig. 3. Nonlinear response of the background plasma medium. (a) Evolution of the potential strength v₀ for different laser intensities in the region 0 µm < x < 30 µm, −2 µm < y < 2 µm within the laser spot. (b) Characteristic time τ of plasma homogenization for different laser intensities. The black dotted line marks the pulse duration. The blue and red shadings in (a) and (b) mark the nonrelativistic and relativistic intensity regimes, respectively.

Fig. 4. Enhanced laser light branching by photoionization at a moderate laser intensity of 10¹⁶ W/cm². (a) and (b) Comparison of electron density (in units of n_c) and laser intensity (in W/cm²) at t = 1095 fs with and without photoionization. (c) Evolution of the local potential strength v₀(x) with photoionization included. (d) Strength Ẽz(ϕ) (see the text for definition) at t = 35.3 and 1095 fs with and without photoionization. The insets in (a) show the autocorrelation functions of the electron density, where the white bars are of length 5 µm. The red dashed lines in (b) show the calculated spread angle Θ of the laser branches.

Fig. 5. Suppression of laser light branching at a relativistic laser intensity of 10²⁰ W/cm². (a) Distribution of the electron density (in units of n_c) at t = 283 fs. (b) Enlargement of the region in the red dashed square in (a). The inset shows the autocorrelation functions of the electron density in this region, and the white bar is of length 5 µm. (c) Distribution of electron density at t = 1095 fs. (d) Distribution of laser intensity (in W/cm²) at t = 1095 fs. (e) Evolution of the local potential strength v₀(x). The red dashed lines in (d) mark the calculated spread angle Θ of the laser light.

Fig. 6. Intensity-dependent branching properties of intense laser light. (a) Spread angle Θ (in radians) of laser branches at t = 1095 fs for different initial laser intensities. The red and blue curves are obtained from simulations (solid curves in 2D, dotted curves in 3D) with uneven and homogeneous plasma backgrounds, respectively. (b) Distance from source to first caustics d₀ (in μm) for different laser intensities. The blue solid curve is obtained from simulations at the time at which the first caustics appear. The blue shading shows the evolution of d₀. The red dashed curve is the result from our quasilinear scaling.

Fig. 7. Three-dimensional branched flow pattern (in W/cm²) at t = 1095 fs for an incident laser intensity of 10¹⁶ W/cm². Projections of the y = 0 and z = 0 planes are shown on the left back side and bottom, respectively, of the figure box. The red curves outline the spread angle Θ of the laser branches, and the projection of the x = 15.6 µm plane (the branching point, located by the black dashed lines) is shown at the right back side.