Laser Filamentation as a New Phase Transition Universality Class

We show that the onset of laser multiple filamentation can be described as a critical phenomenon that we characterize both experimentally and numerically by measuring a set of seven critical exponents. This phase transition deviates from any existing universality class and offers a unique perspective of conducting two-dimensional experiments of statistical physics at a human scale.

Figure 1

Formation of a structured disconnected filamentation pattern from an initially smooth one in a 100 TW beam. Experimental record [(a)–(e)] and numerical simulation [(f)–(j)] evolution of the fluence profile, after propagating in air for (a) 1.25 m, (b) 2.5 m, (c) 5 m, (d) 10 m, and (e) 15 m. Numerical simulations are shown here for (f) 1 m, (g) 8 m, (h) 10.6 m, (i) 11.7 m, and (j) 14.4 m. The fluence has been thresholded at the same value in all pictures, corresponding to $0.8\mathrm{TW}/{\mathrm{cm}}^2$ for numerical simulations. Clusters are colored according to their relative size in each image.

Figure 2

Close-up on the [(a)–(c)] experimental and [(d)–(f)] numerical multiple filamentation patterns of Fig. 1, at propagation distances (a) 5 m, (b) 10 m, and (c) 15 m for the experimental data and (d) 10.6 m, (e) 11.7 m, and (f) 14.4 m for their numerical counterparts. Clusters corresponding to laser filaments survive all along the propagation, even when the filaments begin to vanish at long distances.

Figure 3

(a) Experimental mean cluster size (surface) as a function of the lattice filling factor $p$. (b) Maximum cluster size with respect to the system size $L$. We disregarded the percolating cluster appearing when $p$ exceeds $p_{\mathrm{c}}=0.5$ from the surface calculation.

Figure 4

Evolution of (a) the percolation probability, (b) the filling factor $p$, and (c) the correlation length as a function of the propagation distance $z$, defining the phase transition between the percolating and nonpercolating states.

Figure 5

(a) Evolution of the normalized cluster size distributions $n_s$ with respect to the propagation distance. A large percolating cluster is visible until approximately $z=10\mathrm{m}$. Beyond, a mode emerges around $2{\mathrm{mm}}^2$, corresponding to a robust size associated with individual filaments. (b) Normalized cluster size distribution for $z=11.7\mathrm{m}$ with respect to the cluster area in log scale. The typical size corresponds to the spatial extension of the photon bath immediately surrounding a plasma filament.