Extreme events in resonant radiation from three-dimensional light bullets

We report measurements that show extreme events in the statistics of resonant radiation emitted from spatiotemporal light bullets. We trace the origin of these extreme events back to instabilities leading to steep gradients in the temporal profile of the intense light bullet that occur during the initial collapse dynamics. Numerical simulations reproduce the extreme valued statistics of the resonant radiation which are found to be intrinsically linked to the simultaneous occurrence of both temporal and spatial self-focusing dynamics. Small fluctuations in both the input energy and in the spatial phase curvature explain the observed extreme behavior.

Figure 1

Experimentally measured spectrum (logarithmic scale) for a $1.9 \mu \mathrm{m}$ wavelength pump pulse (dashed line is input spectrum) over the whole spectral range showing also the RR peak.

Figure 2

(a) Selection of 20 representative spectra recorded at nominally constant input energy and focusing conditions. (b) Statistical distribution of the RR energy (calculated from the integrated spectrum) and zoomed in along the vertical axis on the lower count rate range (0–100)—the full vertical range of data is shown in log scale in the inset.

Figure 3

Experimentally recorded RR energy as a function of input energy. The gray line indicates $2\times$ the significant energy mark $W_s$.

Figure 4

(a) Experimentally measured energy distribution of the input pump pulse (normalized to its mean value). (b), (c) The same data, postselected so as to keep only data with a smaller fluctuation (standard deviations of 0.28% and 0.15%, respectively) around a fixed mean value. (d)–(f) Histograms of the RR energy counts for the input energy distributions shown in (a)–(c): selecting input pump pulses with a narrow energy distribution clearly also narrows the RR energy $\mathsf{L}$-shaped distribution. The shaded areas indicate events that are larger than $2W_s$.

Figure 5

(a) Numerically simulated RR energy vs input energy and spatial phase curvature. (b) Superimposed RR spectra corresponding to all input energy and spatial phase curvature values used shown in (a).

Figure 6

Numerical results: (a) statistics of the RR energy (inset shows RR energy versus input energy for zero-phase curvature). (b) On-axis temporal profiles of the light bullet corresponding to different steepnesses of the shock fronts, which give rise to RR with low energy and high energy.