Triggering filamentation using turbulence

We study the triggering of single filaments due to turbulence in the beam path for a laser of power below the filamenting threshold. Turbulence can act as a switch between the beam not filamenting and producing single filaments. This positive effect of turbulence on the filament probability, combined with our observation of off-axis filaments, suggests the underlying mechanism is modulation instability caused by transverse perturbations. We hereby experimentally explore the interaction of modulation instability and turbulence, commonly associated with multiple filaments, in the single-filament regime.

Figure 1

Experimental setup. Turbulence is applied to the collimated beam before entering the water cell. The distance traveled from the beginning of the cell to the measurement screen is denoted by $z$. The image on the measurement screen is recorded by a high-speed camera capturing each individual laser shot.

Figure 2

Simulation of the pulse propagation. Because of the high dispersion the pulse length increases drastically, due to which the pulse peak power decreases at an equal rate. At the turning point of focusing to defocusing, the peak power has dropped from 14.2 GW to 2.0 MW, which is below the filamentation threshold.

Figure 3

(a) Filament probability $p(\ge 1)$ as a function of propagation distance. (b) Looking only at the young filaments, $p_{\mathrm{young}}(\ge 1)$, gives an indication of the filament onset distance. (c) The relative occurrence $p_{\mathrm{rel}}(\ge 1)$ of young and dying filaments observed at each propagation distance, for $C_n^2=6.7\times {10}^{-9}{\mathrm{m}}^{-2/3}$.

Figure 4

Examples of filaments as recorded by the camera for $P_{\mathrm{in}}=14.2$ GW and $C_n^2=6.7\times {10}^{-9} {\mathrm{m}}^{-2/3}$. (a) Young filament at $z=10$ cm. (b) Fading filament at $z=36$ cm. The cross denotes the beam center.

Figure 5

Filament positions at $z=10$ cm, $P_{\mathrm{in}}=14.2$ GW, and $C_n^2=6.7\times {10}^{-9} {\mathrm{m}}^{-2/3}$ based on 142 668 shots for which 5228 filaments were recorded.

Figure 6

(a) Example of the probability density function for $z=10$ cm at $C_n^2=6.7\times {10}^{-9} {\mathrm{m}}^{-2/3}$. (b) Sum of squared errors. Experimental settings that contained too few data points were excluded from the analysis.