Figure 1

(Color online) Experimental setup. Case A: turbulence is applied on the beam prior to filamentation and a camera records for each shot the white light spot on a screen placed $7\mathrm{m}$ after the focusing lens. The distance between the aperture and the entrance of the turbulence cell is $10\mathrm{cm}$ and the distance between the output plane of the cell and the lens is $30\mathrm{cm}$. Case B: turbulence is applied on the filament after the self-focusing of the beam. The distance between the aperture and the lens is $270\mathrm{cm}$.Reuse & Permissions

Figure 2

(Color online) Position of the $100\mu \mathrm{J}$ beam center in the absence of turbulence before (a) and after (b) horizontal reshaping.Reuse & Permissions

Figure 3

(Color online) Position of the filament white light spot on the screen in cases A (a) and B (b) for a turbulence parameter of $C_n^2=1.7\times {10}^{-11}{\mathrm{m}}^{-2∕3}$.Reuse & Permissions

Figure 4

(Color online) Experimental results for 256 shots in case A with strong turbulence $C_n^2=1.7\times {10}^{-11}{\mathrm{m}}^{-2∕3}$. (a) Example of beam cross section at $7\mathrm{m}$ beyond the entrance of the turbulence cell. (b) Filament positions after correction of the systematic error in the horizontal direction. 127 (49%) shots were retained for which filamentation occurred. (c) Histogram of the transverse displacements fitted by a Weibull probability distribution [continuous curve in (c) and (d)] with parameters $p=1.52$ and $w_W=1.78\mathrm{mm}$. (d) details the fit procedure which amounts to determining the slope of the function $\ln [-\ln (1-\Psi )]$ of the cumulated number $\Psi$ of filaments found within a circle of radius $r$.Reuse & Permissions

Figure 5

(Color online) Experimental results presented as in Fig. 4 for 251 shots (98%) in case A with very weak turbulence $C_n^2=2.1\times {10}^{-13}{\mathrm{m}}^{-2∕3}$. The Weibull distribution of transverse displacements [continuous curve in (c) and (d)] has parameters $p=1.13$ and $w_W=0.41\mathrm{mm}$.Reuse & Permissions

Figure 6

(Color online) Experimental results presented as in Fig. 4 for 233 shots (91%) in case B with strong turbulence $C_n^2=1.7\times {10}^{-11}{\mathrm{m}}^{-2∕3}$. The Weibull distribution of transverse displacements [continuous curve in (c) and (d)] has parameters $p=1.76$ and $w_W=0.35\mathrm{mm}$.Reuse & Permissions

Figure 7

(Color online) Filamentation rate (top) and average filament deviation $⟨\delta r⟩$ (bottom) of a $3\mathrm{mJ}$ laser beam as function of the $C_n^2$ (in ${\mathrm{m}}^{-2∕3}$) in the chamber for case A (a) and B (b). The black diamonds show the deviation for a $100\mu \mathrm{J}$ pulse propagating linearly under the same turbulent conditions, and the dashed red curve is a calculation using formula (5).Reuse & Permissions

Figure 8

(Color online) Numerical simulation results presented as in Fig. 4 for 200 shots in case A with strong turbulence $C_n^2=1.7\times {10}^{-11}{\mathrm{m}}^{-2∕3}$. The probability function for the Weibull distribution [continuous curve in (c) and (d)] has parameters $p=1.81$ and $w_W=0.83\mathrm{mm}$.Reuse & Permissions

Figure 9

(Color online) Numerical simulation results presented as in Fig. 4 for 200 shots in case A with the screen at $z=7\mathrm{m}$, weak turbulence $C_n^2=2.2\times {10}^{-12}{\mathrm{m}}^{-2∕3}$. The Weibull distribution [continuous curve in (c) and (d)] has parameters $p=0.87$ and $w_W=0.50\mathrm{mm}$.Reuse & Permissions

Figure 10

(Color online) Numerical simulation results presented as in Fig. 4 for 200 shots in case A with the screen at $z=6\mathrm{m}$, weak turbulence $C_n^2=2.2\times {10}^{-12}{\mathrm{m}}^{-2∕3}$. The parameters for the Weibull distribution [continuous curve in (c) and (d)] are $p=1.75$ and $w_W=0.73\mathrm{mm}$.Reuse & Permissions

Figure 11

(Color online) Filamentation distance as a function of $P∕P_{cr}$: distance to observe a gain of ${10}^4$ by MI (dash-dotted curve); collapse distance in nonturbulent air (dashed curve); and collapse distance in turbulent air (solid curve, $C_n^2={10}^{-13}{\mathrm{m}}^{-2∕3}$).Reuse & Permissions

Figure 12

(Color online) Distribution of filamentation distances, defined as the minimal distance for which the peak intensity exceeds the threshold of ${10}^{13}\mathrm{W}∕{\mathrm{cm}}^2$ in case A. The focus of the lens is at $400\mathrm{cm}$ and the collapse distance without turbulence is at $390\mathrm{cm}$. The statistics is performed over 200 shots for each $C_n^2$. (a) $C_n^2=9\times {10}^{-10}{\mathrm{m}}^{-2∕3}$. (b) $C_n^2=1.7\times {10}^{-11}{\mathrm{m}}^{-2∕3}$. (c) $C_n^2=2.2\times {10}^{-12}{\mathrm{m}}^{-2∕3}$. (d) $C_n^2=2.1\times {10}^{-13}{\mathrm{m}}^{-2∕3}$. The peak intensity is below threshold for 57% of the shots in case (a), 1% in case (b), and is above threshold in cases (c) and (d).Reuse & Permissions

Figure 13

(Color online) Same as in Fig. 12 but for the threshold of $8\times {10}^{12}\mathrm{W}∕{\mathrm{cm}}^2$. The peak intensity remains below threshold for 7% of the shots for (a) $C_n^2=9\times {10}^{-10}{\mathrm{m}}^{-2∕3}$ and is above threshold for all shots for weaker turbulence (b)–(d).Reuse & Permissions

Figure 14

(Color online) Numerical simulation results presented as in Fig. 4 for 60 shots in case B with the screen at $z=6\mathrm{m}$, very strong turbulence $C_n^2=9\times {10}^{-10}{\mathrm{m}}^{-2∕3}$. The parameters for the Weibull distribution [continuous curve in (c) and (d)] are $p=1.74$ and $w_W=0.077\mathrm{mm}$.Reuse & Permissions