Organizing Multiple Femtosecond Filaments in Air

We show that it is possible to organize regular filamentation patterns in air by imposing either strong field gradients or phase distortions in the input-beam profile of an intense femtosecond laser pulse. A comparison between experiments and $3+1$ dimensional numerical simulations confirms this concept and shows for the first time that a control of the transport of high intensities over long distances may be achieved by forcing this well ordered propagation regime. In this case, deterministic effects prevail in multiple femtosecond filamentation, and no transition to the optical turbulence regime is obtained [Mlejnek et al., Phys. Rev. Lett. 83, 2938 (1999)].

Figure 1

Filamentation patterns obtained with a 10 mJ pulse propagating in air beyond a (a) trefoil or a (b) five-foil diaphragm. (c) Intensity (continuous curves, scale on the left axis) and electron density (dashed curves, scale on the right axis) in the core of the most intense filament. Fine curves: tre­foil diaphragm. Thick curves: fivefold diaphragm. (d) Isosur­face for the fluence distribution for $0.2\mathrm{J}/{\mathrm{c}\mathrm{m}}^2$ (with a fivefold diaphragm).

Figure 2

(a) Numerically computed filamentation pattern obtained by forcing astigmatism in the input beam for a propagation distance of 7 m. (b) Fluence distribution measured at 3.7 m from the defocusing lens. The beam energy is 7.7 mJ; the curvature of the wave front is $f=7.7\mathrm{m}$; the astigmatism in input beam is $\alpha =4.8\times {10}^{-2}{\mathrm{m}}^{-1}$.

Figure 3

Measured filamentation patterns at the propagation distance (a) $z=4.2\mathrm{m}$; a trefoil mask with a central stop on the input beam was used. (b) Blue filaments (400 nm) measured at $z=30\mathrm{m}$; a circular diaphragm was used.