Diffraction-ray optics of laser-pulse filamentation

We present a qualitative description of the laser-pulse filamentation phenomenon based on light field representation as a self-consistent ensemble of specific localized wave structures known as the diffraction-ray (light) tubes. These light tubes are energetically independent from each other and, at the same time, they are in close field interaction through the phase front of the light wave. The trajectories of light tube centroids represent the evolutionary line of the Poynting vector transverse component. Light tubes do not intersect in space although they can be nested, and the tubes do not exchange light energy with each other. Spatial shape and area of light tubes can vary during pulse propagation, reflecting the influence of different physical processes manifesting themselves upon radiation propagation in a medium. This diffraction-ray approach applies the attributes of the amplitude and phase analysis to the problem of laser radiation self-action and sheds light on the onset and termination conditions of laser-pulse filamentation.

Figure 1

(a) Peak pulse intensity, (b) density of laser plasma, and (c) beam radius upon laser-pulse filamentation in air.

Figure 2

Trajectories of “instantaneous” DRs $R_d$ for different pulse time slices: (a) $\tau =-1$, (b) 0, and (c) $+1$.

Figure 3

(a) Pulse fluence profile $F\left(r,z\right)$. (b) Time-averaged DR trajectories $R_{dF}\left(r,z\right)$. (c) Space-time intensity distribution $I\left(t,z\right)$. (d) Temporal DR traces ${\tau }_{\mathrm{dis}}\left(t,z\right)$.

Figure 4

Effective air permittivity distribution during laser-pulse filamentation.

Figure 5

DRTs (solid lines) and ERs (dash-dotted line) for Gaussian pulse filamentation with (a) $\eta =3$ and (b) 6.

Figure 6

(a) Transverse intensity profile of Bessel-Gaussian and Gaussian beams. (b) Threshold power for light tube self-channeling as a function of tube radius.

Figure 7

(а) Effective rays of light tubes during pulse filamentation with $\eta =6$. (b) Normalized tube energy ($z=11\mathrm{m}$).