All-optical suppression of relativistic self-focusing of laser beams in plasmas

It is demonstrated that a catastrophic relativistic self-focusing (RSF) of a high-power laser pulse can be prevented all-optically by a second, much weaker, copropagating pulse. RSF suppression occurs when the difference frequency of the pulses slightly exceeds the electron plasma frequency. The mutual defocusing is caused by the three-dimensional electron density perturbation driven by the laser beat wave slightly above the plasma resonance. A bienvelope model describing the early stage of the mutual defocusing is derived and analyzed. Later stages, characterized by the presence of a strong electromagnetic cascade, are investigated numerically. Stable propagation of the laser pulse with weakly varying spot size and peak amplitude over several Rayleigh lengths is predicted.

Figure 1

(Color online) Normalized power for matched solutions $W_0$ (black line) and $W_1$ [red (dark gray) line] for (a) $\tilde{\Omega }<1$ [$\tilde{\Omega }=0.75$ (dashed line), $\tilde{\Omega }=0.9$ (solid line)], (b) $\tilde{\Omega }>1$ [$\tilde{\Omega }=\sqrt{3∕2}$ (dotted line), $\tilde{\Omega }=1.25$ (dashed line), $\tilde{\Omega }=3.18$ (solid line)].

Figure 2

(Color online) Peak intensity versus propagation distance (in units of $Z_{R_0}$). The laser is either monochromatic [solid red (dark gray) line] or bicolor with the power partition $W_0∕W_1=17∕3$ [$\tilde{\Omega }=3.18$, dashed red (dark gray line); $\tilde{\Omega }=1.25$, yellow (light gray) and black line]. Black curve is obtained from the bienvelope theory, others are from WAKE simulations. Inset shows the initial stage of evolution.

Figure 3

(Color online) Radial and axial profiles of laser intensity taken at $z=0$ (black line) and $z=2Z_{R_0}$ [red (dark gray) line]. Top: Isocontours at the level $\exp (-2)$ of the peak intensity. Bottom: Axial lineouts of normalized intensity. Left-hand column, initially monochromatic pulse with $W_{\mathrm{tot}}=1.1$; middle column, bicolor pulse with the power partition $W_0∕W_1=17∕3$, $W_0+W_1=W_{\mathrm{tot}}$, $\tilde{\Omega }=3.18$; right-hand column, bicolor pulse with the same power partition and $\tilde{\Omega }=1.25$.

Figure 4

Absolute value of the normalized coefficient of plasma wave-induced cross focusing, $G_{\mathrm{norm}}=G_{N_e}^{\Omega }\left(z\right)∕G_{N_e}^{\Omega }\left(0\right)$, versus propagation distance for the simulation of Figs. 3c, 3f.

Figure 5

(Color online) Spectral evolution of (a) laser radiation and (b) plasma density perturbations from the simulation of Figs. 3c, 3f. Radially integrated spectra are shown for $z=0$ (black line), $z=Z_{R_0}$ [red (dark gray) line], $z=2Z_{R_0}$ [yellow (light gray) line]. Frequencies are in units of ${\omega }_{pe}$.