Improving the Self-Guiding of an Ultraintense Laser by Tailoring Its Longitudinal Profile

Self-guiding of an ultraintense laser requires the refractive index to build up rapidly to a sufficient value before the main body of the pulse passes by. We show that placing a low-intensity precursor in front of the main pulse mitigates the diffraction of its leading edge and facilitates reaching a self-guided state that remains stable for more than 10 Rayleigh lengths. Furthermore, this precursor slows the phase slippage between the trapped electrons and the wakefield and leads to an accelerating structure that is more stable, contains more energy, and is sustained longer. Examples from three-dimensional particle-in-cell simulations show that the conversion efficiency from the laser to the self-trapped electrons increases by an order of magnitude when using the precursor.

Figure 1

3D PIC simulations demonstrate that a pulse with sharp rise time diffracts while a pulse with tailored profile remains guided. (a) The laser electric field $E_z(x,t=0)$ for a pulse with sharp rise time (red) and for the precursor of a tailored pulse (blue); the main bodies of the two pulses are identical. The top half of a 2D slice of $E_z(x,y,t=0)$ for a pulse with sharp rise time is shown in (b) and the bottom half of a slice of $E_z(x,y,t=0)$ for a tailored pulse in (c). Contours have been drawn for $(e{\omega }_0{E}_z/m_{e}c)=\pm 1.6$, $\pm 4.8$. Plots (d), (e), and (f) correspond to (a), (b), and (c) at ${\omega }_{0}t=55951.6$.

Figure 2

Electron density isosurfaces and slices from two 3D PIC simulations, the same as in Fig. 1. In (a) and (b) a pulse with sharp rise time [Fig. 1] is used. In (c) and (d) the pulse has a tailored profile [Fig. 1]. Panels (e) and (f) show the electric field $E_x(x)$ along the laser propagation axis with red (blue) lines for the sharp (tailored) profile.

Figure 3

(a) The maximum decelerating field (which scales with the accelerating field) and (b) the amplitude of the laser electric field, shown in terms of the propagation distance from three simulations: without a precursor for $a_0=8$, and with a precursor for $a_0=8$ and $a_0=5.3$.

Figure 4

(a) Energy distributions after 0.737 cm shown from a simulation of a pulse with (without) a precursor blue (red). The energy of particles above 100 MeV is $\sim 0.73\mathrm{J}$ and $\sim 0.43\mathrm{J}$, respectively. The charge $Q(p_x)={\int }_{p_x}^{\infty }f(p_x^{\prime })d{p}_x^{\prime }$ is shown with broken or dotted lines. (b) Two spectra after 1.625 cm for two tailored pulses with different initial $w_0,a_0$ but the same power profile. The blue and dotted lines are from the same simulation as in (a). The energy in electrons above 100 MeV (1 GeV) is 2.74 J (1.9 J) for the simulation with $a_0=5.3$ and 2.61 J (1.86 J) for the simulation with $a_0=8$.