High-quality high-order harmonic generation through preplasma truncation

By introducing preplasma truncation to cases with an initial preplasma scale length larger than $0.2\lambda$, the efficiency of high-order harmonics generated from relativistic laser-solid interactions can be enhanced by more than one order of magnitude and the angular spread can be confined into near-diffraction-limited divergence. Numerical simulations show that density truncation results in more compact oscillation of the surface electron sheet and the curvature of the reflection surface for the driving laser is greatly reduced. This leads to an overall improvement in the harmonic beam quality. More importantly, density truncation makes the harmonic generation weakly dependent on the preplasma scale length, which provides a way to relax the extremely high requirement on the temporal contrast of the driving laser pulse. A feasible scheme to realize the required preplasma truncation is also proposed and demonstrated by numerical simulations.

Figure 1

Schematic of HHG in laser-solid target interactions with different preplasma ramp shapes. The brown (green) arrows represent the incident (reflected) lasers. The purple layers represent the compressed electron sheets. The red lines show the plasma density distributions along the $x$ direction. $n_{\mathrm{ref}}$, $n_{\mathrm{cut}}$, and $n_{\max }$ denote the reflection density, truncation density, and maximum plasma density of the solid target, respectively.

Figure 2

Harmonic spectra for the cases $L=0.1\lambda$ (case S), $L=0.2\lambda$ without preplasma truncation (case A), and $L=0.2\lambda$ with truncation at $n_{\mathrm{cut}}=7n_c$ (case B).

Figure 3

(a) and (b): Spatiotemporal evolution of electron density along a fixed line with $y=0$. (c) and (d): Typical trajectories of the electrons composing the oscillating mirror. The background shows harmonic emission filtered by $N\ge 10\text{th}\text{order}$ (top color bar). The colors along the trajectories represent the normalized longitudinal momentum $p_x=\gamma v_x/c$ of the electrons (right color bar). The left column [(a) and (c)] and right column [(b) and (d)] figures correspond to the cases without and with $n_{\mathrm{cut}}=7n_c$, respectively.

Figure 4

(a) Relative electron density distribution in the phase space $n_e(x,4{\gamma }^2)$. Only electrons with $\gamma >1.5$ are counted. (b) Temporal waveform of harmonic fields filtered by $N\ge 10\text{th}\text{order}$. The peak of the driving laser reaches the target surface at about $t=17T_0$.

Figure 5

Plasma density $n_e$ profiles for cases (a) without preplasma truncation and (b) with $n_{\mathrm{cut}}=7n_c$ at $t=17T_0$. The red lines show the outlines of the plasma surface at different cases.

Figure 6

Angular divergence of harmonics for cases (a) without preplasma truncation and (b) with $n_{\mathrm{cut}}=7n_c$. The radial dimension represents the harmonic order. The green rectangles represent the targets, and the red arrows represent the incident laser. The color bars show the logarithm of normalized harmonic intensity.

Figure 7

(a) Harmonic spectra (only peak points shown) for the preplasma scale lengths of $L=0.1{\lambda }_0$ and $0.4{\lambda }_0$, with $n_{\mathrm{cut}}=7n_c$ and without truncation. (b) Relative efficiency of harmonic yield ${\sum }_{N\ge 2}|E\left({\omega }_{{}_N}\right){|}^2$ for cases with different plasma scale lengths.

Figure 8

(a) Dependence of harmonic intensity (${\sum }_{N\ge 10}|E\left({\omega }_{{}_N}\right){|}^2$) on $n_{\mathrm{cut}}$ for $a_0=3$. (b) Optimal truncation density $n_{\mathrm{cut}}$ for HHG varying with laser intensity. The laser incidence angle in (a) and (b) is $\theta ={45}^{\circ }$. (c) Dependence of harmonic intensity on $\theta$ and $n_{\mathrm{cut}}$. The laser intensity in (c) is $a_0=5$.

Figure 9

(a) Feasible experimental scheme for high-quality HHG by preplasma truncation. The violet beam represents the truncation pulse with circular polarization. It normally irradiates on the solid target and generates a steplike profile in the preplasma. The red beam represents the main laser pulse. It excites the relativistic oscillation of truncated plasma surface and then generates harmonics. (b) Ion charge density distributions at different instants. The top half shows the initial density distribution with preplasma scale length $L=0.2\lambda$. The bottom half shows the truncated density distribution after being compressed by a circularly polarized laser with $a_0=0.3$, $w_0=6{\lambda }_0$, and $\tau =10T_0$. The red line shows the outline of plasma surface at $t=2\mathrm{ps}$.

Figure 10

(a) Ion charge density profiles at different instants after being compressed by a circularly polarized laser. The initial preplasma scale length is $L=0.5{\lambda }_0$. (b) Effective truncation density for truncation pulse with different intensities.