Generation of extreme-ultraviolet and x-ray light from a propagating nanometer electron layer in few-cycle laser interaction with solid targets

A new generation mechanism of coherent extreme-ultraviolet (XUV) and x-ray radiation presents in the few-cycle laser interaction with solid density plasma. Two-dimensional simulations show that the XUV and x-rays intensities do not have power law or exponential law dependence on the frequency which is followed by the high harmonic spikes generated through the coherent-wake-emission or relativistically oscillating mirror processes. The XUV and x rays are actually nonlinearly scattered by the successively propagating nanometer electron layers formed in the combined effects of the ponderomotive forces of the incident laser pulse and the electric force due to the charge separation. The nanometer electron layers move in the laser field and the characteristic electrons have their directions bended several times due to the change of the laser's magnetic field. At every bending point, these electrons emit strong synchrotron radiation along a direction that deviates from the reflected laser, even if the normalized drive laser amplitude is at $a_0\approx 1$. The simulation results for two cases with and without the density profile truncation indicate that the efficiency of this mechanism strongly depends on the preplasma.

Figure 1

(a) The setup of the initial laser-plasma conditions with different preplasma ramp shapes. The incident laser beam radiates on the target front surface with an incidence angle $\alpha ={45}^{\circ }$. (b) The distribution of the laser electric field $E_y$ at the initial moment. (c) Two different kinds of preplasma density profiles on the laser axis. The solid blue line represents without (w/o) the density profile truncation, and the dashed red line represents with the profile truncation.

Figure 2

Distributions of the reflected laser electric field $E_x$ in (a) spatial space ($x,y$) and (b) the corresponding wave vector space ($k_x,k_y$) in units of $k_0$, where $k_0$ is the wave vector of the incident laser pulse, at $t=10.0T_0$ without (w/o) truncation. Two radiation bands whose frequencies are cross extreme ultraviolet (XUV) and x-ray wave bands are found in panel (b). (c) The angular distribution of the spectra in units of degrees. The $\theta$ direction is shown in panel (b), where $\theta =0^{\circ }$ is the normal laser reflection direction.

Figure 3

Distributions of (a) the reflected laser electric field $E_x$ and (b, c) the corresponding frequency spectra in units of laser frequency ${\omega }_0$ at point A in Fig. 1 without truncation. The orders are from (b) 1st to 4th and (c) 11th to 25th. The frequency spectra are with the normalized intensity (i.e., Norm. Intens.). (d) The frequency spectrum (the solid blue line) with the x-ray wave band and (e) the corresponding inverse fast Fourier transformation (iFFT) after filtering [the dashed orange line in panel (d)] at point B in Fig. 1 without truncation.

Figure 4

The temporal evolution of the electron density $n_e$ at (a) $t=6.25T_0$, (b) $t=7.0T_0$, and (c) $t=7.5T_0$.

Figure 5

The temporal evolution of (a) the electron density $n_e$, (b) the logarithmic wave vector intensity, and (c) the laser electric field $E_y$ (the charge separation electric field is also overlaid on this colormap) on the $x=-0.5 \mu \mathrm{m}$ line. (d) The distribution of the laser electric field (LEF, the dashed green line), the charge separation electric field (CSEF, the dotted blue line), and their summing field (LEF $+$ CSEF, the solid red line) at $t=6.35T_0$ [i.e., the dashed black line in panel (c)].

Figure 6

(a) Typical trajectory of electron motion in laser preplasma interaction without truncation. The green point represents the initial position of the selected electron while the magenta point represents its final position (the same below). The color of the trajectory represents the electron's kinetic energy (the same below). The background color shows the distribution of the electron density $n_e$ at $t=8.25T_0$. (b) The distribution of the electron density $n_e$ at $x=1.0 \mu \mathrm{m}$ [the dashed black line in panel (a)]. (c) The energy of the selected electron (the solid blue line) and the magnetic field $B_z$ (the dashed red line) that the electron experiences.

Figure 7

Distributions of the reflected laser electric field $E_x$ in (a) spatial space ($x,y$) and (b) the corresponding wave vector space ($k_x, k_y$) in units of $k_0$, where $k_0$ is the wave vector of the incident laser pulse, at $t=10.0T_0$ with truncation.

Figure 8

Distributions of (a) the reflected laser electric field $E_x$ and (b, c) the corresponding frequency spectra in units of laser frequency ${\omega }_0$ at point A in Fig. 1 with truncation. The orders are from (b) 1st to 4th and from (c) 10th to 60th (the solid blue line). The frequency spectra are with the normalized intensity (i.e., Norm. Intens.). (d) The corresponding inverse fast Fourier transformation (iFFT) of the frequency spectrum with near the 20th order after filtering (the dashed orange line) at point B in Fig. 1 with truncation.

Figure 9

(a) Typical trajectory of the electrons' motion in the laser preplasma interaction with truncation. The background color shows the distribution of the electron density $n_e$ at $t=8.25T_0$. (b) The distribution of the electron density $n_e$ at $x=1.4 \mu \mathrm{m}$ [the dashed black line in panel (a)].