Plasma high-order-harmonic generation from ultraintense laser pulses

Plasma high-order-harmonic generation from an extremely intense short-pulse laser is explored by including the effects of ion motion, electron-ion collisions, and radiation reaction force in the plasma dynamics. The laser radiation pressure induces plasma ion motion through the hole-boring effect, resulting in frequency shifting and widening of the harmonic spectra. The classical radiation reaction force slightly mitigates the frequency broadening caused by the ion motion. Based on the results and physical considerations, parameter maps highlighting the optimum regions for generating a single intense attosecond pulse and coherent XUV radiation are presented.

Figure 1

1D PIC simulations of HHG. The $x$ and $y$ axes represent harmonic numbers and intensity $I_n$, respectively. The frequency shift (deviation from the vertical green dashed lines) is clearly seen. (a) With and without the ion motion at a plasma density $n_e=200$ and with a constant laser amplitude $a\left(t\right)=a_0$ for $0<t<T_d$. (b) With a laser pulse of temporal profile $a\left(t\right)=a_0{sin}^2(\pi t/T_d)$, where $T_d=20T_l$ $(T_l$ is the laser period) at a plasma density $n_e=80$. (c) HHG with different plasma density gradients $L$. The maximal plasma density is $n_e=200$ with the same laser profile as in (a), except $T_d=5T_l$. The vertical green dashed lines correspond to integer harmonics from selection rules defined in Ref. [12].

Figure 2

2D PIC simulations with different targets and incident angles. The intensities are normalized to the intensity of the 17th harmonic for normal incidence and the 16th harmonic for oblique incidence. (a) Gold plasma with a density gradient $L={\lambda }_l/8$. (b) Carbon plasma with $L={\lambda }_l/16$. The laser pulse has temporal $a\left(t\right)=a_0\left\{tanh[(t-T_s)/W]-tanh[(t-T_e)/W]\right\}/2$ and transverse $a(t,y)=a\left(t\right)exp(-y^2/{\sigma }^2)$ profiles, where $a_0=40,W=T_l={\lambda }_l/c$, and $\sigma =4{\lambda }_l$. The laser pulse has a maximum intensity from $T_s=5T_l$ to $T_e=13T_l$.

Figure 3

2D PIC simulations of HHG. The black (dark) lines accounts for the RR force while the magenta (light-gray) lines do not. (a) Normal incidence $\theta =0$; (b) oblique incidence $\theta =\pi /4$. (c) Transverse motion $(y$ axis) of the electron $(X_{es}/{\lambda }_l$, solid lines) and ion $(X_{is}/{\lambda }_l$, dotted lines) layers. The electron and ion layers are defined at the position with density $n_e=Z{n}_i=a_0{n}_c$. (d) Relative position $(y$ axis) of the electron layer, $(X_{es}-X_{is})/{\lambda }_l$, with respect to the ion layer. (c) and (d) are for the 1D normal incidence case. The laser has the same profile as in Fig. 1 except $a_0=250$ and the plasma density is $n_e=1100n_c$.

Figure 4

Parameter maps for optimum HHG for (a), (b) normal incidence and (c), (d) oblique incidence $\left(\theta ={45}^{\circ }\right)$ with $p$ polarizations. (a), (c) are for the gold plasma; (b), (d) are for the carbon plasma. The color bar represents the harmonic numbers. The middle dotted and dashed black lines are plotted for the 50th harmonic in each case. See the text for the explanation.