Model of high-order harmonic generation from laser interaction with a plasma grating

Harmonic generation from linearly polarized high-intensity short-pulse laser normally impacting a solid plasma grating is investigated using analytical modeling and particle-in-cell simulation. It is found that when the radiation excited by the relativistic electron quiver motion in the laser fields suitably matches a harmonic of the grating periodicity, it will be significantly enhanced and peak with narrow angular spread in specific directions. The corresponding theory shows that the phenomenon can be attributed to an interference effect of the periodic grating on the excitation.

Figure 1

Interaction configuration. The linearly laser beam incidents normally on the grating surface with its electric field polarized along the $\widehat{y}$ axis. $\ell , h$, and w are the grating periodicity and the height and width of the tooth, respectively. $z=0$ is the interface of the tooth plasma and vacuum.

Figure 2

The angular distribution of $K_n$, or the contribution of a single quivering electron to the emitted radiation, for $n=1$ to 50 (right to left) and $a_0=3$.

Figure 3

The interference parameter $F_n$ for the harmonics (a) $n=1$ to 4 and (b) $n=4$ to 16. Here, the tooth gap and grating length are $\ell ={\lambda }_0/4$ and $L=20{\lambda }_0$, respectively.

Figure 4

The angular distribution of $P_n$ for $a_0=3$, giving the relative radiation power of the $n=4\to 16$ harmonics from a grating surface. The parameters of the grating is same as Fig. 3.

Figure 5

Snapshot of radiation field components (a) $E_z$, (b) $E_y$, and (c) $B_x$ at $t=14{\tau }_0$. (d) Electron density distribution and phase spaces (e) ($y,P_z$) and (f) ($y,P_y$) at $t=8{\tau }_0$. $E$ and $B$ are normalized by $m_e{\omega }_{0}c/e$ and $n_e$ is normalized by $n_c$.

Figure 6

(a) Temporal profile of the normalized radiation fields at $\theta \sim 5^{\circ }$ and (b) the corresponding spectrum. (c) Angular distribution of the intensity of three harmonics from the grating surface. The inset in (a) shows the a magnified segment of the structure of the generated attosecond radiation pulse.