Electro-Optic Shocks from Ultraintense Laser-Plasma Interactions

Second harmonic radiation in the form of an electro-optic shock is produced in the blowout regime of a laser wakefield in a plasma. The shock is produced by the interaction between the laser field and the electron sheath surrounding the electron cavitation region. Because the sheath is thin, phase matching is unimportant, and the radiated energy grows secularly with the interaction length. The angle of emission is given by the Cherenkov angle associated with the ratio of the second harmonic phase velocity to the fundamental phase velocity. The shock formation is investigated in three dimensions via analysis and particle-in-cell simulations.

Figure 1

Schematic of electro-optic shock generation in a plasma bubble as viewed in the laser frame. The red area represents the laser radiation. The central wave number is indicated by ${\mathbf{k}}_0$. The black curves are electron streamlines. The shock formation occurs in the sheath, where the streamlines are highly concentrated.

Figure 2

3D ray tracing image of the charge density in the $2\times {10}^{19}{\mathrm{cm}}^{-3}$ case. The laser pulse propagates to the right and slightly down. Red corresponds to $n_e=0$, while blue corresponds to $n_e\approx {10}^{20}{\mathrm{cm}}^{-3}$. The blue area furthest to the right is the electron sheath which emits the electro-optic shock.

Figure 3

Isosurfaces of the spatial Fourier transform of $E_x$. Panel (a) is for an ambient plasma density of $2\times {10}^{19}{\mathrm{cm}}^{-3}$ and $t=1.7\mathrm{ps}$. The red surfaces enclose spectral amplitudes above 60% of the local maximum, and the blue 20%. Panel (b) is for $8\times {10}^{19}{\mathrm{cm}}^{-3}$ and $t=0.85\mathrm{ps}$. The red surfaces are 36%, and the blue are 18%.

Figure 4

Polar plot of intensity vs azimuth as computed by simulation (solid line) and theory (dashed line). The polarization direction corresponds to $\varphi =\{0°,180°\}$.