Divergence control of relativistic harmonics by an optically shaped plasma surface

The unique spatial and temporal properties of relativistic high harmonics generated from a laser-driven plasma surface allow them to be coherently focused to an extremely high intensity reaching the Schwinger limit. The ultimately achievable intensity is limited by the harmonic wavefront distortions during the interactions. Here we demonstrate experimentally that the harmonic divergence can be controlled by an optically shaped plasma surface with a prepulse that has the same spatial and temporal distribution as the main laser pulse. Simulations are also performed to explain the experimental observation, and we find that the harmonic wavefront curvature from a dented surface can be precompensated by a convex plasma. Our work suggests an active approach to control the harmonic divergence and wavefront by an optically shaped target. This can be critical for further high harmonics applications.

Figure 1

(a) The schematic illustration of the experimental setup. (b) A convex plasma surface is generated by prepulse P1 introduced by an ultrashort pulse shaper. (c) A planar plasma surface is generated by prepulse P2 introduced by a small mirror M1. M is the main pulse.

Figure 2

The spectra of high-order harmonics obtained with prepulse P1 in experiments: (a) harmonics are measured at specular direction when the laser incidence angle is ${40}^{\circ }$; (b) harmonics are measured off the reflected laser axis at ${60}^{\circ }$ to the target normal direction when the laser incidence angle is ${20}^{\circ }$. The red dashed lines mark the scaling $I\propto H^{-8/3}$.

Figure 3

The raw spectral images of harmonic radiations from a convex plasma surface (a) and a plane plasma surface (b). (c) The angular distributions of the 26th-order harmonic in the two cases. (d) The measured divergences (FWHM) of harmonics from 21st to 31st orders by a planar surface. The blue dashed line indicates the diffraction-limited divergence.

Figure 4

The plasma density maps of targets (a), (b), snapshots of the magnetic field component $B_z$ during the interactions at $t=36T_0$ (c), (d), spatial distribution of the reflected magnetic field $B_z$ after the interactions at $t=48T_0$ (e), (f) and the divergence of harmonics from fifth to ninth orders (g), (h) for transversely Gaussian-shaped (left column) and uniform density distribution (right column). The laser is incident from the lower left corner and reflected towards the upper left.

Figure 5

Simulation results at a higher laser intensity ($a_0=37$). Snapshots of the magnetic field component $B_z$ during the interactions at $t=24T_0$ (a), (b), and spatial distribution of the reflected magnetic field $B_z$ after the interactions at $t=48T_0$ (c), (d) for transversely Gaussian-shaped (left column) and uniform density distribution (right column). (e) Normalized intensities of the reflected fields along their wavefronts (the dotted green lines) in panels (c) and (d).