Fig. 1. (a) Schematic of the hologram generation. The patterns of the holograms satisfy the conditions of Equation (2a) with (b) and (c) . The patterns of the holograms satisfy the conditions of Equation (2b) with (d)\, and (e) .

Fig. 2. Schematic of the surface plasma hologram (SPH) formation and ultra-intense vortex-laser generation. (a) The object laser with mode LG and the reference laser interfere at the surface of the flat plasma target. The target surface shows the intensity of the interfering laser. (b) The isosurface of the proton density at the target surface at , and ps, respectively. (c) A read-out laser irradiates the SPH, is diffracted by the SPH, duplicates the vortex phase of the object laser and converts it to an ultra-intense vortex laser in the focus.

Fig. 3. (a) The transverse distribution of electric fields of the interference laser at . (b) The intensity distribution of the interference laser and its transverse ponderomotive force at at . (c) The distribution of electron density and (d) the difference between electron density and proton density at . The density distributions of (e) electrons and (f) protons at at .

Fig. 4. The reconstructed phase profiles of the object laser obtained through (a) theoretical calculations and (b) numerical simulations, as well as the laser electric fields obtained through (c) theoretical calculations and (d) numerical simulations.

Fig. 5. (a) 3D isosurface distribution of the electric field at . The (, ) projection plane on the right-hand side is taken at . The (, ) projection plane of laser intensity at the bottom is taken at , and the (, ) projection plane at the rearside is taken at . (b)–(d) The distribution of the transverse electric field at different cross-sections ranging from to at (simulation results). (e)–(g) Same as (b)–(d) but from Fresnel–Kirchhoff’s diffraction formula.

Fig. 6. (a) Transverse distribution of the vortex laser intensity at at . (b) Laguerre–Gaussian (LG) mode spectrum at at . (c) Evolution of the laser total angular momentum (AM) (black line) and energy conversion efficiency to the vortex-laser pulse (red line). (d) Evolution of the averaged AM of laser photons. Here the gray area marks the stage when the laser is in the focal volume.

Fig. 7. (a) The averaged depth of the SPHs in the (, ) plane. (b) The ratio of output vortex-laser intensity to the incident read-out laser intensity (/) in the (, ) plane. Scaling of the laser total AM (, black circles), the energy conversion efficiency to the vortex laser (, red circles) and the ratio of output vortex-laser intensity to the incident read-out laser intensity (, blue circles) (c) with regard to the laser electric field amplitude and (d) the focus spot size of the incident read-out laser.