  Ultra-short high-power lasers can deliver extreme light intensities ($\ge
10^{20}$ W/cm$^2$ and $\leq 30 f$s) and drive large amplitude Surface Plasma
Wave (SPW) at over-dense plasma surface. The resulting current of energetic
electron has great interest for applications, potentially scaling with the
laser amplitude, provided the laser-plasma transfer to the accelerated
particles mediated by SPW is still efficient at ultra-high intensity. By mean
of Particle-in-Cell simulations, we identify the best condition for SPW
excitation and show a strong correlation between the optimum Surface Plasma
Wave excitation angle and the laser's angle of incidence that optimize the
electron acceleration along the plasma surface. We also discuss how plasma
density and plasma surface shape can be adjusted in order to push to higher
laser intensity the limit of Surface Plasma Wave excitation. Our results open
the way to new experiments on forthcoming multi-petawatt laser systems.

Plasma Physics