Relativistically intense XUV radiation from laser-illuminated near-critical plasmas

Pulses of extreme ultraviolet (XUV) light, with wavelengths between 10 and 100$\,$nm, can be used to image and excite ultra-fast phenomena such as the motion of atomic electrons. Here we show that the illumination of plasma with near-critical electron density may be used as a source of relativistically intense XUV radiation, providing the means for novel XUV-pump--XUV-probe experiments in the non-linear regime. We describe how the optimal regime may be reached by tailoring the laser-target interaction parameters and by the presence of preplasma. Our results indicate that currently available laser facilities are capable of producing XUV pulses with duration $\sim 10~\text{fs}$, brilliance in excess of $10^{23}$ photons/s/mm$^2$/mrad$^2$ (0.1% bandwidth) and intensity $I\lambda^2 \gtrsim 10^{19}~\text{W}\text{cm}^{-2}\mu\text{m}^2$.