Compact intense extreme-ultraviolet source.

High-intensity laser pulses covering the ultraviolet to terahertz spectral regions are nowadays routinely generated in a large number of laboratories. In contrast, intense extreme-ultraviolet (XUV) pulses have only been demonstrated using a small number of sources including free-electron laser facilities [1-3] and long high-harmonic generation (HHG) beamlines [4-9]. Here we demonstrate a concept for a compact intense XUV source based on HHG that is focused to an intensity of $2 \times 10^{14}$ W/cm$^2$, with a potential increase up to $10^{17}$ W/cm$^2$ in the future. Our approach uses tight focusing of the near-infrared (NIR) driving laser and minimizes the XUV virtual source size by generating harmonics several Rayleigh lengths away from the NIR focus. Accordingly, the XUV pulses can be refocused to a small beam waist radius of 600 nm, enabling the absorption of up to four XUV photons by a single Ar atom in a setup that fits on a modest (2 m) laser table. Our concept represents a straightforward approach for the generation of intense XUV pulses in many laboratories, providing novel opportunities for XUV strong-field and nonlinear optics experiments, for XUV-pump XUV-probe spectroscopy and for the coherent diffractive imaging of nanoscale structures.