Submicrometer focusing of isolated attosecond XUV pulses approaching 10${}^{16}$ W/cm${}^2$

We demonstrate submicrometer focusing of isolated attosecond pulses (IAPs) in the extreme ultraviolet (XUV) region using a custom ellipsoidal mirror. The obtained focal spot sizes were verified using knife-edge measurements with a sharp silicon edge, confirming reproducible dimensions down to 0.46 $\mu$m $\times$ 0.36 $\mu$m (FWHM), approaching the diffraction limit. Focusing a 1.1-GW tabletop IAP source yields a peak intensity of 3 $\times$ 10${}^{15}$ W/cm${}^2$, and a realistic pathway toward 10${}^{16}$ W/cm${}^2$ is obtained by optimizing the beamline throughput. These results establish a practical route toward attosecond nonlinear optics in both gas and solid phases, driven by intense XUV fields.