Model of in-situ focusing of extreme ultraviolet high-order harmonics from a nanostructured MgO surface

We present a numerical model for the in-situ generation and focusing of extreme-ultraviolet (XUV) high harmonics via a Fresnel zone plate etched into a dielectric (MgO) surface. Our simulations show that propagation of the intense infrared field driving high-harmonic emission through the etched surface rings introduces well controlled amplitude and phase modulations of the XUV field emitted from the surface itself that enhance the focusing efficiency up to 25%, beyond that of both conventional amplitude-modulated transmission XUV zone plates as well as ideal phase-only zone plates. Rings with a width comparable to the wavelength of the infrared driver exhibit strongest XUV emission with a larger phase modulation due to enhancement of the infrared field. On the contrary, a smooth phase modulation is achieved in the outskirts of the zone plates, where the width of the rings is much smaller than the infrared driving wavelength. These findings highlight the potential of sub-wavelength metasurface design in optimizing nanostructured optical elements for XUV nano-spectroscopy and on-chip XUV beam shaping.