Free light-shape focusing in extreme-ultraviolet radiation with self-evolutionary photon sieves

Extreme-ultraviolet (EUV) radiation is a promising tool, not only for probing microscopic activities but also for processing nanoscale structures and performing high-resolution imaging. In this study, we demonstrate an innovative method to generate free light-shape focusing with self-evolutionary photon sieves under a single-shot coherent EUV laser; this includes vortex focus shaping, array focusing, and structured-light shaping. The results demonstrate that self-evolutionary photon sieves, consisting of a large number of specific pinholes fabricated on a piece of Si₃N₄ membrane, are capable of freely regulating an EUV light field, for which high-performance focusing elements are extremely lacking, let alone free light-shape focusing. Our proposed versatile photon sieves are a key breakthrough in focusing technology in the EUV region and pave the way for high-resolution soft X-ray microscopy, spectroscopy in materials science, shorter lithography, and attosecond metrology in next-generation synchrotron radiation and free-electron lasers.