Two-stage reflective optical system for achromatic 10 nm x-ray focusing

Recently, coherent x-ray sources have promoted developments of optical systems for focusing, imaging, and interferometers. In this paper, we propose a two-stage focusing optical system with the goal of achromatically focusing pulses from an x-ray free-electron laser (XFEL), with a focal width of 10 nm. In this optical system, the x-ray beam is expanded by a grazing-incidence aspheric mirror, and it is focused by a mirror that is shaped as a solid of revolution. We describe the design procedure and discuss the theoretical focusing performance. In theory, soft-XFEL lights can be focused to a 10 nm area without chromatic aberration and with high reflectivity; this creates an unprecedented power density of 10 20 W cm −2 in the soft-x-ray range.