Micro-focusing of soft X-ray pulses by grazing-incidence toroidal mirrors

The design of optical systems for micro-focusing of extreme-ultraviolet (XUV) and soft X-ray pulses through grazing-incidence toroidal mirrors is presented. Aim of the configuration here presented is to provide a micro-focused image through a high demagnification of the source with almost negligible aberrations and a long exit arm to accommodate at the output a large experimental chamber. We present the analytical and numerical study of two configurations to fulfill these requirements with two toroidal mirrors. The first mirror provides a demagnified image of the source in the intermediate plane that is free from defocusing but has a large coma aberration, the second mirror is mounted in Z-shaped geometry with respect to the previous one, in order to give a stigmatic image with a coma that is opposite to that provided by the first one. Some examples are provided to demonstrate the capability to achieve spot sizes in the 5-15 mu m range both applied to high-order laser harmonics and free-electron-laser radiation.