Micro-focusing of attosecond pulses by grazing-incidence toroidal mirrors

The design of optical systems for micro-focusing of extreme-ultraviolet (XUV) attosecond pulses through grazing-incidence toroidal mirrors is presented. Aim of the proposed configuration is to provide a micro-focused image through a high demagnification of the XUV source with the following characteristics: i) almost negligible aberrations; ii) long exit arm to easily accommodate at the output the experimental setups required for the applications of the focused attosecond pulses; iii) possibility to have an intermediate region where the XUV beam is collimated, in order to insert a plane split-mirror for the generation of two XUV pulse replicas to be used in a XUV-pump/XUV-probe setup. We present the analytical and numerical study of two optical configurations characterized by two sections based on the use of toroidal mirrors. The first section provides a demagnified image of the source in an intermediate focus that is free from defocusing but has a large coma aberration. The second section consists of a relay mirror that 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 section. An example is provided to demonstrate the capability to achieve spot sizes in the 5-15 μm range with a demagnification higher than 10 in a compact envelope.