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

Summary form only given. The design of optical systems for micro-focusing of extreme-ultraviolet (XUV) attosecond pulses through grazing-incidence toroidal mirrors is presented. Aim of the configuration is to provide a micro-focused image through a high demagnification M of the XUV source (i.e. M > 10), with almost negligible aberrations.Toroidal mirrors are a cheaper alternative to the use of more expensive Cartesian surfaces (ellipsoidal and paraboloidal), but they give high residual aberrations especially when used to give high demagnification [1]. Furthermore, a configuration with high demagnification using a single mirror has the drawback of the short exit arm q: in fact, once the entrance arm p has been fixed, the higher the demagnification the shorter the exit arm, since q = p/M. The small space available at the exit may be insufficient to accommodate the experimental set-up, therefore an additional mirror to realize a relay section with a suitable length of the exit arm may be required. In addition to this, in case of XUV pump-probe experiments, the beam has to be split in two delayed sections through a plane split-mirror working in parallel beam; this requires to replace the first mirror with a section with a collimating mirror to provide the parallel beam and a condenser mirror to focus and demagnify the two delayed beams. We present two configurations that fulfill these requirements. 1) C1 consists of two mirrors: M1 provides the high demagnification and M2 is the relay section that is required to increase the length of the exit arm. 2) C2 consists of three mirrors: M1 and M2 provide the collimating-focusing section and M3 is the relay section. Both configurations provide a micro-focused image of the XUV attosecond source and a suitable length of the exit arm. Furthermore, C2 provides an intermediate sector with parallel beam where a plane split-mirror may be mounted for XUV pump-probe experiments. The configurations are schematically shown in Fig. 1.The analytical and numerical study of the configurations is discussed. In both cases, the first section provides a stigmatic image of the source in the intermediate plane, that is free from defocusing but has a large third-order aberration, namely coma, due to the high demagnification. The relay mirror is mounted in Z-shaped geometry with respect to the previous one, so that it gives a stigmatic image with a coma that is opposite to that provided by the first section [2]. The mirror geometrical parameters (i.e. the incidence angle and the ratio between its entrance and exit arms) are calculated to give an image that is almost coma-free, since the coma of the second section compensates almost completely for the coma of the first one. Some examples are provided to demonstrate the capability to achieve spot sizes in the 5-15 μm range with a demagnification higher than 10. Finally, the effects of the residual aberrations given by the toroidal mirrors on the sub-femtosecond pulse duration are discussed.