## 1 Introduction  
Laser pulses as short as a few femtoseconds are nowadays available for high-resolution time-domain spectroscopic applications to many areas of science from solid-state physics to biology [1]. While optical lasers have offered unique insights into ultra-fast femtosecond dynamics, structural arrangement and motion of nuclei are not directly accessible from measured optical properties. Thisgap has been filled by the availability of coherent ultrashort sources in the extreme-ultraviolet (XUV) and soft X-rays, such as high-order laser harmonics (HHs) and free-electron-lasers (FELs). HHs, which are generated through nonlinear interaction between atoms and ultrashort laser pulses, are table-top ultrashort sources with high brightness, coherence and peak intensity [2]. The HH spectrum is described as a sequence of peaks corresponding to the odd harmonics of the fundamental laser wavelength with an intensity distribution characterized by a plateau whose extension is related to the pulse intensity. The combination of the use of advanced phase matching mechanisms and interaction geometries, as well as intense ultrafast laser has made it possible to obtain HH radiation up to the water window region (2.3-4.4 nm) [3,4]. Moreover, the radiation generated with the scheme of the HHs using few-optical-cycles laser pulses is nowadays the main tool for the investigation of matter with sub-femtosecond resolution [5,6]. The use of the XUV emission in a narrow band requires the spectral selection of a single harmonic with a suitable monochromator that has to preserve the temporal duration of the XUV pulse as short as the time resolution required for the experiment. Free-electron-laser (FEL) sources are nowadays available to generate spatially coherent XUV/X-ray radiation with characteristics similar to the light from conventional optical lasers, ultrashort time duration and an increase of 6-8 orders of magnitude on the peak brilliance with respect to third-generation synchrotron sources [7, 8, 9]. Monochromators may be required in FEL beamlines either to increase the spectral purity of the source or to select the FEL radiation at the high harmonics and to filter out the fundamental [10]. The monochromator demanded for the spectral selection of ultrashort pulses has to preserve the temporal duration as short as in the generation process. A time broadening can be tolerated if the pulse duration at the output is maintained anyway shorter than the temporal resolution required by the experiment. For a Gaussian profile with no phase or frequency modulation, the half-height duration \(\Delta\tau\) has a lower limit expressed by:  
\[\Delta\tau=\frac{2\ln 2}{\pi\cdot}\frac{\lambda^{2}}{\Delta\lambda}\cong\frac{0.44}{c}\frac{\lambda^{2}}{\Delta\lambda} \tag{1}\]  
where \(\lambda\) is the pulse central wavelength, \(\Delta\lambda\) is the half-height spectral width of the pulse and \(c\) is the speed of light in vacuum. In order to preserve the pulse duration at the output, the bandwidth that is selected by the monochromator has to be larger than \(\Delta\lambda\) and the transfer function has to be almost constant within the bandwidth. The latter condition is always verified if the monochromator is realized by reflecting optics, since the variations of the reflectivity within the bandwidth \(\Delta\lambda\) are usually negligible. The use of XUV monochromators realized by gratings at grazing incidence is discussed here. A grating introduces inevitably a stretch of the pulse duration by the pulse-front tilt, giving a distortion of the temporal profile of the pulse. In fact, each ray that is diffracted by two adjacent grooves is delayed by \(m\lambda\), where \(m\) is the diffraction order. The pulse-front tilt is given by the total difference in the optical paths of the diffracted beam, that is \(m\lambda\)N, where N is the number of the illuminated grooves. For example, let us consider a 200 gr/mm grating illuminated by radiation at 20 nm over a surface of 10 mm.