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In this chapter, we discuss the use of reflective diffraction gratings to manipulate the phase of ultrashort pulses in the extreme ultraviolet (XUV) and soft X-ray spectral regions. Gratings may be used to condition the spectral phase of ultrashort pulses, e.g., to compensate for the pulse chirp and compress the pulse, similarly to what is routinely realized for visible and infrared pulses. The chirped pulse amplification technique has been already proposed for soft X-ray free-electron laser radiation; however, it requires the use of a compressor to compensate for the pulse chirp and get closer to the Fourier limit. There are fundamental differences when operating the gratings at wavelengths shorter than ≈40 nm on a broad band: (a) the gratings are operated at grazing inci‐ dence; therefore, the optical design has to be consequently tailored to this peculiar geometry; (b) the grating efficiency is definitely lower; therefore, the number of diffractions has to be limited to two. We discuss the different configurations that can be applied to the realization of a grating stretcher/compressor.

Phase Manipulation of Ultrashort Soft X-Ray Pulses by Reflective Gratings