Temporal pulse shaping aspects of refractive X-ray lenses

Refractive X-ray lenses are frequently used components at modern X-ray free-electron laser facilities. This work investigates the temporal effects of refractive optics on ultra-short X-ray pulses, particularly focusing on pulse elongation. We present a model using full Fresnel theory to study the beam profile at the focus in space and time. Refractive X-ray lenses not only change the temporal structure of the pulse, the focus size is also dependent on the incoming pulse duration. Further, we present a simplified ray-tracing model to estimate the pulse stretching effect of compound refractive lenses (CRLs), which we find to be dependent only on the dispersion and the absorption of the CRL material.