Two-color photoionization in XUV-FEL and laser fields

We address several questions related to the nonlinear ionization processes observed when atoms are in the simultaneous presence of intense and coherent infrared (IR) and extreme ultraviolet (XUV) laser pulses. This topic is of much interest in the context of the current development of new XUV coherent sources, either from high-order harmonics or from freeelectron laser (FEL) devices, like the one available at FLASH in Hamburg, that can be synchronized with IR lasers. In this paper, we discuss the advantages and limitations of the so-called soft-photon approximation, which, we will show here, provides most useful insights in the analysis of different processes involving these two fields.