## 2 Sideband Method for X-ray Pulse Characterization  
**Temporal pulse characterization with photoelectrons**  
Two-color photoionization experiments using the combination of intense free-electron laser femtosecond pulses in the extreme ultraviolet (XUV) to X-ray wavelength range and optical or NIR pulses offer great potential to determine the temporal characteristics, i.e., pulse durations and the relative temporal arrival time, of the FEL pulses. Although studies of two-color photoionization of atoms in weak resonant optical/NIR fields are well established at synchrotron radiation facilities [70], it is only with the availability of short wavelength FELs that experiments have been performed, in which electrons ejected by the XUV or X-ray field can also be effectively \"dressed\" by the intense NIR laser field. Overlapping the two intense ultrashort pulses temporally and spatially in a gaseous target leads to the appearance of additional structures in the photoelectron spectrum, which are the clear indication of the two-color process. Ionization by the XUV or soft X-ray pulse creates electrons with typically a few tens and up to few hundreds of eV kinetic energy. The additional interaction with the intense NIR fields induces absorption or emission of NIR photons resulting in extra lines in the photoelectron spectrum (Figure 3a) spaced by the photon energy of the NIR photons (1.55 eV for 800 nm) (e.g., [71]). These lines are called'sidebands' and are ideal candidates for a first characterization of the FEL pulses. In addition, the quasi-monochromaticity of the FELs makes it possible to observe, for high dressing fields, absorption and emission of more than one NIR photon [72; 73], avoiding interference effects present in similar experiments with broader-bandwidth XUV pulses of high-harmonic-generation sources [74]. In the following we will always use the term 'X-ray' for the FEL pulses, meant to cover the  
Figure 2: General setup for laser-dressed photoelectron spectroscopy. Typical experimental setup and measurement principle for a two-color ultrafast temporal characterization measurement. The picture shows the experimental setup in the atomic, molecular and optical science (AMO) hutch at the Linac Coherent Light Source (LCLS). The X-ray laser and the near-infrared (NIR) dressing laser are coupled into the vacuum chamber and are collinearly focused onto a neon gas target. The generated photoelectrons are then energy resolved with a magnetic bottle electron spectrometer. The inset on the left depicts two distinctive cases of temporal overlap of the XFEL with respect to the streaking field, one at the zero crossing and one at a maximum of the NIR vector potential. The respective photoelectron spectra are also shown. More details are given in the text in Section 3.1.1 and in Figure 7 (reproduced with permission from [69], Copyright Nature Publishing Group, 2014). whole spectral range from XUV (>10 eV) over soft X-rays (>100 eV) to hard X-rays (>5 keV), to discern them from other short-wavelength sources as e.g., high harmonic-generated XUV pulses. Besides using the sideband structures in the photoelectron spectra for the study of photoionization dynamics in strong external fields, the sideband intensity provides a clear indication of the temporal and spatial overlap between the FEL and the NIR laser beams. Since sidebands appear only when the two laser pulses overlap (see Figure 3b), their intensity exhibits a characteristic dependence on the relative time delay between the ionizing and the dressing pulses. For free-electron lasers based on the SASE process, such as FLASH, LCLS and SACLA, the X-ray and NIR pulses are generated separately by the FEL and the optical laser system. These two independent sources are only linked by a common externally working synchronization system [76]. Although the synchronization has been improved tremendously during the last years <30 fs root mean square (rms) [77], the pulse-to-pulse arrival time fluctuations exceed very often the pulse durations of the two pulses.