## 1 Introduction--Laser-Assisted Time-Domain Characterization at Free-Electron Lasers
### Ultrafast temporal characterization for novel attosecond X-ray experiments
achieved by X-band radiofrequency transverse deflector (XTCAV) measurements on the spent electron bunch after propagation through the undulator [52]. Very recently, the concept of machine learning has successfully been used for the prediction of XFEL pulse properties, based on the online measurement of numerous accelerator specific parameters [53]. Nevertheless, these techniques all constitute indirect characterization methods and need direct time domain measurements for their exact calibration. **Direct measurement methods**  
The usual characterization techniques for ultrashort optical pulses are not readily transferrable to the X-ray regime. Autocorrelation setups have been developed for VUV wavelengths [54; 55], but are hard to establish in the X-ray range due to the corresponding relatively small nonlinear interaction cross sections and phase-matching bandwidth for most materials, together with the lack of suitable beam splitting and combining optics and the ensuing stability issues. Other standard cross-correlation schemes like spectral phase interferometry for direct electric-field reconstruction (SPIDER) [56] are, on the other hand, hindered by the requirement for reliable phase modulators for X-ray pulses or are restricted to the implementation at seeded FELs [57]. Various methods with solid state targets have been used for FEL characterization, which are based on an FEL-induced transient change of the refractive index of material, as demonstrated in Ref. [58]. The most common scheme remains that of probing the cross-correlation between FEL and IR pulses, and single-shot streaking geometries have been implemented (see e.g., [59]). In general, their temporal resolution is inherently limited by the electron relaxation dynamics in condensed matter, and these measurements are usually destructive towards the X-ray beam. Thus, these concepts are not part of this review dealing specifically with ultrashort XFEL pulse characterization on the femtosecond and sub-femtosecond time scales. For the sake of completeness, we should remind the reader of the particularly noteworthy four-wave mixing scheme pioneered by [PERSON] and co-workers [60; 61], in which the interaction of three photons with matter results in the generation of a fourth \"signal\" photon whose color and direction fulfils the phase-matching conditions; this method probes the third-order nonlinear susceptibility \(\chi^{(3)}\), and although technically more complicated has an enormous advantage in terms of background suppression. Let us finally note that in the framework of high harmonic generation, a four-wave mixing scheme has been successfully used with a gaseous target [62]. In light of the reckoning above, the method of choice to directly measure the ultrashort XFEL pulse duration is the concept of time-resolved optical laser-dressed photoelectron (PE) spectroscopy in gaseous media, which is a well-established technique for temporal characterization of attosecond pulses in the XUV spectral region. This scheme has been theoretically described in [63; 64] and successfully demonstrated in numerous time-resolved measurements of laser-based XUV sources [65; 66; 67]. This setup, shown exemplarily in Figure 2, provides a direct, non-invasive, single-shot, low-photon intensity, photon energy-independent and high-repetition rate-compatible pulse characterization method. The essential parts of the theory for the purpose of the temporal XFEL pulse characterization shall be briefly discussed in the following section. As will be shown, a number of variants of this technique exist, each with their own individual merits for a specific range of X-ray pulse durations and required temporal resolution. While the method relying on the sideband measurement (Section 2) is relatively easy to implement with standard Ti:sapphire laser systems, its information about single X-ray shot characteristics is limited.