## 2 Sideband Method for X-ray Pulse Characterization
In this case the emission of Auger electrons rather than photoelectrons can be measured instead, but still a de-convolution procedure and a comparison with simulated spectra has to be applied to extract the information about the X-ray pulse duration (Figure 5). Figure 5: Auger sideband spectra. (**a**) NIR-dressed neon Auger electron energy spectra as a function of the relative delay time \(\delta\) between the NIR (\(\tau_{\rm NIR}\) = 100 fs) and the X-ray pulses (\(\tau_{\rm X-ray}\) = 75 fs); (**b**) Comparison of experimentally obtained cross-correlation widths with those calculated within the soft-photon approximation (SPA) using the following parameters (in full width at half maximum (FWHM)): \(\tau_{\rm X-ray}\) = 40 fs–140 fs, \(\tau_{\rm NIR}\) = 100 fs and \(\delta\) = 140 fs, \(I_{\rm NIR}\) = 1.2 \(\times\) 10\({}^{12}\) W cm\({}^{-2}\) (reproduced with permission from [51], Copyright IOP Publishing, 2011). **X-ray pulse characterization including polarization**  
Sidebands were also used to determine other characteristics of the X-ray photon beam, namely its degree of polarization. For the first experiment using linearly polarized FEL and NIR pulses, it was demonstrated that the sideband intensity depends in a sensitive and characteristic way on the relative orientation between the two linear polarization vectors [88]. Since this dichroic effect is caused by a different ratio of the partial waves contributing to the outgoing electron (e.g., s- and d-waves in case of a two-photon ionization in He), which can be calculated very precisely by theory, it can in turn also be used to determine the degree of polarization of the FEL beam. This was demonstrated at FERMI, the first seeded FEL producing circularly polarized X-ray pulses [10]. By measuring the circular dichroism in the electron angular distribution of the first sideband (Figure 6), it was possible to determine the degree of circular polarization as well as the sign of the helicity. The measured value for the polarization at the experimental station (about 95%) [89] is in excellent agreement with estimates, taking into account an almost perfect polarization at the end of the undulator and the contribution from the optical elements of the beamline. A similar method, i.e., the measurement of the circular dichroism in the sideband yields of electrons emitted from the inner shell of molecular oxygen, was also applied for the determination of the degree of circular polarization produced by the DELTA undulator at LCLS [90]. Here, the above discussed issue concerning the sideband separation in relation to the relatively large bandwidth of a SASE based XFEL was overcome by dressing the molecules with a frequency-doubled optical laser, ensuring a sufficient energy spacing of the individual sidebands. All these examples show that the measurements of sidebands, which are produced by the simultaneous interaction of the X-ray pulse and the NIR dressing field, provide detailed information about the X-ray pulse characteristics, especially on the pulse duration, the relative arrival time and its degree of polarization. This will certainly be used in future experiments at new, not yet well-characterized FEL facilities, but also the investigation of the dynamics of the two-color photoionization in itself is still of large interest. These measurements will permit a focus on particular  
Figure 6: Angle-resolved spectra and dichroism. Experimental (top) and simulated (bottom) angle- and energy-resolved electron spectra (**a**,**b**) and circular dichroism (**c**,**d**) in He 1s photoionization at low NIR laser intensity (\(7.3\times 10^{11}\) Wcm\({}^{-2}\)). The respective intensities are indicated by the color scales on top of the graphs (reproduced with permission from [89], Copyright Nature Publishing Group, 2014). aspects of the ionization process, e.g., the intensity dependence of the electron angular distribution or near-threshold phenomena [86; 91].