## 4 Outlook  
### Angular Streaking--Full Time-Energy SASE Pulse Retrieval  
All intensity dependent experiments at free-electron lasers are highly affected by the effective pulse durations and SASE caused sub-spikes in the XFEL pulses. Mostly, such experiments rely on  
Figure 24: Chicane delay vs. two-color pulse delay measured with the PALM, and their correlation \(\rho\) (reproduced with permission from [110], Copyright Optical Society, 2017). Figure 25: Arrival time accuracy as a function of electron kinetic energy, as shown in [109] (reproduced with permission from [109], Copyright Optical Society, 2014). The blue crosses are the data points, while the red curve is the square root function that best fits them. pulse energy measurements by gas detectors or other methods averaging over the intensity distribution of the XFEL pulses. However, the physical processes under investigation often depend on the peak intensity, which is hidden in the unresolved spike structure of the pulses. In addition to the strong impact on the broad field of non-linear physics, developments towards mode-locking [114; 115; 116] and the generation of X-ray pulses on the attosecond timescale [34; 35; 36; 37] are currently in progress and will ultimately originate the scientific field of attosecond X-ray physics. This imminent breakthrough demands unprecedented time resolution for the temporal characterization of the structure of SASE XFEL pulses under various modes of operation. Such possibilities desperately need a direct single-shot method to diagnose not merely the X-ray pulse duration, but also the full temporal coherence properties of the XFEL pulses including the spectral chirp of the X-rays and the stochastic sub-spikes of the SASE pulses. Another essential requirement for every ultrafast experiment that relies on a synchronized optical laser for pump or probe is precise information about the relative arrival time between the two lasers. Steady progress in this regard has been made [51; 52; 58; 69; 101; 103; 117; 118; 119; 120], as was demonstrated throughout this review, and electron acceleration designs relying on superconducting linear accelerators [19; 20] open up even better prospects for temporal synchronization [121]. Nevertheless, a complete and direct single-shot measurement in the time domain that reports both the exact XFEL pulse temporal structure and arrival time simultaneously and which is applicable over a broad range of X-ray pulse durations remains elusive. A possible solution to all these challenges could be the method of two-color angle-resolved circular streaking spectroscopy of photoelectrons or Auger electrons, dubbed 'angular streaking' in the following for brevity. The measurement builds on the above described experiences with linear X-ray photoelectron streaking spectroscopy [69; 103]. The need for a measurement technique capable of coping with varying pulse shapes and arrival times with respect to the lab time frame on a shot-to-shot basis is recognized and taken into account in this setup by employing a streaking laser with circular polarization in combination with a ring-like arrangement of 16 high-efficiency time-of-flight spectrometers [122]. This scheme has recently also been theoretically described [123; 124] and evaluated for application at realistic XFEL parameters by a quasiclassical description supported with numerical calculations based on a quantum-mechanical approach (see Figure 26). Figure 26: Simulation of circular streaking. Color-scaled streaking spectra as a function of the emission angle of photoelectrons produced by an ultrashort X-ray pulse (FWHM of the field is 2.8 fs) assisted by the THz field of 1.7 \(\times\) 10\({}^{10}\) W cm\({}^{-2}\) intensity, 300 fs duration and 28.2 THz frequency. The electron kinetic energy (without the THz field) is 100 eV. In the inset, the X-ray and THz pulses are shown in arbitrary units. Time (in fs) is counted from the onset of the THz pulse. The black and red lines are, respectively, the \(x\)- and \(y\)-component of the THz field.