## 3 Linear Streaking Measurements at Free-Electron Lasers
### Experimental implementation
#### 3.1.2 Laser-Driven Terahertz Streaking for Complete Temporal Characterization
At this temporal overlap, the arrival time as well as the temporal profile and duration of the FEL pulse can be accessed with highest resolution. If the streaked photoelectron spectrum is significantly broader than the initial bandwidth of the ionizing FEL pulse, the temporal profile of the FEL pulse can be recovered directly from the measured spectrum. In this case, also referred to as the strong streaking regime, the energy gradient that is imprinted onto the electron wavepacket by the streaking field is much larger than the initial energy variation caused by an FEL pulse with an initial energy chirp. As a result, the degree of spectral broadening is assumed to depend only on the duration of the FEL pulse and the gradient of the THz streaking field. To make a calibrated transformation from the streaked photoelectron spectra to the time domain, the THz vector potential must be known. Due to timing jitter at FELs, the vector potential cannot typically be determined directly from the streaking spectrogram as is the case in attosecond spectroscopy. Rather, at XFELs the transformation map is determined in a two-step process. First, the electric field shape is evaluated independently by electro-optic-sampling. Second, the electric field is scaled by evaluating a distribution of streaking measurements over all possible time delays. Measurements that overlap with a maximum of the vector potential result in maximal kinetic energy shift, as depicted in Figure 14, panel b. The maximum kinetic energy shift can then be inverted to determine the absolute THz electric field strength:  
\[\Delta W_{\text{max}}\approx\frac{e\lambda_{L}}{\pi c\sqrt{2m_{e}}}\sqrt{W_{i}} E_{0} \tag{4}\]  
Here, \(\lambda_{L}\) is the streaking laser wavelength, \(E_{0}\) is the maximum electric field, \(W_{i}\) is the initial electron energy and \(c\) is the velocity of light in vacuum. With the transformation map and under the assumptions listed above, the temporal profile of the FEL pulse can be retrieved from a single-shot streaked spectrum as illustrated in Figure 15.  
THz streaking can be used to simultaneously determine the arrival time of the FEL pulse. But, it is important to note that the information provided by this diagnostic is far more complete than a simple arrival time. In fact, the FEL pulse profile is given on a time-base defined by the THz streak ramp that is locked to the experiment environment, if the same femtosecond laser pulse that is used the generate the THz streaking pulse is also used to pump dynamics in an independent experiment. With this complete information, it is possible to define a single point as the \"arrival time\". This point could be given by the center-of-mass of the FEL pulse, or the position of the peak intensity of the FEL pulse, or at a certain  
Figure 14: Schematic of FEL pulse characterization by THz streaking. Three distinct measurements are depicted in frames (**a–c**). FEL induced photoemission from a noble gas, which replicates the FEL temporal profile (black filled area), is broadened and shifted, or “streaked”, depending on the instant of overlap with the THz pulse. The THz streaking pulse electric field is shown in blue, while the corresponding vector potential is drawn in red in all three panels. On the right vertical axis, the resulting kinetic energy of the photoelectrons is indicated: in black the field-free spectrum, defined by the SASE FEL bandwidth in the unstreaked case (**a**), and in gray spectra for the streaked cases, at overlap with an extremum (**b**) or at the zero-crossing (**c**) of the THz vector potential. In (**c**), overlap occurs near the zero-crossing of the THz vector potential where the arrival time and temporal profile can be accessed with the highest resolution (reproduced with permission from [103], Copyright Nature Publishing Group, 2012). intensity threshold. The exact definition would depend on the dynamics being observed, but crucially, any definition can be chosen when the pulse is characterized on an experimentally relevant time base.