## 3 Linear Streaking Measurements at Free-Electron Lasers
### Experimental implementation
Recording the photoelectron spectrum with the TOF spectrometer consequently enables characterization of the FEL pulse (reproduced with permission from [103], Copyright Nature Publishing Group, 2012). A characteristic single-shot measurement reproduced from reference [103] is shown in Figure 19. The streaked spectrum is shown in panel a. The retrieved temporal profile, with conversion map as a dashed line, is shown in panel b. The statistical error in the single-shot spectrum is calculated according to the number of electrons collected within the energy resolution window of the detector. As the photoelectron spectrum is heavily oversampled, boxcar integration is performed across the spectrum, resulting in a smooth error envelope that bounds the measured spectrum. The reconstructed FEL pulse exhibits a dominant central feature with a width of (53 \(\pm\) 5) fs FWHM and has weaker satellite features at approximately 100 fs from the main peak. The temporal profile shown in Figure 19 is given on a time base that is locked to the laser that generates the streaking THz pulse. This information can be condensed into a single arrival timestamp by calculating the center-of-mass of the retrieved FEL pulse profile. To evaluate the short-term timing jitter at FLASH \(\sim\)450 consecutive FEL pulses, collected near time-zero were analyzed. The results are  
Figure 19: Single-shot FEL pulse profile. (**a**) Example of a measured streaked photoelectron spectrum. The shaded error envelope is calculated by boxcar integration, based on the number of electrons collected within the TOF energy resolution window of the time-of-flight spectrometer. The blue dots are raw data points in the measured streaked spectra. Orange curve shows the spectra after Fourier filtering to remove high-frequency noise. Blue curves are filtered, streaked spectra following deconvolution of the photoelectron spectrometer resolution. (**b**) Retrieved temporal profile for this FEL shot. Orange and blue curves are the mapped intensity structures corresponding to the Fourier-filtered spectrum and the deconvolved spectrum in panel (**a**), respectively. The energy-to-time conversion map is depicted as the dashed gray line in panel (**b**), with the corresponding energy axis on the right (reproduced with permission from [103], Copyright Nature Publishing Group, 2012). Figure 18: Proof-of-principle streaking measurement at FLASH. (**a**) The single-cycle THz electric field. (**b**) Single-shot spectrogram composed of 12,000 consecutive shots. (**c**) The averaged spectrogram, with approximately 400 shots binned at each 100-femtosecond time step. The duration of the THz streaking ramp is indicated by the dashed white lines in the right panel, giving the dynamic range of the measurement, which is \(\sim\)600 fs. (Figure from [95]). displayed in Figure 20. The shot-to-shot analysis is shown in panel (a), and the distribution of arrival times, which is the timing jitter, is shown in panel (b). The Gaussian fit to the distribution has a width 87 fs rms, which is a measure of the short-term timing jitter between the FEL and the pump-probe laser. This value is consistent with the expected performance of the electronic laser synchronization [83]. The accuracy of the relative arrival time information is mainly influenced by the stability of the mean FEL photon energy. During our measurements, it fluctuated with a level of 1 eV rms, which corresponds to a time-of-arrival uncertainty of ~6 fs rms. THz generation in LiNbO\({}_{3}\) is attractive, as the rise time of the streaking field is ~600 fs, resulting in a dynamic range that allows for measurement of all pulses, with lengths that can exceed 100 fs in duration. But the streaking power is limited. Alternatively, THz streaking fields can be generated by collinear optical rectification of infrared laser pulses in the organic electro-optic salt 4-\(N\),\(N\)-dimethylamino-4\({}^{\prime}\)-\(N^{\prime}\)-methyl-stilbazolium toyslate (DAST).