## 3 Linear Streaking Measurements at Free-Electron Lasers
### Photoelectron streaking  
In a conventional streak camera, the temporal profile of the incident photon pulse is imprinted on an electron wavepacket through photoemission. The electronic wavepacket--or in the case of high X-ray intensities--the burst of photoelectrons is subsequently deflected transversely by a fast voltage ramp. In this way, the temporal profile of the incident light pulse is mapped to the spatial coordinate on the electron detection screen. Due to energy dispersion in the photocathode and limitations in the gradient of the voltage ramp, the temporal resolution that can be achieved in a conventional streak camera is limited to the picosecond level.  
To reach few-femtosecond or even sub-femtosecond resolution, a similar concept is applied in the attosecond streak camera. Here, the electromagnetic field of a near-infrared laser pulse is used to project the temporal properties of the X-ray pulse onto a photoelectron wavepacket created through ionization of a noble gas.  
In state-of-the art attosecond physics, a carrier-envelope phase-stable few-cycle laser pulse at a central wavelength of 750 nm is used to generate attosecond XUV pulses through high harmonic generation [6]. The resultant XUV pulses are intrinsically synchronized to the field of the driving laser pulse, assumed to be fully coherent and additionally assumed to be identical from shot to shot. Attosecond streaking spectroscopy was first applied to characterize these XUV pulses.  
Figure 7 shows a sketch of a typical experimental setup and illustrates the basic principle of streaking. The X-rays eject electrons from gas atoms via the photoelectric effect, and set them free with a kinetic energy equal to the X-ray photon energy minus the specific electron binding energy of the atomic shell. These photoelectrons can be described as free electron wave packets for our experimental conditions. The temporal structure of the generated photoelectron wave packet mimics that of the incoming XFEL pulse and its width is directly related to the X-ray pulse duration [93].  
For the streaking measurement, the XUV pulse is focused on a noble gas target and temporally and spatially overlapped with an intense laser pulse (the temporal overlap can be adjusted by varying the optical path lengths between the XUV and NIR beams). Photoelectrons emitted during the streaking pulse are accelerated by an amount that depends on the instantaneous electric field amplitude or vector potential \(A(t)\) at the precise moment of ionization. For the polarization and detection oriented as in Figure 7, the shift in kinetic energy relative to the field-free case is given by:  
\[\Delta W(t_{0})\approx e\sqrt{\frac{2W_{i}}{m_{e}}}A(t_{0}), \tag{1}\]  
where \(W_{i}\) is the initial kinetic energy of the photoelectron, and \(e\) and \(m_{e}\) are the electron charge and mass. For extended XUV pulses, the variation of the laser electric field during the photoemission results in different final momenta for electrons ejected at different times. If the photoemission is confined to within one half-cycle of the laser field (1.25 fs for a carrier wavelength of 750 nm), the initial kinetic energy distribution of the photoelectrons released by the XUV pulse from the noble gas target will be uniquely broadened and shifted by the overlapping NIR streaking field. In general, the temporal profile and spectral phase of the ionizing XUV pulse can be determined by analyzing the broadening of the detected photoelectrons.  
Scanning the relative delay between the ionizing XUV pulse and NIR streaking pulse allows consecutive measurements to be accumulated and a time-resolved spectrogram to be constructed. By applying an appropriate retrieval algorithm [94], the streaking pulse and XUV pulse, with temporal profile and spectral phase can be retrieved from this multi-shot measurement.