## 4 Seeding Lasers  
The possibility to produce highly coherent soft X-ray externally seeded FEL pulses relies on the capability of the seed laser to imprint its coherence properties into the relativistic electrons through the energy modulation. Such a process critically depends on the laser beam quality. While seeded FEL has been demonstrated to be feasible at a low repetition rate [81], its implementation with FLASH's pulse burst timing structure featuring the in-burst repetition rate of up to 1 MHz is not trivial. In the EEHG mechanism FEL properties, such as wavelength and pulse length, are determined by the second seed laser that is thus required to provide short pulses (50 fs) and tunable wavelength. Moreover, it has also been shown that EEHG spectral properties and coherence critically depend on the quality of the second seed laser beam that is required to be as close as possible to the Fourier limit [92]. The seed laser parameters required for external seeding using the HHGH and EEHG method are summarized in Table 7. The high laser pulse energy required includes some margin to take into account possible losses along the complex laser transport line described in the next section. The seed laser system being developed in-house starts with a powerful picosecond Yb-amplifier chain. The seed laser 1 is generated with a third harmonic generation stage while seed laser 2 is based on a near infrared optical parametric chirped pulse amplifier (OPCPA) which is pumped by the second harmonic of the Yb-amplifier followed by a cascaded sum frequency generation stage (ccSFG). In the ccSFG stage the OPCPA output is mixed with the near-infrared output of the Yb-amplifier twice in two subsequent stages. Figure 5: (**a**) Genesis [83; 84] simulation for a FEL power amplification of the EEHG bunching in the FLASH1 radiator (grey and white areas represent active undulator and drift, respectively); (**b,c**) temporal and (**e,f**) spectral profiles of the FEL after the 4 th and 6 th radiator module, respectively. (**d**) Evolution of the FEL temporal profile (normalized) along the radiator length. The laser system is based on recent developments for the pump-probe laser installed at the European XFEL where a Yb chirped pulse amplifier (CPA) system comprising a Yb:seed oscillator, a Yb:fiber-laser front-end, and a 5 kW burst-mode Yb:YAG InnoSlab amplifier [93]. The system was developed to drive a near infrared OPCPA. The Yb:CPA system for the seeding laser follows these developments and has two 1030 nm center wavelength outputs: a short pulse output, delivering a 3 MHz train of compressed pulses of 300 fs duration and 5 uJ energy and a high energy output, delivering a 1 MHz train of compressed pulses of 800 fs duration and 4 mJ energy. The burst-length is limited to 600 us. Longer bursts would lead to significant changes in beam size and pointing of the high energy output due to thermal transients in the InnoSlab amplifiers. The fixed wavelength of the seed laser 1 pulse is generated straight forward via third harmonic generation of a 0.3 mJ portion of the compressed high energy output. Simulations and preliminary experiments showed that we can generate more than 100 uJ pulse energy of approximately 600 fs duration which fulfils the requirements for the seed laser 1 pulse. The generation of the tunable seed laser 2 relies on an efficient chirped sum frequency generation scheme [94]. First the short IR pulse output drives a white-light supercontinuum which is amplified in a first broad-band non-collinear optical parametric amplifier (NOPA) to more than 300 nJ. These ultra-broadband seed pulses are negatively chirped by dispersive mirrors in order to match the pulse duration of the second harmonic of the high energy output. Their bandwidth supports 50 fs pulses after amplification in two sub-sequent NOPA stages to more than 200 uJ. The output is tunable between 680 nm and 950 nm by adjusting the delay between seed and pump pulses.