## 2 Experimental Setup
The Pockels cell assembly for the generation of the shaped bursts is implemented directly behind the Satsuma seed laser system, just before the stretcher. At this point, the single-pulse duration is about 350 fs. This ensures that there is no significant impact on the single pulse duration by the Pockels cell switch, even if it is operated at the rising edge, as described before. The shaping assembly consists of a double KD*P Pockels cell (Levsop Ltd., Basildon, UK) followed by a polarizer. The input polarization is aligned, such that initial transmission is low and pulses can pass only if the voltage is applied. During the burst duration, every single pulse is switched separately. The Pockels cell driver (Bergmann Messgerate Entwicklung KG, Murnau, Germany) uses a push-pull configuration to allow for short opening times, which minimizes the energy dissipation at the 1 MHz repetition rate phase. Temporal control of the Pockels cell is realized with a delay generator card (BME_SG08p, Bergmann Messgerate Entwicklung KG, Murnau, Germany) synchronized to the internal fs-oscillator of the seed laser using the signal of an internal photo diode. The on-board memory of this delay generator allows one to store 251 delay settings for each channel. For every trigger event, the next delay is applied, allowing one to use different delays for the individual pulses. To achieve a total of one thousand different delays, according to the number of pulses within a single pulse, four of the six output channels are bundled via a trigger combination circuitry, which also ensures a constant delay of 30 ns between the on and off switch of the cell. These on/off trigger events are finally distributed to the trigger inputs of the two push-pull high voltage switches of the Pockels cell driver to achieve an alternating polarity of the voltage at the Pockels cell for consecutive pulses. This is achieved by a so-called splitter box (Bergmann Messgerate Entwicklung KG, Murnau, Germany). This alternating voltage polarity mode is an essential measure to avoid piezoelectric ringing of the cell, which could otherwise disturb the precise control of the laser pulse amplitude, due to fluctuations in the polarization of the laser pulse after passing the cell. All measurements presented in the following were carried out using two photo diodes DET100A (Thorlabs GmbH, Munich, Germany), one measuring light leaking through a plane mirror before the Pockels cell and one after the shaping section. The results are based on the relative height of both signals with respect to each other to compensate for pulse-to-pulse variations of the energy of the seed laser. A direct measurement was not possible, since the pulse-to-pulse energy fluctuations were comparably large (about \(\pm 30\%\)). Despite this measure, not all instabilities could be removed, as the energy instability of our front-end laser had also some influence on the temporal synchronization, which can be seen as a high frequency oscillation of the measured amplitudes. The reason for this is the voltage level of the photo diode used for synchronization. A fluctuation in the pulse energy in the oscillator therefore transfers into a jitter, since the level is reached at different times. For a better visibility of the shaping effect, this noise was removed in the following by applying a band stop filter to the data. The unfiltered data points are also displayed as light grey curves in the background.