## 1 Introduction  
The so-called \"burst mode\" is a special operation scheme for a pulsed laser system. In this mode, the system produces pulses at a relatively high energy and repetition rate, for a short period in time, ranging from some microseconds to several tens of milliseconds. After this so-called \"burst\", a time period without laser operation allows for thermal relaxation of the system. During the burst, the laser system approaches the efficiency of a continuously-pumped system, while due to the limited time of operation, the cooling requirements for the components are vastly reduced in comparison to continuously-operated systems with a similar output power. This finally allows one to realize comparably small systems with outstanding performance parameters. In addition to these advantages, several applications have been developed that specifically use the unique parameters offered by a burst-mode laser. Among these are, for example, the detection of fast processes in combustion diagnostics with methods like particle image velocimetry (PIV), planar laser-induced fluorescence (PLIF) analysis, planar Rayleigh scattering or planar Doppler velocimetry (PDV) [1; 2; 3; 4]. Furthermore, such pulse bursts may be applied in laser ablation [5; 6] or in photoinjectors, which are used to create electron pulses in conventional particle accelerators [7]. A crucial point for the usability of such a laser as a tool in science and industry is a well-defined energy distribution between the different pulses within the burst. So far, in most cases, a uniform distribution is desired. Due to the characteristics of the subsequent amplifiers, the generation of such an energy distribution throughout the amplified pulse burst is a demanding task already. There are, e.g., changes in the gain due to various reasons, like unbalanced extraction and excitation or heating of the material. These effects lead to specific burst shapes after amplification, similar to those observed in Ti:sapphire systems [8]. Such an unbalanced extraction can be precompensated by adjusting the initial inversion at the beginning of the burst. An equilibrium value can be obtained, e.g., by fine-tuning the start time of the pump with respect to the arrival of the pulse burst [7; 9; 10]. Other effects with sufficiently long time constants, like the heating of the active medium, can be partly counteracted by, e.g., a temporal modulation of the excitation. Though the application of these techniques has already allowed for the generation of very stable bursts, they do not allow for the generation of bursts with an arbitrary energy distribution. Such a possibility could further broaden the range of applications. For example, it has been demonstrated in materials processing that the diameters and deformations of laser-drilled holes could be reduced by applying temporally-modulated pulse bursts [11]. Here, we present a method using a Pockels cell with fixed peak voltage and rise time for shaping the bursts. Since the laser pulse duration can be considered to be very short as compared to the Pockels cell's switching time, temporally shifting the laser pulse across the rising edge modulates its polarization. Hence, in combination with a polarizing optic, the transmitted pulse energy can be varied arbitrarily. This allows one to generate bursts with a freely adjustable energy distribution and, additionally, to pre-compensate any amplitude modulations introduced by the following amplifiers. A similar technique to shape femtosecond laser pulse bursts after amplification, but within a passive cavity, has recently been published [12]. There, the disadvantage is that the splitting of the pulses occurs only after amplification. Shaping at this point of the amplifier chain implies that a single short pulse isto be amplified in advance. As the acceptable fluence within the amplifier is significantly lower for a single pulse than for a burst, this reduces the amplifier efficiency, particularly for materials with a high saturation fluence, such as Yb:CaF\({}_{2}\).