Modeling and simulation of ultra-short pulse amplification

Ultra-short pulses with high average power are required for a variety of technical and medical applications. Single, multi-pass, and regenerative amplifiers are used, in order to increase the power of ultra-short lasers. Typical laser crystals for such amplifiers include Ti:Sapphire or Yb:YAG laser crystals. Difficulties in the amplification of ultra-short pulses include gain narrowing effects and dispersion effects in the laser crystal. In particular, these complications arise, when a pulse stretcher is needed before amplification of the laser beam. We present a technique to model and simulate the amplification of ultra-short pulses. This technique allows to model both gain narrowing effects and decrease of beam quality caused by amplification of the laser beam. This requires a detailed 3-dimensional simulation of population inversion. Gain narrowing effects are taken into account by analyzing the gain of the spectrum of the laser beam. It is important to distinguish amplifiers with one or only two passes and a regenerative amplifier. These two different kind of amplifiers are modeled by different approaches. A regenerative amplifier is modeled by a set of time dependent rate equations. However, a single pass amplifier is modeled by a set of spatial dependent rate equations. In both cases, a system of rate equations arises from spectral discretization of the laser beam. Detailed simulation results are presented.