Modeling and optimization of single-pass laser amplifiers for high-repetition-rate laser pulses

Abstract

We propose a model for a continuously pumped single-pass amplifier for continuous and pulsed laser beams. The model takes into account Gaussian shape and focusing geometry of pump and seed beam. As the full-wave simulation is complex we have developed a largely simplified numerical method that can be applied to rotationally symmetric geometries. With the tapered-shell model we treat (focused) propagation and amplification of an initially Gaussian beam in a gain crystal. The implementation can be done with a few lines of code that are given in this paper. With this code, a numerical parameter optimization is straightforward and example results are shown. We compare the results of our simple model with those of a full-wave simulation and show that they agree well. A comparison of model and experimental data also shows good agreement. We investigate in detail different regimes of amplification, namely the unsaturated, the fully saturated, and the intermediate regime. Because the amplification process is affected by spatially varying saturation and exhibits a nonlinear response against pump and seed power, no analytical expression for the expected output is available. For modeling of the amplification we employ a four-level system and show that if the fluorescence lifetime of themore » gain medium is larger than the inverse repetition rate of the seed beam, continuous-wave amplification can be employed to describe the amplification process of ultrashort pulse trains. We limit ourselves to this regime, which implies that if titanium:sapphire is chosen as gain medium the laser repetition rate has to be larger than a few megahertz. We show detailed simulation results for titanium:sapphire for a large parameter set.« less