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Computer modelling of solid state laser systems

A computer modelling program has been developed to model the extraction of an ideal 4-level laser system based on the equations of Franz and Nodvik (1963) with the capability of handling realistic temporal shapes of the pump pulse and various overlap geometries of the pump and laser radiation. Two different simulation programs are used to account for different laser pumping geometries. A cylindrical geometry is used for axial pumping, and a Cartesian geometry is used for transverse pumping. In both cases, the laser beams and gain medium are divided into smaller radial and axial zones according to the geometry in use. Absorption of the pump radiation and amplification of output radiation is calculated separately for each cell of the gain medium. Overlap fractions are used to determine the amount of energy from the pump and extraction beams which are present in a particular gain zone. The simulation algorithm calculates absorption and amplification within the gain region for each time step then propagates the laser and pump radiation forward one time step. The fraction of spontaneous emission that propagates along with the laser beam is also amplified but accounted for separately from the laser beam for amplifier systems. The simulation program calculates the spatial and temporal profile of the output pulse energy and accompanying ASE. The geometry assumes collimated or diverging wavefronts for the laser radiation with different beam radii for different passes to allow simulation of expanding beam or unstable resonator geometries. Currently the modelling code is being used to simulate oscillation and short pulse amplification in Ti:sapphire crystals. Initial comparisons with published experimental results show close agreement with the simulation. The ultimate goal will be to model the performance of multistage short pulse amplifier systems.