Analytic and numeric modeling of diode laser pumped YB:YAG laser oscillators and amplifiers

A series of analytic and numeric models were developed and are presented, for quasi three level Yb:YAG laser oscillators and amplifiers. These models were applied to published experiments for Yb:YAG thin disk laser oscillators. Good agreement was obtained between our model and both earlier models and published experimental results. Unlike earlier models, ours are specifically suitable for modeling high power laser oscillators and amplifiers employing a strongly pumped Yb:YAG gain medium. We applied our analytic model to predict the upper limit of the performance of a multi thin disk Yb:YAG laser amplifier operating at 77 K neglecting thermal gradient induced lensing, birefringence and bending of the thin disk. Our modeling showed that the considered multi thin disk Yb:YAG laser amplifier system can generate laser output with very good beam quality while maintaining high extraction efficiency. Our analytic modeling results on the strongly pumped Yb:YAG thin disk was confirmed by our numeric model. As a zeroth order approximation, we applied the analytic model to evaluate the extraction efficiency of an Yb:YAG slab amplifier system. Our modeling showed that a slab shaped Yb:YAG gain medium is much more efficient than a disk shaped gain medium for the same volume of Yb:YAG crystal operating at the same temperature. A very efficient computer code was developed to model the laser dynamics in a slab shaped Yb:YAG gain medium with only about 10% error due to neglecting diffraction.