Based on the theory of quasi-three-level rate equations modified by amplified spontaneous emission, the stored energy density and the small signal gain of the cryogenic Yb:YAG regenerative amplifier for a given geometry for pulsed pumping in three dimensions are theoretically studied using the Monte Carlo simulation. The present model provides a straightforward procedure to design the Yb:YAG parameters and the optical coupling system for optimization when running at cryogenic temperature. A fibe
