Simulation and experimental improvement of a pulsed Cr,Tm,Ho:YAG (CTH:YAG) laser is presented. In order to simulate the CTH-Laser a generalized version of the Dynamic Mode Analysis (gDMA) is introduced, which includes an abstract formalism to describe arbitrary rate equations. This novel version of DMA enables the coupling between individual modes of the resonator and the complex excitation dynamics of the CTH state system. With the proposed method gDMA a full 3D simulation was conducted and the beam quality of the generated pulses could be calculated for various crystal diameters. Based upon the simulation results the crystal diameter was decreased in experiment. This reduction led to an improvement of M from 36 to 27, which is in good agreement with the experimental results. Additionally, the pulse energy depending on the pump power exhibits a close agreement with the experimental measurements. Moreover, the strength of each interionic mechanism in Cr,Tm,Ho:YAG is analyzed and the back transfer from Holmium to Thulium is identified to be the most dominant loss source for stimulated emission at 2090 nm. All in all, the presented extension of DMA represents an accurate and efficient method to simulate the amplification of higher order modes in gain media with strong interionic mechanisms.
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