Modeling and Simulation of Solid‐State Lasers: From Mathematics to Industrial Application

Solid‐state lasers are widely used for different industrial applications ranging from material processing to medical applications. For designing and optimization of a solid‐state laser an accurate simulation tool is need. Such a simulation tool has to be able to simulate different kind of physical effects like thermal effects, depolarization caused by stress inside a laser crystal, non‐linear gain, and mode competition. In order to calculate output power and beam quality, we apply an extension of the dynamic mode analysis concept (DMA) (see [1]). This model is based on a 3‐dimensional discretization of population inversion and a system of complex rate equations. The resulting mathematical equation system is a large system of ODE's, which has to be solved by a suitable method including time step control. The difficulty in such a simulation is the extreme change of parameters. As a consequence the output signal might be a pulsed signal with high output power of pulse width 1 ns and time period 1 ms. In order to solve such a system of ordinary differential equations accurately, we present a suitable numerical method. Simulation results with industrial applications are presented.