## Simulation of Solid-State-Lasers

Simulation of the physical processes in a laser cavity is helpful for designing laser with optimal beam quality and output power. These simulations include ray-tracing for pump light, thermal lensing effects in crystal, beam calculation and simulation of population inversion by rate equations. One issue is to simulate the optical laser beam inside the resonator in order to estimate output power and beam quality. For this purpose, we have developed a new method called the dynamic mode analysis (DMA). The idea of this method is to approximate a laser beam by a set of Gaussian modes. The power of each mode can be calculated by rate equations. Figure 1(a) shows the calculated output beam and Figure 1(b) the corresponding population inversion. The subject of an ongoing research project is to extend the dynamic mode analysis for passive Q-switch lasers and intra-cavity frequency doubling.

The use of Gaussian modes is restricted to certain lasers with low or medium output power. However, in case of high output power, a more accurate simulation technique is required. The Finite Element method is suitable for this purpose. Figure 2 shows a comparison between these methods for a simple resonator consisting of a crystal and two mirrors at both end faces. This method is being extended for more general laser resonators in the framework of another ongoing research project.

References:

- B. Heubeck and C. Pflaum and G. Steinle. New Finite Elements for Large-Scale Simulation of Optical Waves, SIAM J. Sci. Comput. 31(2), pages 1063-1081, (2008).
- M. Wohlmuth, C. Pflaum, K. Altmann, M. Paster, and C. Hahn. Dynamic multimode analysis of Q-switched solid state laser cavities, Optics Express , Vol. 17, Issue 20, pp. 17303-17316, 2009.
- Wohlmuth M., Altmann, K., Hemmer M., Goehre M., Pflaum C., Richardson M., Proceedings of "Dynamic Multimode Analysis of High-Power Lasers with Super-Gaussian Beam Profile Using Precombined Gaussian Modes" , OSA ASSP 2010, AMB25 (2010).
- Wohlmuth M. and Pflaum C.: Dynamic multimode analysis of high-power 3-level lasers. Physics Procedia Volume 5, Part 2, Pages 291-298. (2010).
- Wohlmuth M., Altmann K., Pflaum C.: New Approaches for the Dynamic 3-D Simulation of Solid-State Lasers, Proceedings of OSA ASSP 2009, OSA ASSP 2009, TuB20 (2009).
- Wohlmuth M., Altmann K., Pflaum C: Finite Element simulation of solid state laser resonators. Proceedings SPIE 7194, 7196-16 (2009).
- Wohlmuth M., Altmann K., Werner J., Pflaum C.: Dynamic 3D modeling of solid state laser resonators using a coupled thermo-optical finite element analysis. In: Proc. SPIE 7578 (2010).

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