Research on output spot evolution of multi-pass gain Tm:YLF slab laser based on multi-transverse mode competition

In this paper, the multi-transverse mode competition rate equation model of the Tm:YLF slab laser is established based on the cavity structure of multi-pass gain. As the pump power increased, the changing trend of the number of particles in each mode is analyzed. The direction of beam quality change is also mastered, verified by the three-pass gain laser with the evolution of pump power. Due to the limited compression capacity of the x-axial output spot of the three-pass gain laser, the output spot changes significantly under different cavity lengths and output mirror curvatures. By discussing the output spot evolution, it is known that the large curvature output mirror and the appropriate cavity length can optimize the output spot. Finally, under the pump power of 72 W, the four-pass gain laser obtains a laser output of 1.8 W. It's beam quality is MX2 = 1.77;MY2 = 1.99, the optical–optical conversion efficiency is 2.5 %, and the slope efficiency is 15 %. The beam quality of a three-pass gain laser is MX2 = 2.67; MY2 = 1.70, the optical–optical conversion efficiency is 3.2 %, and the slope efficiency is 11 %. It is verified that the compression of the four-pass gain laser is stronger than that of the three-pass gain laser on the x-axis, laying the foundation for developing a compact multi-pass gain laser.