Objective Laser is a device that can emit high energy radiation, and its excellent characteristics make it to be widely used and paid attention to by researchers in various fields. Its most important part is the laser crystal. During the operation of the laser, the crystal will generate a lot of heat inside the crystal because of the crystal thermal effect such as quantum deficit, and cause the gradient distribution of stress and crystal deformation, which seriously affects the beam quality of the laser. Therefore, studying the thermal effect of crystals is an important step to design and manufacture lasers with high beam quality. In this paper, through the simulation of the working state of the laser, the monitoring of the temperature field and stress field inside the crystal is tested, so as to provide data and theoretical support for better laser design.

Methods In order to simulate the working state of the laser and monitor the temperature field and stress field, the model conditions are simplified based on the actual situation. The temperature distribution in the crystal is analyzed by the Poisson equation in the thermodynamic theory, and the stress distribution in the incident direction is analyzed by the mechanical theory. Then the geometric model is established by finite element analysis, and the theoretical model close to the working state of the crystal is obtained by combining them. The boundary conditions around the crystal are analyzed and the physical field constraints are given to the model. Finally, the control variable method is used to analyze the variables in the system.

Results and Discussions  The initial conditions are as follows. The model size is 3 mm×3 mm×4 mm, doping concentration is 5.0 at.%, absorption coefficient of 940 nm pump light is 5.6 cm⁻¹, thermal conductivity is 0.13 W·cm⁻¹·K⁻¹, Gauss order is 1, cooling temperature T₀ is 291 K. The coefficient of thermal expansion is 7.8×10⁻⁶ K⁻¹. When the laser pump power is 50 W and the spot radius of the pump surface is 400 μm, the maximum temperature rise of the pump end face is 59.2 K (Fig.3), the maximum stress on the system is 2.380×10⁸ N/m² (Fig.8), and the maximum deformation is 6.456 7×10⁻⁴ mm (Fig.9). When only temperature gradient is considered, the relationship between thermal focal length and power is obtained (Fig.10). If other conditions remain unchanged, when the Gauss order is 1, 2, and 3 respectively, the corresponding maximum temperature rise of the pump end face is 59.18 K, 75.24 K, and 83.99 K (Fig.5). If other conditions remain unchanged, when the half-diameter of the pump light spot is 300 μm, 350 μm, 400 μm, 450 μm, and 500 μm respectively, the corresponding maximum temperature rise of the pump end face is 105.21 K, 77.30 K, 59.18 K, 46.76 K, and 37.88 K (Fig.6). If other conditions remain unchanged, when the pump power is 50 W, 60 W and 70 W respectively, the maximum temperature rise of the reaction is 59.18 K, 71.02 K and 82.85 K (Fig.7).

Conclusions The light energy distribution is a function of power, spot radius and Gaussian order, and the properties reflected by power, spot radius and Gaussian order are the properties of light energy distribution, and it can be seen that the light energy density is positively correlated with the temperature field and stress field. In addition, the temperature field, stress field and thermal stress variables are also positively correlated. There are many factors affecting thermal focal length, but the most important one is temperature gradient distribution.