In this paper, a mathematical model of the thermal stress and thermal strain in the laser medium was presented. An analytical solution was further derived for the thermal stress and thermal strain in the laser rod through the method of Thermoelastic Displacement Potential and the method of Love Displacement Function. The analytical solution results show that under the traction free boundary conditions, the longitudinal rise of fluid temperature has little effect on the thermal stress profile in the laser rod. However, the thermal strain field caused by both the temperature and the thermal stress fields has an evident variation in the longitudinal direction, which will affect the laser transmission characteristics and the beam quality.

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