A study of the axisymmetric thermal strain in a laser rod with longitudinal temperature rise

This paper presented a mathematical model of the axisymmetric thermal stress and thermal strain in the laser medium. Then an analytical solution was derived through the Thermoelastic Displacement Potential method using a Love Displacement Function. The analytical results show that under the traction-free boundary conditions, the longitudinal rise of fluid temperature has an unnoticeable effect on the thermal stress profile in the laser rod; however, the thermal strain field has an evident variation in the longitudinal direction, which will significantly affect the laser transmission characteristics and the beam quality. Numerical simulation was also performed for the thermal stress and thermal strain in the laser rod by using the temperature distribution obtained from the conjugate numerical simulation as the thermal load. The numerical results agree well with the analytical solution in the main section of the laser rod except that it better exhibits the end effects.