Temperature distributions and thermal deformations of mirror substrates in laser resonators

For finite-thickness media with convective surface losses, the three-dimensional temperature distributions and thermal deformations of mirror substrates in laser resonators that are due to absorption of laser light with a Gaussian power-density profile are calculated by use of the well-known Green's function methods. Some expressions and theoretical profiles of the temperature distributions and thermal deformations as functions of the radius and the thickness of a mirror substrate are obtained. The results of the calculations show that the rise in temperature is closely related to the absorption coefficient of the medium as well as to the convective heat-transfer coefficient, that the initial thermal deformations of mirror surfaces increase quickly at the beginning of laser heating and that then the thermal deformations are insensitive to laser heating times. Meanwhile, thermal deformations of a silicon mirror are experimentally demonstrated by use of CO(2) laser irradiation. The experimental trends of thermal deformations are in agreement with the theoretical profiles.