Laser-induced temperature distributions and thermal deformations in sapphire, silicon, and calcium fluoride substrates at 1.315 μm

Some expressions for temperature distributions and thermal deformations of silicon, sapphire, and calcium fluoride window substrates at 1.315 μm are derived in terms of Green's function methods. Profiles for temperature rise and thermal deformation as functions of laser power, irradiating time and cylindrical coordinates are given. The calculated results show that under conditions of irradiating by a 10-kW intense laser with Gaussian shape, maximum temperature rises in Al 2 O 3 , CaF 2 , and Si substrates are 5.6°C, 6.0°C, and 35°C, respectively. The amounts of thermal distortion in Al 2 O 3 , CaF 2 , and Si substrates is 0.28, 0.99, and 0.40 μm, respectively. At the initial stage of substrate laser irradiation, the temperature rises and thermal deformation increases quickly. After about 2 s, the increments of the temperature and thermal deformation become small. The trend of thermal deformation versus the heating time is in relative agreement with our experiment.