Heat Diffusion Near Absorbing Centers in Laser Materials

The solutions to the heat diffusion equation for spherical absorbing centers in laser materials are presented. The ratio of the volume specific heats for the absorbing center and the laser host is found to determine three regions of behavior. Series expansions for small times and for very large times also are given in each of the three regions. Rapidly converging representations for the complementary error function of complex arguments are developed in order to evaluate numerically the region for which the volume specific heat ratio is greater than three fourths.