Temperature rise induced by a laser beam II. The nonlinear case

The steady‐state solution of the nonlinear heat‐conduction equation when the thermal conductivity is strongly temperature dependent is expressed (for arbitrary geometry and heat source) in terms of the corresponding solution for the linear heat‐conduction case. This permits a closed‐form expression for the maximum temperature rise when a Gaussian laser beam hits the surface of a crystal, as well as integral representations for the spatial distribution of the temperature rise. This solution is essential in understanding laser annealing.