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

Abstract

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.