Spatial distribution of temperature rise induced by a Gaussian laser beam

Abstract

An analytic solution has been found for the steady state temperature rise induced by a laser beam with a Gaussian radial extent exp(−r2/w2) and exponential absorption, exp(−αz). Numerical results are presented for Si. The rapid decrease of thermal conductivity with increasing temperature causes our solution of the nonlinear heat conduction equation to give a much larger temperature rise than would be produced using the linear heat conduction equation with the room temperature conductivity.