A general solution is presented for the temperature rise produced by the absorption of a scanning Gaussian laser beam in a solid target. In normalized coordinates, the temperature rise is found to depend only on the ratio of the scan speed to the rate of heat diffusion in the solid and the ratio of the beam radius to the absorption depth. For slow scan speeds the solution simplifies to the steady-state approximation in which the power input is balanced by heat conduction into the solid. For fast scan speeds the solution approaches the energy density limit in which the temperature rise is proportional to the integrated beam intensity. For highly absorbing materials the solution simplifies to the surface absorption approximation. The general solution demonstrates the conditions under which each approximation can be used. Similar solutions are found for the related case of pulsed exposure by a stationary beam. The solution is demonstrated experimentally by exposing thermal paper with a CO2 laser.
© 1984 Optical Society of America
Equations on this page are rendered with MathJax. Learn more.