Theory of multilayers heated by laser absorption

In this paper solutions of the heat conduction equation are presented for multilayer samples heated by a periodically modulated axisymmetric laser beam. The sample may contain any number of thin layers on a thick substrate. This new theory combines exact optical absorption, multilayers, contact resistance between layers, and ease of calculation. The solutions are based on a local Green's function formalism, and no approximations are made as to the form of absorption of energy in the sample from the heating laser. The method involves integral transforms (Fourier and Hankel) and the normal component of the heat fluxes across the layer boundaries can be found analytically in transform space. To calculate temperatures in real space one numerical integration is required. Temperature results are presented in the form of magnitude and phase plots at the frequency of the modulated laser beam. One application for these results is photothermal deflection experiments for the measurement of thermal conductivity in multiple films on a thick substrate. The temperature and beam deflection calculations are very efficient and can be carried out easily on a personal computer.