Romanian Reports in Physics, Vol. 65, No. 3, P. 997–1005, 2013 Dedicated to Professor Valentin I. Vlad’s 70 th Anniversary THE DETERMINATION OF TWO PHOTON THERMAL FIELDS IN LASER-TWO-LAYER SOLIDS WEAK INTERACTION USING GREEN FUNCTION METHOD M. OANE 1 , R. MEDIANU 1,* , G. GEORGESCU 1 , D. TOADER 1 , A. PELED 2 1 National Institute for Laser, Plasma and Radiation Physics, Str. Atomistilor 409, Magurele, 077125, Romania 2 Holon Institute of Technology, 52 Golomb Str., Holon 58102, Israel *E-mail: rares.medianu@inflpr.ro Received March 26, 2013 Abstract. The goal of this paper is to improve our previous model; which considered the thermal fields for laser-periodic multilayer structures interaction. Our new model, based on the assumption of a weak interaction, takes into account non-linear effects like two photon absorption. It is assumed that the laser beam is in the IR and the interaction between the laser field and target (for example optical components) is weak, thus one can consider a small variation for the laser intensity. The Green function method, is used since it is a more adequate technique to solve the heat equations. Since the heat equation is a linear one in the sense that we have two solutions of the heat equation, than the sum of solutions is also a solution of the same heat equation, it is possible to use this property in order to “manipulate” the heat equations. Our approach is for a 1D model. Key words: heat equation, Green function method, two-photons, multi-layer. 1. INTRODUCTION Many practical applications require the detailed study of the thermal behavior of various systems. The difficulties arise when these systems are inhomogeneous with respect to the parameters involved in the heat diffusion process. Currently, the heat diffusion equation has no analytical solution for this case. However a wide range of methods exist to approximate the solution of the heat diffusion equation in inhomogeneous systems, starting from the numerical methods and ending with the exact analytical solution for a few particular cases, each of them in turn presenting specific advantages and disadvantages [1-6].