Poly-Si crystallization mechanism is examined by conducting numerical simulations, combining the thermal diffusion equation with a rigorous coupled wave analysis method. The ripples at the boundary of poly-Si grains are modeled as a grating surface structure. Under laser beam irradiation, the melting front profiles are accurately analyzed by including surface diffraction, polarization of the laser, and laser energy density. For two different lasers, XeCl excimer laser (λ = 308 nm) and Yb:YAG solid state laser (λ= 343 nm), the energy density range at which poly-Si grains are gradually ordered was determined. Furthermore, the energy density window of the Yb:YAG laser is found to be four times larger than that of XeCl laser. On the other hand, the Yb:YAG laser may produce amorphous-Si phase after completing the crystallization process. It is suggested that this amorphous-Si phase could be avoided, if a double pulse laser is used.