The framework of this thesis is the numerical simulation of the interaction of light with rough metallic surfaces which can be the origin of giant enhancements of the electromagnetic field due to plasmonic resonances. The abrupt profile of these surfaces have characteristic sizes of a few nanometers of width and a few tens of nanometers of height. The main difficulty in the simulation of such phenomena is in the scale difference of the wavelength of the incident wave and the size of the roughness as well as the abrupt variations of the magnetic field at the surface. A suited method of simulation is the numerical resolution of surface integral equations for periodic profile of the surface. This method was implemented in C++ and the main part of this work was the calculation of the pseudo-periodic Green function. The intensity of the refracted beam and that of the electromagnetic field maps are rigorously calculated from the obtained solution. We showed by applying this method that plasmonic resonances situated in the cavity of gratings with Gaussian shaped grooves of nanometric sizes have an electrostatic behaviour similar to that of the rectangular grooves, in particular, a very low specular reflectivity at the resonance. The current performances of computers limit the studies to gratings with a small period. In order to overcome these limitations, we considered a function basis enabling to decompose a functions into its components of different resolutions: the wavelets. This work ends with a discussion on the potential of two different applications of the wavelets to the resolution of integral equations.
