Recently, the use of an atomic force microscope silicon-nitride tip as a scanning near-field optical microscope probe to collect the optical near field close to a surface, has been successfully demonstrated. However, several questions about such a setup are still unanswered : the influences of the surface topography and the polarization of light on the imaging process are not clearly understood : the scattering cross sections of the reflected and transmitted light are not accurately estimated. With the aim of clarifying these questions, in this article we propose numerical simulations performed on a two-dimensional model of a SiN tip within the framework of the Green’s function technique. The treatment provides precise calculations of the near and far fields by exploiting an iterative numerical scheme based on the parallel use of the Lippman-Schwinger and Dyson’s equations. A remarkable result demonstrates that a branch of the SiN tip acts as an optical waveguide. Consequently, a significant amount of light is scattered in directions where scanning near-field optical microscope setups using SiN tips do not detect, A modification of the experimental configuration leading to the detection of this signal is suggested.