Green's method for solving the Helmholtz scalar equation with applications to refractive index media

In this work, we present a formalism based on scalar Green’s functions to deal with electro-magnetic scattering problems. Although the formulations of the Mie theory and Born approximations in terms of electromagnetic scattering are well known and relevant, they have certain disadvantages; complexity, computational time, few symmetries, etc. Therefore, the study with scalar Green functions allows one to deal with these problems with greater simplicity and efficiency. However, the information provided by the vector formulation is sacrificed. Nevertheless, different cases of electromagnetic scattering of dielectric media with different dimensions, geometries, and refractive indices will be presented. Thus, we will be able to verify the capacity of this scalar method to predict light scattering problems.