The interaction between light and matter is usually modeled by approximating the material under study as a continuum. The magnitude of the material's polarization in the presence of an electric field is dependent on the atomic response via the well-known Lorentz-Lorentz relation. These continuous medium models can be used to see many light-matter effects including non-linear interactions.The goal of this thesis is to adapt and use novel computational methods to explore the microscopic origins of non-linear optical effects. The Microscopic Particle-in-Cell (MicPIC) technique, initially developed to model the laser-driven dynamics of strongly-coupled plasmas, is extended to study the non-linear scattering of light by a collection of dipoles in the atomic limit. In this thesis, we find that in one-dimensional chains of individual scatterers there are apparent boundary effects and the generation of even harmonics that do not appear in continuous media calculations.These finite structures of dipoles also exhibit a lower average response from each at odd harmonic frequencies of the driving light frequency.These results are in contradiction with the commonly used Lorentz-Lorenz relation, derived for a dipole in a 3D material with infinite volume, and suggest that MicPIC is more appropriate for calculations of nanostructures than models using the Lorentz-Lorenz relation.