In this article we illustrate important characteristics of the diffraction of cold atoms from periodic light potentials generated from coupling a light wave to dielectric nanostructures. We apply a recently developed theoretical approach to investigate the behavior of Cs atoms dropped onto a periodically modulated optical dipole potential where the period of the modulation is controlled by the periodicity of the dielectric array. These nanostructures take the form of one-dimensional line gratings or two-dimensional point gratings. We discuss several important parameters critical to the successful realisation of laboratory experiments and future atom-optical instrumentation using this new kind of atomic diffraction medium.