In this article we illustrate important characteristicsof the diffraction of cold atoms from periodic light potentialsgenerated from coupling a light wave to dielectric nanostructures.We apply a recently developed theoretical approach to investigatethe behavior of Cs atoms dropped onto a periodically modulatedoptical dipole potential where the period of the modulation iscontrolled by the periodicity of the dielectric array. Thesenanostructures take the form of one-dimensional line gratings ortwo-dimensional point gratings. We discuss several importantparameters critical to the successful realisation of laboratoryexperiments and future atom-optical instrumentation using this newkind of atomic diffraction medium.