Deducing the Talbot Effect from Electrodynamics

We propose a model based on Maxwells equations to describe the Talbot effect. After solving the model analytically, we prove that its solution is equivalent to the one amply found in the literature in the asymptotic limit. By considering the paraxial limit, we showcase how the rational Talbot effect arises, and derive an ideal paraxial distribution that would give such effects. We give a proof of $L^2$ convergence to these ideal distributions for any such grating. The universal nature of the Talbot effect makes our findings pertinent for a variety of physical systems and technological applications.