2025/07/01 by Gabriel Ybarra Marcaida, Marcaida, Gabriel Ybarra
Computer Science · Engineering · #Advanced Optical Imaging Technologies #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Interactive and Immersive Displays #Mathematical Physics (math-ph) #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.2507.00820
openalex publication_date 2025/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 L2 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.