Résumé
Periodic nanostructures play an important role in fluctuation-induced phenomena such as Casimir-Lifshitz forces and near-field radiative heat transfer, but their numerical analysis can become costly when rigorous electromagnetic solvers are used. This work presents a simplified version of the Fourier Modal Method (FMM) for the study of periodic media. Starting from the standard FMM formulation, where the electromagnetic fields are expanded in Fourier space and propagated through each layer via matrix exponential operators, we introduce a first-order Taylor approximation of the propagation operator for sufficiently thin grating layers. This simplification replaces the exponential dependence by a linear form, significantly reducing the computational burden while preserving the general structure of the method. The resulting model keeps the same truncation framework as the classical FMM and is especially well suited to nanostructures whose corrugation height is small compared with the wavelength. Numerical validations performed on representative systems, including metallic crossed gratings and graphene strip gratings, show very good agreement between the simplified and classical formulations in the thin-layer regime. These results indicate that the simplified FMM is an efficient and accurate tool for studying radiative heat transfer andrelated dispersion-force phenomena in periodic nanostructures.