Résumé
In the context of fluctuational electrodynamics, an approach for the computation of the Casimir-Lifshitz force and the near field radiative heat transfer has been established under a unified formalism involving, as a main ingredient, the S matrices of the interacting objects [1]. Thus an important part of the computational effort relies on the efficient evaluation of these matrices. To show how crucial this step can be and how match it deserves attention, we will consider the simple example of graphene strips gratings. The S matrix of such a structure can be obtained through different approaches. The simplest one is the classical Fourier Modal Method (FMM) [2] where the graphene is taken into account through its surface conductivity. This method is very simple but suffers from a serious drawback for it doesn’t handle properly the singularity of the electric field at the level of the strips edges [2]. Another, commonly used, approach is the well-known Rigorous Coupled Wave Analysis (RCWA) in which the graphene strips are given finite thickness and their 2D conductivity is converted into a dielectric permittivity for the resulting rods. This method is more efficient but at a highest computational cost compared to the classical FMM. For this type of structures, we will show that the best approach is the FMM augmented by a set of Local Basis Functions [3] devised to account for the field singularities at the surface of the grating.Bibliography[1] R. Messina and M. Antezza, Scattering-matrix approach to Casimir-Lifshitz force and heat transfer out of thermal equilibrium between arbitrary bodies, Phys. Rev. A 84, 042102 (2011).[2] A. Khavasi, Fast convergent Fourier modal method for the analysis of periodic arrays of graphene ribbons, Opt. Lett. 38, 3009(2013).[3] Y. Jeyar, M. Antezza and B. Guizal, Electromagnetic scattering by a partially graphene-coated dielectric cylinder: Efficient computation and multiple plasmonic resonances, Phys. Rev. E 107, 025306 (2023).