Résumé
The Fourier Modal Method [1] (FMM) is very popular and efficient approach for modelling diffraction from gratings. It can be applied to graphene gratings either by using the Zero Thickness Model (ZTM) i.e. using directly the optical conductivity of graphene in the boundary conditions, or by using the Finite Thickness Model (FTM) where graphene is seen as a slab of atomic thickness and a relative dielectric permittivity deduced from its optical conduc- tivity. For 1D gratings, the FMM based on the ZTM proves to be very efficient for the transverse electric polarization case (electric filed parallel to the direction of invariance of the strips) but suffers from low convergence in the transverse magnetic polarization case (magnetic filed parallel to the direction of invariance of the strips). This is due to a an inappropriate use of the Fourier factorization rules [1]. The FMM based on the FTM, on the other hand, doesn’t experience such a limitation but at the expense of solving an eigenvalue problem inside the grating which has been given a finite thickness. This is very demanding from the computational point of view because solving an eigenvalue problem has a cost scaling with the third power of the dimension of the matrices in play. This increases the computational cost of the approach especially for crossed gratings. Furthermore, a in a recent work [2], the authors have shown the it is possible to avoid solving this eigenvalue problem if the grating has a deep subwavelength thickness. This condition is exactly fulfilled by graphene under the FTM where it is assumed to have an atomic thickness. I will show that using such a simplification lowers the computational cost of the FMM-FTM while giving reliable and accurate results.