3D modeling of metamaterials at oblique incidence and effective analysis
Résumé
The straightforward modeling of a metamaterial at its characteristic scale is a broad issue. The use of the “material” word implies that one can measure macroscopic quantities from it (such as an effective permittivity or an effective permeability). This approach has yet to be validated for any angle of incidence. The dependence of the refractive index on this angle becomes especially strong when the system is in the grazing incidence configuration, or as it starts guiding light. An effective model thus becomes of great importance if one wants to model the behavior of complex integrated devices based on metamaterials. The studies presented here have been done as part of the ANR METAPHOTONIQUE project, whose first purpose is to design metametarials operating on top of SOI guiding structures (Silicon on Insulator) at 1.55 micron. We present results of 3D simulations, done through the FDTD method, of a metamaterial of which the optical response has been computed at normal incidence and oblique incidence. We show that the full properties - the permittivity and permeability tensors - of such structures can be retrieved numerically thanks to that data and the use of optimization methods. We then study the range of validity of the effective index model, and if this model applies in the guided light configuration.