Nonlocal Fourier modal method for analyzing nonlocal plasmonic periodic nanostructures

In accordance with growing scientific interests in nanoplasmonic structures, along with the increasing ability to fabricate them using proper nanotechnologies, we have developed a methodology to incorporate nonlocal optical responses, described with a simple hydrodynamic model, into the numerical Fourier modal method (FMM) technique to enable broadening of the simulation portfolio of such physical phenomena in plasmonic nanostructures. Here, we have newly incorporated the nonlocal response approximation (NRA) into the periodic FMM technique (called NonLocFMM) described with a proper hydrodynamic model, and we show in several examples that this implementation is capable of numerically analyzing periodic plasmonic systems, such as nonlocal periodic multilayers and resonant gratings. The implementation was performed in such a way that a future possible generalization of the hydrodynamic nonlocal description will be feasible, as well as the aperiodization of the technique. Such an extension is, indeed, viable and will be the subject of a subsequent paper.