In accordance with growing scientific interests in nanoplasmonic structures, along with the increasing ability to fabricate them using proper nanotechnologies, and current interest in nonlocal optical responses, first, 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. It is generally accepted that nonlocal interactions are most pronounced on structures with nanometer unit sizes and affect the shape of spectral functions of characterizing quantities in the resonance region. We have relied on our previous profound experience, mainly with the periodic (for one-dimensional - 1D and two-dimensional - 2D cases) extensively to various rather complex problems. Here, based on this experience, we have newly incorporated the nonlocal-response approximation into the periodic FMM technique, described with a proper hydrodynamic model, showing in several examples that this implementation is capable of numerically analyzing periodic plasmonic systems, such as nonlocal periodic multilayers and resonant gratings. Secondly, for some simple structures it is possible to find analytical solutions which can then be used to build semi-analytical approaches for the analysis of some more complex structures. Thus the second part is focused on the analytical description of nonlocal manifestations of both a planar metal layer and a bilayer, using the transfer matrix approach.
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