  In the framework of the hydrodynamic model describing the response of
electrons in a metal, we show that arrays of very narrow and shallow metallic
slits have an optical response that is influenced by the spatial dispersion in
metals arising from the repulsive interaction between electrons. As a simple
Fabry-Perot model is not accurate enough to describe the structure's behavior,
we propose to consider the slits as generalized cavities with two modes, one
being propagative and the other evanescent. This very general model allows to
conclude that the impact of spatial dispersion on the propagative mode is the
key factor explaining why the whole structure is sensitive to spatial
dispersion. As the fabrication of such structures with relatively large gaps
compared to previous experiments is within our reach, this work paves the way
for future much needed experiments on nonlocality.
