  The repulsion between free electrons inside a metal makes its optical
response spatially dispersive, so that it is not described by Drude's model but
by a hydrodynamic model. We give here fully analytic results for a metallic
slab in this framework, thanks to a two-modes cavity formalism leading to a
Fabry-Perot formula, and show that a simplification can be made that preserves
the accuracy of the results while allowing much simpler analytic expressions.
For metallic layers thicker than 2.7 nm modified Fresnel coefficients can
actually be used to accurately predict the response of any multilayer with
spatially dispersive metals (for reflection, transmission or the guided modes).
Finally, this explains why adding a small dielectric layer[Y. Luo et al., Phys.
Rev. Lett. 111, 093901 (2013)] allows to reproduce the effects of nonlocality
in many cases, and especially for multilayers.
