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-mode 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 one to reproduce the effects of nonlocality in many cases, and especially for multilayers.

• Received 10 January 2017
• Revised 14 June 2017

DOI:https://doi.org/10.1103/PhysRevB.96.041406