Fresnel coefficients and Fabry-Perot formula for spatially dispersive metallic layers

摘要

The repulsion between free electrons inside a metal makes its opticalresponse spatially dispersive, so that it is not described by Drude's model butby a hydrodynamic model. We give here fully analytic results for a metallicslab in this framework, thanks to a two-modes cavity formalism leading to aFabry-Perot formula, and show that a simplification can be made that preservesthe accuracy of the results while allowing much simpler analytic expressions.For metallic layers thicker than 2.7 nm modified Fresnel coefficients canactually be used to accurately predict the response of any multilayer withspatially 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 nonlocalityin many cases, and especially for multilayers.