Numerical tool to take nonlocal effects into account in metallo-dielectric multilayers.

We provide a numerical tool to quantitatively study the impact of nonlocality arising from free electrons in metals on the optical properties of metallo-dielectric multilayers. We found that scattering matrices are particularly well suited to take into account the electron response through the application of the hydrodynamic model. Though effects due to nonlocality are, in general, quite small, they, nevertheless, can be important for very thin (typically below 10 nm) metallic layers, as in those used in structures characterized by exotic dispersion curves. Such structures include those with a negative refractive index, hyperbolic metamaterials, and near-zero index materials. Higher wave vectors mean larger nonlocal effects, so that it is not surprising that subwavelength imaging capabilities of hyperbolic metamaterials are found to be sensitive to nonlocal effects. We find in all cases that the inclusion of nonlocal effects leads to at least a 5% higher transmission through the considered structure.