Optical properties of quasi-two-dimensional systems: Nonlocal effects

We obtain formulas for the reflection amplitude for $s$- and $p$-polarized light of a quasi-two-dimensional system in terms of averages of its conductivity response to the electric and displacement fields. Then we apply our results to a simple model Hamiltonian with parameters adjusted to an inversion layer and to a metallic monolayer in order to compare the reflectance, the ellipsometric coefficients, and the electric field calculated with a nonlocal response versus the ones calculated with several local approximations derived from the same Hamiltonian.