  We explore the outcomes of detailed microscopic models by calculating second-
and third-harmonic generation from thin film surfaces with discontinuous
free-electron densities. These circumstances can occur in structures consisting
of a simple metal mirror, or arrangements composed of either different metals
or a metal and a free electron system like a conducting oxide. Using a
hydrodynamic approach we highlight the case of a gold mirror, and that of a
two-layer system containing indium tin oxide (ITO) and gold. We assume the gold
mirror surface is characterized by a free-electron cloud of varying density
that spills into the vacuum, which as a result of material dispersion exhibits
epsilon-near-zero conditions and local field enhancement at the surface. For a
bylayer consisting of a thin ITO and gold films, if the wave is incident from
the ITO side the electromagnetic field is presented with a free-electron
discontinuity at the ITO/gold interface, and wavelength-dependent,
epsilon-near-zero conditions that enhance local fields and conversion
efficiencies, and determine the surface's emission properties. We evaluate the
relative significance of additional nonlinear sources that arise when a
free-electron discontinuity is present, and show that harmonic generation can
be sensitive to the density of the screening free-electron cloud, and not its
thickness. Our findings also suggest the possibility to control surface
harmonic generation through surface charge engineering.
