  We study electromagnetic pulse propagation in an indium tin oxide nanolayer
in the linear and nonlinear regimes. We use the constitutive relations to
reconstruct the effective dielectric constant of the medium, and show that
nonlocal effects induce additional absorption resonances and anisotropic
dielectric response: longitudinal and transverse effective dielectric functions
are modulated differently along the propagation direction, and display
different epsilon-near-zero crossing points with a discrepancy that increases
with increasing intensity. We predict that hot carriers induce a dynamic
redshift of the plasma frequency and a corresponding translation of the
effective nonlinear dispersion curves that can be used to predict and quantify
nonlinear refractive index changes as a function of incident laser peak power
density. Our results suggest that large, nonlinear refractive index changes can
occur without the need for epsilon-near-zero modes to couple with plasmonic
resonators. At sufficiently large laser pulse intensities, we predict the onset
of optical bistability, while the presence of additional pump absorption
resonances that arise from longitudinal oscillations of the free electron gas
give way to corresponding resonances in the second and third harmonic spectra.
A realistic propagation model is key to unraveling the basic physical
mechanisms that play a fundamental role in the dynamics.
