  We investigate second harmonic generation, low-threshold multistability,
all-optical switching, and inherently nonlocal effects due to the free-electron
gas pressure in an epsilon-near-zero (ENZ) metamaterial slab made of
cylindrical, plasmonic nanoshells illuminated by TM-polarized light. Damping
compensation in the ENZ frequency region, achieved by using gain medium inside
the shells' dielectric cores, enhances the nonlinear properties. Reflection is
inhibited and the electric field component normal to the slab interface is
enhanced near the effective pseudo-Brewster angle, where the effective
\epsilon-near-zero condition triggers a non-resonant, impedance-matching
phenomenon. We show that the slab displays a strong effective, spatial
nonlocality associated with leaky modes that are mediated by the compensation
of damping. The presence of these leaky modes then induces further spectral and
angular conditions where the local fields are enhanced, thus opening new
windows of opportunity for the enhancement of nonlinear optical processes.

Optics