  We theoretically predict efficient optical second-harmonic generation (SHG)
from a few hundred nanometer thick slab consisting of a quadratic nonlinear
anisotropic medium whose linear principal permittivities are, at the
fundamental wavelength, very small and have different signs (indefinite
medium). We show that, by illuminating the slab with a p-polarized fundamental
wave (with intensity of a few MW/cm^2), a highly efficient scattering of the
second-harmonic field occurs when the conditions of linear complete slab
transparency for the fundamental wave are met. The high efficiency of the SHG
process, stems from the large non-plasmonic enhancement of the longitudinal
field, perpendicular to the slab surface, produced by the very small value of
the slab dielectric permittivities. A suitable nano-structured composite is
proposed and numerically designed for observing the novel non-phase-matched and
highly efficient SHG process from nano-structures.
