  Using a hydrodynamic approach we examine bulk- and surface-induced second and
third harmonic generation from semiconductor nanowire gratings having a
resonant nonlinearity in the absorption region. We demonstrate resonant,
broadband and highly efficient optical frequency conversion: contrary to
conventional wisdom, we show that harmonic generation can take full advantage
of resonant nonlinearities in a spectral range where nonlinear optical
coefficients are boosted well beyond what is achievable in the transparent,
long-wavelength, non-resonant regime. Using femtosecond pulses with
approximately 500 MW/cm2 peak power density, we predict third harmonic
conversion efficiencies of approximately 1% in a silicon nanowire array, at
nearly any desired UV or visible wavelength, including the range of negative
dielectric constant. We also predict surface second harmonic conversion
efficiencies of order 0.01%, depending on the electronic effective mass,
bistable behavior of the signals as a result of a reshaped resonance, and the
onset fifth order nonlinear effects. These remarkable findings, arising from
the combined effects of nonlinear resonance dispersion, field localization, and
phase-locking, could significantly extend the operational spectral bandwidth of
silicon photonics, and strongly suggest that neither linear absorption nor skin
depth should be motivating factors to exclude either semiconductors or metals
from the list of useful or practical nonlinear materials in any spectral range.
