  We study second harmonic generation in nonlinear, GaAs gratings. We find
large enhancement of conversion efficiency when the pump field excites the
guided mode resonances of the grating. Under these circumstances the spectrum
near the pump wavelength displays sharp resonances characterized by dramatic
enhancements of local fields and favorable conditions for second harmonic
generation, even in regimes of strong linear absorption at the harmonic
wavelength. In particular, in a GaAs grating pumped at 1064nm, we predict
second harmonic conversion efficiencies approximately five orders of magnitude
larger than conversion rates achievable in either bulk or etalon structures of
the same material.
