  We predict and experimentally observe the enhancement by three orders of
magnitude of phase mismatched second and third harmonic generation in a GaAs
cavity at 650nm and 433nm, respectively, well above the absorption edge. Phase
locking between the pump and the harmonics changes the effective dispersion of
the medium and inhibits absorption. Despite hostile conditions the harmonics
become localized inside the cavity leading to relatively large conversion
efficiencies. Field localization plays a pivotal role and ushers in a new class
of semiconductor-based devices in the visible and UV ranges.
