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