Light emitting diode (LED) structures are described that include a first layer and a light-generating layer, wherein light generated in the light-generating layer generally emerges from the LED structure through the upper surface of the first layer. The coupling out of light generated by spontaneous emission is enhanced by the presence of patterning in the first layer, which may take the form of an embedded photonic quasicrystal, a photonic structure comprising an amorphous array of subregions, or a zone plate structure. The invention provides the benefit of improved light extraction from the LED without undesirable far field illumination patterns.