According to one aspect of the present invention, a light emitting diode (LED) structure including an active core layer and at least one substrate layer having a first refractive index, comprises a 2-dimensional photonic quasicrystal in the structure, the photonic quasicrystal comprising an array of regions having a second refractive index, the array exhibiting long range order but short range disorder. The long range order is associated with diffractive properties of the structure and gives rise to uniform-far field diffraction patterns from the LED. The present invention enjoys the benefit of improved light extraction from LEDs without undesirable far field illumination patterns.