A high efficiency, and possibly highly directional, light emitting diode (LED) with an optimized photonic crystal extractor. The LED is comprised of a substrate, a buffer layer grown on the substrate (if needed), an active layer including emitting species, one or more optical confinement layers that tailor the structure of the guided modes in the LED, and one or more diffraction gratings, wherein the diffraction gratings are two-dimensional photonic crystal extractors. The substrate may be removed and metal layers may be deposited on the buffer layer, photonic crystal and active layer, wherein the metal layers may function as a mirror, an electrical contact, and/or an efficient diffraction grating.