The invention is a light emitting diode that exhibits high reflectivity to incident light and high extraction efficiency for internally generated light. The light emitting diode includes a reflecting layer that reflects both the incident light and the internally generated light. A multi-layer semiconductor structure is deposited on the reflecting layer. The multi-layer semiconductor structure has an active layer that emits the internally generated light. An array of light extracting elements extends at least part way through the multi-layer semiconductor structure and improves the extraction efficiency for internally generated light. The light extracting elements can be an array of trenches, an array of holes, an array of ridges or an array of etched strips. The light emitting diode improves the efficiency of light recycling illumination systems.