This specification discloses LEDs in which the light emitting active region of the semiconductor diode structure is located within an optical cavity defined by a nanostructured layer embedded within the semiconductor diode structure on one side of the active region and a reflector located on the opposite side of the active region from the embedded nanostructured layer. The reflector may, for example, be a conventional specular reflector disposed on or adjacent to a surface of the semiconductor diode structure. Alternatively, the reflector may or comprise a nanostructured layer. The reflector may comprise a nanostructured layer and a specular reflector, with the nanostructured layer disposed adjacent to the specular reflector between the specular reflector and the active region.