Disclosed herein are light emitting diodes (LEDs) having a high efficiency. A light emitting diode including an active light emitting layer within a semiconductor layer is provided. The semiconductor layer has a mesa shape. The light emitting diode also includes a substrate having a first surface on which the semiconductor layer is positioned and an outcoupling surface opposite to the first surface. Light generated by the active light emitting layer is incident on the outcoupling surface and propagates toward an optical element downstream of the outcoupling surface. The light emitting diode also includes a first anti-reflection coating adjacent to the outcoupling surface; an index-matched material between the outcoupling surface and the optical element, wherein an index of refraction of the index-matched material is greater than or equal to an index of refraction of the optical element; and/or secondary optics adjacent to the outcoupling surface.