A light-emitting device includes a substrate that is at least partially transparent to optical radiation and has a first index of refraction. A diode region is disposed on a first surface of the substrate and is configured to emit light responsive to a voltage applied thereto. An encapsulation layer is disposed on a second surface of the substrate and has a second index of refraction. An antireflective layer is disposed between a second surface of the substrate and the encapsulation layer. The antireflective layer has a graded index of refraction having values in a range between about the first index of refraction at a first surface of the antireflective layer and about the second index of refraction at a second surface of the antireflective layer. The encapsulation layer may also be omitted and the antireflective layer may separate the substrate, which has a first index of refraction, from air, which has a second index of refraction. Non “flip-chip” embodiments are also disclosed.