A light-emitting device (300) includes a substrate (305) that is at least partially transparent to optical radiation and has a first index of refraction. A diode region (315, 320, 325) is disposed on a first surface (310b) of the substrate and is configured to emit light responsive to a voltage applied thereto. An encapsulation layer (370) is disposed on a second surface of the substrate and has a second index of refraction. An antireflective layer (365) is disposed between a first surface (310a) of the substrate (305) and the encapsulation layer (370). The antireflective layer (365) 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 (365) and about the second index of refraction at a second surface of the antireflective layer (365). The encapsulation layer (370) may also be omitted and the antireflective layer (365) may separate the substrate (305), which has a first index of refraction, from air, which has a second index of refraction. Non “flip-chip” embodiments are also disclosed.