Light-emitting devices, and related components, systems and methods are disclosed. A light-emitting device can include a multi-layer stack of materials including a light-generating region and a first layer supported by the light-generating region. During use of the light-emitting device, light generated by the light-generating region can emerge from the light-emitting device via a surface of the first layer. The light-emitting device can have an edge which is at least about one millimeter long and can be designed so that an extraction efficiency of the light-emitting device is substantially independent of the length of the edge. The surface of the first layer may have a dielectric function that varies spatially according to a pattern. The pattern may be nonperiodic.