A light-emitting device includes a semiconductor diode structure with one or more light-emitting active layers, an anti-reflection coating on its front surface, and a redirection layer on its back surface. Active-layer output light propagates within the diode structure. The anti-reflection coating on the front surface increases transmission of active-layer output light incident below the critical angle ΘC. Active-layer output light incident on the redirection layer at an incidence angle greater than ΘC is redirected to propagate toward the front surface at an incidence angle that is less than ΘC. Device output light is transmitted by the front surface to propagate in an ambient medium, and includes first and second portions of the active-layer output light incident on the front surface at an incidence angle less than ΘC, the first portion without redirection by the redirection layer and the second portion with redirection by the redirection layer.