An illuminator is disclosed, in which an LED module emits short-wavelength light toward a phosphor module, which absorbs it and emits wavelength-conditioned light. The emission is generally longitudinal, with a generally Lambertian distribution about the longitudinal direction. The phosphor module includes a transparent layer, closest to the LED module, and a phosphor layer directly adjacent to the transparent layer. Both layers are oriented generally perpendicular to the longitudinal direction. The illuminator includes a reflector, circumferentially surrounding the emission plane in the LED module and extending longitudinally between the emission plane and the transparent layer. Virtually all the light emitted from the LED module either enters the phosphor module directly, or enters after a reflection off the reflector. The transverse side or sides of the transparent layer support total internal reflection, so that virtually all the light that enters the transparent layer, from the LED module, is transmitted to the phosphor layer. In some applications, the phosphor layer is located at the focus of a concave mirror, which can narrow and/or collimate the light emitted by the phosphor. Adjacent to the phosphor layer and opposite the transparent layer, the phosphor module can include a transparent dome, a heat sink, or nothing.