A hollow sphere with a scattering (e.g., white diffusive) interior surface directs light input from at least one input light source to an exit. The exit has a reflective polarizer that passes light of a selected polarization to an output. Light of other polarization(s) is reflected back into the sphere where it becomes unpolarized because of reflections and may eventually be returned to the exit at the selected polarization. The illuminator is well suited as a light source for light management systems of various configurations.