An illumination device has a dual-emitting LED die structure in which a first p-n diode structure emits primary light having a peak at a first wavelength, and a second p-n diode structure emits primary light having a peak at a second wavelength that is longer than the first wavelength. A phosphor medium is positioned to be stimulated by the primary light of the dual-emitting LED die structure, and in response emits secondary, wavelength converted light, thereby contributing to a combined white illumination. Other embodiments are also described and claimed.