A light engine kernel for a light emitting diode (LED) includes a solid body of transparent material having an index of refraction of at least 1.5. The body has a domed, light-emitting top that is an inverted parabola of revolution, a reflective sidewall that is a compound parabolic concentrator (CPC), and a cavity at a focus of the CPC that is adapted to receive an LED. The domed top may include a phosphor coating of a yellow-emitting phosphor. The cavity may be adapted to receive only a single LED or plural LEDs of the same or different colors on a board. The kernel and LED are not integrally formed, reducing thermal degradation of the phosphor coating and improving application flexibility.