A high-radiance broadband incoherent light source is provided by pumping a body formed from a doped material, such as a Ce:YAG crystal with one or more laser diodes. The laser diodes emit at a stimulus wavelength, which may be an absorption wavelength of the body, and the body fluoresces to emit broadband light in a wide emission band. The body is either disposed in, or forms a light-concentrating cavity, e.g., reflective surfaces, which may be dichroic surfaces, can be formed on or attached to the sides of the body to concentrate the emitted light. The light is captured by a light collector that is coupled to an output face of the body to produce a broadband illumination beam. One or more of the reflective surfaces forming the light-concentrating cavity may form a heat sink.