  We present a microscopic theory of the amplified spontaneous emission of a
spectrally broadband quantum dot superluminescent diode within the quantum
white noise limit. From this multimode quantum theory, we have the ability to
obtain all orders of temporal correlation functions. In particular, we derive
rate equations for the optical power densities, the level occupation of
inhomogeneous ensemble of quantum dots within the diode, as well as the emitted
optical spectra. As the main result, we find the external power spectrum as a
convolution of the intra-diode photon spectrum with a Lorentzian response.
Assuming a Gaussian light-matter coupling results in a similar shaped Gaussian
output spectrum, which agrees very well with available experimental data.
