The new definition of the beam propagation factor for partially coherent light is proposed through the propagation equations of the cross-spectral density.

This kind of beam needs more study on its propagation properties in dispersive media, as well as the beam propagation factor (originally called beam quality factor).

The concept of the beam propagation factor M2 is extended for chromatic laser beams. The definition of the beam propagation factor can be generalized with the weighted effective wavelength.