M2-factor of partially coherent flat-top beams propagating in gain or loss media

According to the second-order moments intensity formula of the beam propagating in the gain or loss media, an analytical expression for M2-factor of partially coherent flat-top beams propagating in the media is derived, and Gaussian-Schell model beams propagation in gain or loss media, which is taken as a particular case, is integrated into a common expression. The research result shows that the M2-factor of partially coherent flat-top beams propagating in the gain or loss media is relative to the propagation distance, the coherent length, the order of the beams and the character of media. The propagation characteristic of the beams propagating in the gain or loss media provides a theoretical basis for the application and control of the beam propagation.