Coupling efficiency of laser beam to multimode fiber

The coupling efficiency of laser beam to multimode fiber is given by geometrical optics, and the relation between the maximum coupling efficiency and the beam propagation factor M2 is analyzed. An equivalent factor MF2 for the multimode fiber is introduced to characterize the fiber coupling capability. The coupling efficiency of laser beam to multimode fiber is calculated in respect of the ratio M2/MF2 by the overlapping integral theory. The optimal coupling efficiency can be roughly estimated by the ratio of M2 to MF2 but with a large error range. The deviation comes from the lacks of information on the detail of phase and intensity profile in the beam factor M2.