Beam quality factor for coherently combined fiber laser beams

The beam quality factor for a coherently combined beam is studied in detail. A theoretical analysis and a numerical calculation are given to illustrate that the M² factor is not a proper means for evaluating the beam quality of a coherently combined beam. The beam propagation factor is introduced to evaluate the beam quality. The effect of phase error on the beam quality is also studied. Results indicate that the beam quality of a coherently combined beam depends mainly on the fill factor of the laser array and not on the number of lasers. It is also revealed that the allowed phase error does not change with the number of lasers in order to ensure the energy encircled in a certain bucket.