Theoretical analysis of beam quality degradation in spectral beam combining of fiber laser array with beam deviation

Aimed to maintain excellent beam quality, the degradation of M2 factor is theoretically studied in compact spectral beam combining (SBC) system of fiber laser array. Considering that the output beams from a laser array usually have axial translation and angular deflection, the correction of incident light field is built by the transformation of coordinates. Using the propagation model and the statistics, properties of the combined beam with perturbations of a single emitter or entire laser array are respectively discussed in detail. The degradation of M2 factor is 0.14(±0.075) when the axial translation of entire laser array satisfies normal distribution with standard deviation of 100 μm. While the angular deflection is introduced with standard deviation of 10/3 mrad, the degradation increases to 3.57(±1.28). Owing to non-overlap ensemble of the incident beam on the grating, the deflection angle will translate the far-field beam spot after the diffraction, which causes a dramatic degradation of the beam quality. Considering the axial translation and the angular deflection simultaneously, the overall effect on the beam quality is dominated by the angular deflection. For applicable requirements of M2 < 2, 3 mrad angular deflection is claimed with axial translation less than 300 μm in the compact SBC system. These analyses provide a valid basis for building the experimental system of SBC.