High power, high beam quality, and compact miniaturization are the development goals of fiber lasers. Spectral beam combination is an effective means to overcome the bottleneck of single-fiber output power and can achieve a high power output of fiber lasers. In most existing spectral beam combining systems, the gap between adjacent subfibers is generally of the order of millimeters or even larger; consequently, the entire system occupies a large space. Therefore, a compact spectral beam combining system based on a precision fiber array is proposed in this study. Many factors affect the beam quality of a combined laser in a spectral beam combining system, including lens aberration, laser line width, grating thermal distortion, and fiber array disturbance, which degrade the beam quality of the combined laser. Research on the influence of fiber array disturbance deviation on beam quality is relatively scarce. Therefore, this study focused on the effects of fiber array disturbance on beam quality factor of a combined laser. Quantitative analysis of the effects of fiber array displacement and pointing disturbance deviation on beam quality factor of the combined laser provides a means of realizing effective control of combined laser beam quality. Unlike in similar studies, this study conducted error analysis of the axial displacement deviation of the fiber array by the M² factor of the combined laser, which makes the theoretical model more practical.

Diffraction propagation theory enables us to derive the light field distribution at each position of a subbeam affected by displacement and pointing deviation. In the observation plane where the combined laser is formed, the near- and far-field light intensities of each subbeam are incoherently superimposed based on the incoherent superposition principle. The traditional intensity second-moment method is used to caclulate beam quality factor of the beam by fitting the relationship between the beam width and propagation distance. Due to the limitations of computer memory and performance, large calculation errors are introduced in the results, resulting in low calculation efficiency. Therefore, based on the Heisenberg uncertainty principle, the expression of beam quality^{factor of the combined laser under the effects of horizontal displacement, axial displacement, and horizontal pointing deviation was derived in this study.}

Under the condition of a constant number of subbeams, variations in beam quality factor of the combined beam with displacement and pointing disturbance deviation of a single-channel/multi-channel beam were simulated and analyzed, and error analysis of beam quality factor of the combined laser with different numbers of subbeams under a certain random displacement and pointing disturbance deviation was conducted. The results are as follows. 1) The beam quality factor of the combined laser is the most sensitive to the disturbance along the horizontal (x-axis) direction of the end face of the optical fiber, which must be controlled in the order of microns (Figs. 4, 5, 7, and 8). 2) The quantitative relationship between the different disturbances of the optical fiber array and beam quality factor of the combined laser was determined, and the specific control requirements of the displacement and pointing accuracy of the optical fiber array were described (Figs. 4, 5, 7-9). 3) When the number of subbeams in the beam combination exceeds 23, under a specific random disturbance, the statistical means of the beam combining laser beam quality factor tend to their respective stable values of 1.37, 1.34, and 1.25, and the standard deviations tend to 0.05, 0.06, and 0.04, respectively (Fig. 9).

In this study, a compact spectral beam combining system is proposed, and an error analysis of the optical fiber array disturbance deviation of the combined laser beam quality is theoretically conducted. The rationality and feasibility of the compact spectral beam combining system are explained to some extent, where these can be extended to other spectral beam combining systems. The specific control requirements of various errors are described. This study provides guidance for the development of high-power and high-beam-quality fiber lasers.