Monitoring and Regulation of Micro-Displacement Deviation in Few-Mode Beam Alignment through Mode Decomposition

Beam alignment enables efficient, stable transmission and control of optical energy and information, which critically depend on precise monitoring and regulation of the three-dimensional (3D) relative positioning between fibers. This study introduces an approach to achieve more accurate 3D measurement of the spatial displacement between two optical fibers in a few-mode configuration, by integrating mode decomposition with a straightforward machine learning algorithm. This method leverages inherent information from the optical field, enabling precise beam alignment with a simple structure and minimal computational effort. In the 3D measurement experiment, the proposed method achieves a coefficient of determination of 0.99 for transverse offsets in the x- and y-directions, and 0.98 for air gap in the z-direction. The RMSE in x-direction, y-direction and z-direction is respectively 0.135 μm, 0.128 μm and 2.42 μm. The time for a single 3D displacement calculation is 4.037e-4 seconds. Furthermore, it facilitates single-step displacement regulation with a deviation tolerance within 0.15 μm and modal content regulation with an accuracy of 4.67%. These results establish a theoretical framework for addressing key challenges in optical path alignment, crosstalk compensation, precision instrument manufacturing, and fiber optic sensing.