Error analysis and optimization algorithm of focal shift on mode decomposition for few-mode fiber beam

Modal decomposition technology is an effective method to study the mode characteristics of laser beam in few-mode fibers. However, certain types of eigenmodes in the fiber can cause focal shift and affect the accuracy of modal decomposition. This article focuses on the influence of the focal shift of Laguerre-Gaussian mode and Linear Polarization mode on modal decomposition, and the research is based on correlation filter and the optimization algorithm of focal shift. The two-step ABCD algorithm is used to simulate and analyze the focal shift phenomenon of the two kinds of eigenmodes and the error influence of focal shift on the mode decomposition; Meanwhile, an iterative algorithm based on Fresnel diffraction is proposed to numerically calculate the light field distribution in focal plane to avoid the influence of focal shift errors. The focal shift analysis and its optimization algorithm make the modal decomposition technology be applicable to engineering applications.