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• Proposed a new analytical method for determining the length of collimators based on a Gradient-index lens with an angle polish. • Beam-steering technology make the system less sensitive to misalignment and fabrication tolerance. • Among the three deviations of the coupling mismatch, the angular deviation has the greatest influence. As high coupling efficiency and return loss are crucial in fiber-optic transmission systems, they have attracted widespread attention. This study proposes a ray-transfer matrix-based mathematical analysis method and experimentally demonstrates a collimator based on a gradient-index lens with an angle polish. The propagation characteristics and coupling mechanisms of the collimators are introduced. A beam-steering technology based on a wedge prism and flat glass is proposed to improve the coupling efficiency of the Gaussian beam using collimators. The proposed method is validated via simulation and experiment. The results are significant in free-space optical communication, optical signal processing, and optical fiber connectors. [ABSTRACT FROM AUTHOR]