In this paper, we derive the closed-form analytical expressions of the power coupling coefficients for a Laguerre-Gaussian beam coupled into a graded-index fiber with either central, offset, or tilted launch. We further generalize to an arbitrary launching condition with the radial offset and the three-dimension angular tilt simultaneously occurring. The analytical results are in good agreement with the numerical ones and can be applied to manufactured graded-index multimode fibers with an index exponent parameter from 1.8 to 2.2. Using the derived analytical expressions, the computation time shortens by at least a four-order of magnitude compared to conventional numerical methods.

中文翻译：

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广义光束发射条件下渐变折射率光纤功率耦合系数的解析表达式


在本文中，我们推导了耦合到具有中心、偏移或倾斜发射的渐变折射率光纤的拉盖尔高斯光束的功率耦合系数的封闭式解析表达式。我们进一步推广到径向偏移和三维角倾斜同时发生的任意发射条件。分析结果与数值结果吻合较好，可应用于折射率指数参数为1.8～2.2的渐变折射率多模光纤的制造。使用推导的解析表达式，与传统数值方法相比，计算时间至少缩短了四个数量级。