Assuming weakly guiding approximation, we examine orbital angular momentum (OAM) mode mixing on account of ellipticity in a fiber and derive a complete set of analytic expressions for spatial crosstalk, using scalar perturbation theory that incorporates fully the existing degeneracy between a spatial OAM mode and its degenerate partner characterized by a topological charge of opposite sign. These expressions, consequently, include an explicit formula for calculating the $2\pi$ walk-off length over which an input OAM mode converts into its degenerate partner, and back into itself. We further explore the applicability of the derived expressions in the presence of spin-orbit interaction. The expressions constitute a useful mathematical tool in the analysis and design of fibers for spatially-multiplexed mode transmissions. Their utility is demonstrated with application to a few mode and a multimode step-index fiber.

中文翻译：

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微椭圆光纤中轨道角动量模态串扰的解析表达式

假设弱引导近似，我们研究了由于光纤中的椭圆度引起的轨道角动量 (OAM) 模式混合，并使用标量扰动理论推导出了一套完整的空间串扰解析表达式，该理论完全结合了空间 OAM 模式和它的简并伙伴以相反符号的拓扑电荷为特征。因此，这些表达式包括一个显式公式，用于计算输入 OAM 模式转换为其退化伙伴并返回自身的 $2\pi$ 走离长度。我们进一步探索了在存在自旋轨道相互作用的情况下派生表达式的适用性。这些表达式构成了分析和设计用于空间复用模式传输的光纤的有用数学工具。