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本文运用空间曲线的本地正交曲线坐标系—Tang氏坐标系上严格的Maxwell方程和弱导边界条件,得出了圆截面单模圆柱螺旋光纤中标量场的耦合方程组,在采用了场和传播常数的摄动展开后得到: (1) 螺旋光纤的场保持一种准线偏振态,偏振方向相对于Serret-Frenet标架以接近于(-τ)的旋转率旋转(τ为光纤中心线的挠度); (2) 上述准线偏振态随传播距离。S而周期性地由1变为略小于1;在给定的S处,出射偏振态随入射偏振角φ而周期性地变化,其周期为π/2。 上述结论与已发表的液芯光纤实验结果完全一致。
In this paper, by using the strict Maxwell equation and the weak boundary condition in local orthogonal curvilinear coordinate system -Tang’s coordinate system of space curve, the coupled equations for the scalar field in a single-mode cylindrical helical fiber with circular cross section are obtained. The perturbation of the propagation constant yields: (1) The field of the helical fiber maintains a quasi-linear polarization with a polarization rotation relative to the Serret-Frenet frame at a rate close to (-τ) (τ is the fiber centerline Of the deflection); (2) the above-mentioned polarization state with the propagation distance. S periodically changes from 1 to slightly less than 1; at a given S, the outgoing polarization states periodically change with the incident polarization angle φ, with a period of π / 2. The above conclusion is completely consistent with the experimental results of liquid core optical fiber.