Schermer Ross T
Opt Express. 2007 Nov 26;15(24):15674-701. doi: 10.1364/oe.15.015674.
This paper introduces a simple, analytical method for generalizing the behavior of bent, weakly-guided fibers and waveguides. It begins with a comprehensive study of the modes of the bent step-index fiber, which is later extended to encompass a wide range of more complicated waveguide geometries. The analysis is based on the introduction of a scaling parameter, analogous to the V-number for straight step-index fibers, for the bend radius. When this parameter remains constant, waveguides of different bend radii, numerical apertures and wavelengths will all propagate identical mode field distributions, except scaled in size. This allows the behavior of individual waveguides to be broadly extended, and is especially useful for generalizing the results of numerical simulations. The technique is applied to the bent step-index fiber in this paper to arrive at simple analytical formulae for the propagation constant and mode area, which are valid well beyond the transition to whispering-gallery modes. Animations illustrating mode deformation with respect to bending and curves describing polarization decoupling are also presented, which encompass the entire family of weakly-guided, step-index fibers.
本文介绍了一种简单的解析方法，用于概括弯曲的弱导光纤和波导的行为。首先对弯曲阶跃折射率光纤的模式进行了全面研究，随后扩展到涵盖更广泛的更复杂波导几何结构。该分析基于引入一个缩放参数，类似于直阶跃折射率光纤的V数，用于弯曲半径。当此参数保持恒定时，不同弯曲半径、数值孔径和波长的波导将传播相同的模式场分布，只是尺寸按比例缩放。这使得单个波导的行为能够得到广泛扩展，对于概括数值模拟结果特别有用。本文将该技术应用于弯曲阶跃折射率光纤，以得出传播常数和模式面积的简单解析公式，这些公式在向回音壁模式转变之后仍有效。还展示了说明模式相对于弯曲变形的动画以及描述偏振解耦的曲线，涵盖了整个弱导阶跃折射率光纤家族。
