Olshansky R
Appl Opt. 1976 Mar 1;15(3):782-8. doi: 10.1364/AO.15.000782.
The excess pulse broadening caused by deviations from the optimal index profile is analyzed for multimode optical fibers. First-order perturbation theory is used to evaluate the effects of arbitrary index perturbations having longitudinal spatial frequencies which are too low to cause mode coupling. A simplified expression is found for the excess pulse broadening in terms of a double integral over a weighting function. Weighting functions are evaluated and used to calculate the effects of two kinds of circularly symmetric perturbations, a Gaussian-shaped bump or dip in the index profile and an oscillating perturbation. These perturbations are found to affect the pulse broadening significantly according to the position and width of the bump and the transverse spatial frequency of the oscillating perturbation. The more narrow bumps and those located at larger core radii are found to have the greatest effect. For a typical multimode fiber, perturbations making 2-18 oscillations along the radius are found to cause significant increases in pulse broadening, while more rapid oscillations are found to have negligible effect. These results indicate the type and degree of index profile control required to keep the pulse broadening below a specified level.
针对多模光纤，分析了因偏离最佳折射率分布而导致的额外脉冲展宽。采用一阶微扰理论来评估纵向空间频率过低而无法引起模式耦合的任意折射率微扰的影响。通过对加权函数进行二重积分，得到了额外脉冲展宽的简化表达式。对加权函数进行了评估，并用于计算两种圆对称微扰的影响，即折射率分布中的高斯形凸起或凹陷以及振荡微扰。发现这些微扰会根据凸起的位置和宽度以及振荡微扰的横向空间频率对脉冲展宽产生显著影响。发现越窄的凸起以及位于较大纤芯半径处的凸起影响最大。对于典型的多模光纤，发现沿半径方向有2 - 18次振荡的微扰会导致脉冲展宽显著增加，而振荡更快的微扰影响可忽略不计。这些结果表明了将脉冲展宽保持在指定水平以下所需的折射率分布控制的类型和程度。
