自聚焦多模光纤模式色散的几何光学与波动光学处理方法

摘要

The graded-index fiber with the parabolic profile has an intermodal dispersion which is about two order smaller than that of the step-index fiber,and is widely used in local area network.The intermodal dispersion of this kind of graded-index fiber was conventionally treated with WKBJ approximate method which is originally used in quantum mechanics.This paper proposes the teaching treatments from the views of geometrical optics and wave optics,and obtains the same result as that calculated with WKBJ method.In the geometrical optics treatment,based on Fermat Principle,we introduce the new concepts of near-axial and far-ax ial rays,and give the solution to the ray equation using a perturbation approximation.In the wave optics treatment,based on the wave equation,the fiber modes in the graded-index fiber are treated as the Hermite-Gaussian modes.The intermodal dispersion is obtained by analyzing the propagation constant with the aid of near-axial and far-axial approximations.With these treatments we obtain the same result,with clearer physical significance.We believe that the teaching treatments proposed in this paper are more appropriate in the undergraduate courses of optical fiber communications.%自聚焦多模光纤相比阶跃型多模光纤,模式色散要小两个数量级,现在广泛用于局域网.对于自聚焦光纤模式色散的处理方法主要是基于原用于量子力学的WKBJ近似方法.本文从几何光学和波动光学两个角度分析处理自聚焦光纤的模式色散,得到了与WKBJ方法完全相同的结果.在几何光学的处理方法中,利用费马原理作指导,引入远轴光线与近轴光线概念的区别,用微扰的近似方法解光线方程,最后得到自聚焦光纤的模式色散.在波动光学的处理方法中,基于波动方程,将光纤模式近似成厄米高斯模式,依然采用近轴近似和远轴近似的概念,通过计算传播常数得到模式色散.两种处理方法得到的模式色散结果一致,且处理过程物理意义清楚,非常适合教学时采用.