On the accuracy of the WKB approximation in optical dielectric waveguides
On the accuracy of the WKB approximation in optical dielectric waveguides
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光介质波导中 WKB 近似的精度
DOI：
10.1007/bf00619733
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发表时间：
1977
影响因子：
3
通讯作者：
M. Adams
中科院分区：
文献类型：
--
作者：
A. Hartog;M. Adams
在阶跃折射率和抛物线折射率分布的情况下，从WKB近似得到的光波导的本征值和场分布与从几何光学和更严格的弱引导LP模式理论得到的结果进行了比较。在所有的情况下，它被发现，零阶WKB近似产生非常准确的本征值提供照顾，在本征值方程中的相位因子的选择。推导了二维和三维任意折射率分布波导所需相位因子的表达式，并给出了射线光学的物理解释。一阶WKB场分布发现，除了在焦散线附近的模式字段到处给出良好的协议。
Eigenvalues and field distributions for optical waveguides obtained from the WKB approximation have been compared with those found from geometrical optics and from more rigorous weakly-guiding LP mode theories in the cases of the step-index and parabolic-index profiles. In all cases it is found that the zero-order WKB approximation yields very accurate eigenvalues provided care is taken in the choice of phase factors in the eigenvalue equation. Expressions are deduced for the required phase factors for guides of arbitrary index profile in both two- and three-dimensions, and physical interpretations are given in terms of ray optics. The first-order WKB field distributions are found to give good agreement with the mode fields everywhere except in the vicinity of the caustics.