A modal impedance‐angle formalism: Schemes for accurate graded‐index bent‐slab calculations and optical fiber mode counting
A modal impedance‐angle formalism: Schemes for accurate graded‐index bent‐slab calculations and optical fiber mode counting
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DOI：
10.1029/2001rs002570
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发表时间：
2003-04
期刊：
影响因子：
1.6
通讯作者：
B. P. de Hon;M. Bingle
中科院分区：
文献类型：
--
作者：
B. P. de Hon;M. Bingle
利用复功率流变分格式可以计算导模沿弯曲板和光纤的传播系数。这种格式可以用阻抗而不是场的特征方程的牛顿迭代格式来表示。通过一种广义坐标变换绕过了阻抗相关Riccati方程的奇异性，该变换涉及弯曲板的角度，或光纤的角度矩阵。采用由此产生的弯曲板的阻抗角形式，数值上的困难消失了，精度随之而来。矢量光纤问题的分析得益于标量弯曲板问题。特别是，功率流和阻抗角形式之间的联系构成了理解的物理基础，即在距离光纤芯一定距离之外，阻抗矩阵相对于传播系数的导数是正定的。反过来，这也为Kuester和Chang在1975年为标量波沿直板传播而开发的模式计数方案在光纤中的全波推广提供了基础。有了这些关键结果，根查找可以变得更加健壮和高效。另一篇论文包含了复功率流变分格式和模态计数定理和模态包套定理的必要证明。
The propagation coefficients of guided modes along bent slabs and optical fibers may be calculated with the aid of a complex‐power‐flow, variational scheme. This scheme can be cast in the form of a Newton iterative scheme for a characteristic equation in terms of impedances rather than fields. Singularities of the associated Riccati equations for the impedances are circumvented via a generalized coordinate transformation, involving an angle for bent slabs, or a matrix of angles for optical fibers. Adopting the resulting impedance‐angle formalism for bent slabs, numerical difficulties disappear, and accuracy ensues. The analysis of the vectorial optical‐fiber problem benefits from its scalar bent‐slab counterpart. In particular, the connection between the power flow and the impedance‐angle formalism forms the physical underpinning for understanding that beyond a certain distance from the fiber core the derivative of the impedance matrix with respect to the propagation coefficient is positive definite. In turn, this provides the basis for the full‐wave generalization for optical fibers of the mode‐counting scheme developed in 1975 by Kuester and Chang for scalar wave propagation along a straight slab. With these key results, root‐finding can be rendered more robust and efficient. A companion paper contains the necessary proofs for the complex‐power‐flow variational scheme and the mode‐counting and mode‐bracketing theorems.