The 4×4 matrix method proposed by Yeh is a robust technique to solve the wave propagation problem in anisotropic media. However, it fails in the isotropic limit. Although the singularity of this method has been widely noted, a comprehensive discussion on the reason behind such a failure has not been reported previously. In this paper, we review the Yeh's 4×4 transfer matrix formulation in multi-layered systems and evaluate it in the limit of isotropic media to obtain a physical meaning of the singularity of the formalism. We demonstrate that the method is built on a constrained polarization vector p, which is subject to the orientation of the wavevector k. When the constraint is released in the limit of isotropic media, p vanishes, and this entails the singularity of the method.

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关于 Yeh 4×4 传递矩阵形式主义的奇点

Yeh 提出的 4×4 矩阵方法是一种解决各向异性介质中波传播问题的稳健技术。然而，它在各向同性极限内失败。尽管这种方法的奇异性已被广泛关注，但之前尚未报道过对这种失败背后原因的全面讨论。在本文中，我们回顾了多层系统中 Yeh 的 4×4 传递矩阵公式，并在各向同性介质的极限下对其进行评估，以获得形式主义奇点的物理意义。我们证明了该方法建立在受约束的偏振矢量 p 上，该矢量受波矢量 k 的方向影响。当约束在各向同性介质的限制中被释放时，p 消失，这意味着该方法的奇异性。