Abstract
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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