On the singularity of the Yeh 4 × 4 transfer matrix formalism

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...

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Bibliographic Details
Published in:Journal of modern optics 2020-05, Vol.67 (9), p.832-836
Main Authors: Garibello, B., Avilán, N., Galvis, J. A., Herreño-Fierro, C. A.
Format: Article
Language:English
Subjects:
4×4 matrix formalism
4×4 matrix formalism singularities
Anisotropic media
Constraints
Formalism
Isotropic media
Multilayers
Singularities
stratified anisotropic materials
Systems analysis
Transfer matrices
Wave propagation
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Summary: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.
ISSN:0950-0340
1362-3044
DOI:10.1080/09500340.2020.1775905