Comment on the transmission matrix for a dielectric interface

In a recent paper the reflection and transmission matrices for a dielectric interface based on Fresnel formulas are derived [Garcia RDM. Fresnel boundary and interface conditions for polarized radiative transfer in a multilayer medium. J Quant Spectrosc Radiat Transfer 2012;113:306–17]. Although the final formulas appear to be correct, we found that there are some significant conceptual and logical flaws in the derivation. Here we explain that the misunderstanding is due to the different physical significances of the Stokes parameters for the coherent and diffuse radiation field and that the so-called transmission factor directly originates from the physical definition of the Stokes parameters. We also clarify a few incorrect interpretations in the aforementioned paper about previously published works. -- Highlights: ► The transmission matrix of the Stokes vector has been derived. ► The derivation is for a flat dielectric interface. ► The difference between the coherent and diffuse Stokes vectors has to be recognized. ► Energy conservation is ensured with the correct definition of the Stokes vector. ► The inconsistency of Garcia's method is analyzed.