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22 September 1995 Fresnel equations and transmission line analogues for diffraction gratings
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A simple and intuitive formalism is presented to describe diffraction in multi-layered periodic structures. We use the well known results from scalar analysis (wave propagation in homogeneous layered media) and show that they can be generalized rather readily to vector problems such as diffraction analysis. Specifically, we derive: (1) generalized Fresnel equations appropriate for reflection and transmission from an infinitely thick grating, (2) a generalized Airy formula for thin-film to describe reflection and transmission of light through a lamellar grating and (3) a matrix propagation method akin that used for multi-layer thin film analysis. The results developed here complement the recent work on R- matrix propagation methods. The R-matrix technique is a modal method that has shown to be a numerically stable for calculating diffraction efficiencies from deep groove gratings. The formalism developed here, while equivalent to the R-matrix technique, is not identical and offers a number of advantages. We will discuss these and other related matters in this paper.
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Sumanth Kaushik "Fresnel equations and transmission line analogues for diffraction gratings", Proc. SPIE 2532, Application and Theory of Periodic Structures, (22 September 1995);

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