Polynomial formulation of reflection and transmission by stratified planar structures

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Abstract
We present a polynomial approach to the calculation of reflection and transmission coefficients of stratified planar structures. Starting with the usual matrix method and generalizing the so-called elementary symmetric functions used in the mathematical theory of polynomials, we show that these coefficients can be expressed in a form so simple that they can be written directly without any calculation for any number of interfaces. We essentially deal with the case of electromagnetic waves; our results can, however, be applied in other fields of physics that use reflection and transmission coefficients and particularly to matter waves satisfying Schrödinger’s equation. Among such applications, our results may provide a useful tool in calculations of quantum wells as seen in a number of applications and experiments.

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