Reflection of light at a flat interface under normal incidence: A renewed macroscopic description.

Abstract

We consider a cubic crystal, layered orthogonally to the incident wave vector, with some arbitrary refractive-index profile. The local electric field experienced by a crystal molecule may be calculated in the macroscopic limit, using a set of linear equations. To evaluate the amplitude reflection coefficient R, we use first- and higher-order Born approximations, and then show that R is the sum (${R}_{1}$+${R}_{3}$+...) of coefficients related to paths presenting one extremum, three extrema, etc. This approach gives a new physical insight into the reflection of light in terms of scattering and nothing but scattering. It also leads to an improved evaluation of the interfacial reflectivity. The different approximate formulas that are derived are compared numerically for a dissymmetric refraction-index profile.