Microscopic description of the reflection of light under normal incidence: validity of the Lorentz approach to interpret a refractive index profile

Abstract

Optical techniques are widely used to study thin layers and more generally interfacial structures. The authors consider the problem raised by a microscopic interpretation of the refractive index and study the reflection of a plane wave under normal incidence, in the dipolar approximation. Calculations of the reflection on a thin homogeneous layer reveal significant differences between macroscopic and microscopic approaches, when the layer thickness is of a few lattice parameters, and it appears that this is mainly due to edge effects. The authors describe microscopically the reflection on a layered interface. It is shown that a macroscopic description may be recovered to very good approximation when an 'apparent' refractive index n_app(z) is introduced. This index is related to both the local polarisability and its gradient. Comparison is established with the Lorentz refractive index profile.