Nonlocal corrections to Fresnel optics: How to extend<i>d</i>-parameter theory beyond jellium models

Abstract

The d-parameter theory for describing the corrections to Fresnel optics of an interface is generalized to include local-field effects arising from discrete atomic structure. The derivation focuses on what effective matching conditions must be applied to macroscopic fields at the interface. These matching conditions on one hand determine reflection and transmission amplitudes that can be measured by experiments, and, on the other hand, they may be parametrized by the elements of a 3\ifmmode\times\else\texttimes\fi{}3 d tensor, which can be calculated by theory. The derivation shows that the d elements completely characterize the first-order corrections to Fresnel optics and indicates when and how different elements may be related by symmetries.