Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack

Abstract

A theoretical method is described for calculating the bidirectional scattering characteristic for any given thin-film multilayer geometry in which the surfaces and interfaces are assumed to be rough, and where statistical inhomogeneities in the optical permittivities may also exist in each layer. The light energy scattered in any direction depends on geometrical thickness, the permittivities of the ideal layer stack and also on the corresponding auto- and cross-correlation functions. The expressions that are obtained for the scattered field are completely general in the sense of the Born approximation of first order in the imperfections and the exciting fields. The contributions of interface and volume scattering can be assumed arbitrarily because both are derived in a unique way. The main new result consists in the occurrence of four different possibilities of coupling between the scattered and exciting waves due to the standing wave character of both light waves. It is easy to show that the case of a columnar structure reduces the theoretical effort and leads to a similarity of this volume case to that of normal interface scattering. The matrix formalism used in analogy to the normal calculations of reflection and transmission coefficients allows a simple physical interpretation of the light propagation through the layer system and straightforward numerical calculations.