Kramers-Kronig analysis for the determination of the optical constants of thin surface films: I. Theory

Abstract

The Kramers-Kronig relationships between the real and imaginary part of a causal transform were applied to the quotient r̂ 123/ r̂ 13 of the Fresnel reflection coefficient of a surface covered with a thin surface film and of the uncovered surface. For very thin surface films the logarithm In ( R 123/ R 13) of the reflectivities and the phase difference Δ ϑ = ϑ 123 − ϑ 13 can be related by Kramers-Kronig equations. The exact form of these equations was derived. The ratio r̂ 123/ r̂ 13 can show one singularity for perpendicular polarized light and two singularities for parallel polarized light. The singularities can be taken into account by forming the Blaschke product. The applications of the derived equations in the reflection spectroscopy of thin surface films are here discussed.