Effect of surface roughness on the Goos-H\"anchen shift

TL;DR

This paper investigates how surface roughness affects the Goos-H"anchen shift by modeling rough surfaces as inhomogeneous media and applying ray optics, providing insights consistent with experimental observations.

Contribution

It introduces a novel approach of modeling surface roughness as a continuous inhomogeneous medium to analyze the GH shift more realistically.

Findings

Modeling surface roughness as an inhomogeneous medium improves understanding of GH shift.

The approach aligns well with experimental data.

Provides a clearer physical interpretation of the GH effect.

Abstract

By considering an optically denser medium with a flat surface, but with natural roughness instead of abstract geometrical boundary which leads to mathematical discontinuity on the boundary of two adjacent stratified media, we have thus established the importance of considering physical surfaces; and thus we studied the Goos-H\"{a}nchen (GH) effect by ray-optics description to shed light on parts of this effect which have remained ambiguous. We replaced the very thin region of surface roughness by a continuous inhomogeneous intermediary medium. Applying Fermat's principle for the incident light ray, few fundamental questions about GH shift are more convincingly addressed which are in excellent agreement, even with the most details of the experimental results.