Effect of surface roughness on the Goos-Hanchen shift

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-Hanchen (GH) effect by ray-optics description to shed light on parts of this effect that 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.