An angular spectrum representation approach to the Goos-Hänchen shift

The reflection of a beam of light at a plane interface is treated using the angular spectrum representation. The Goos-Hänchen shift is found to be proportional to the first derivative of the phase of the reflectance. The second derivative of the phase gives rise to a shift of the reflected beam along its direction of propagation. This new shift, called a focal shift, is different from the extra propagation distance of the beam predicted on the basis of a ray model for total internal reflection. Expressions are presented for the Goos-Hänchen and focal shifts for both s and p polarization.