Theoretical study of the lateral displacement of random fields at interfaces

The lateral displacement of a totally reflected light beam from the position expected by geometrical optics has been known for some time. The effect, known as the Goos-Hänchen shift, may be understood in terms of the phase changes acquired upon reflection at the interface by the plane wave components of the angular spectrum representation of the incident field. In this work, we study the shifts that occur in the reflection of random fields from flat dielectric interfaces. We find that, similar to the well-known effect for beams, random fields can also present lateral shifts in reflection experiments, and that the shifts acquired by speckle patterns are the same as those of an equivalent beam. For tapered speckle beams, we show that the shifts of the mean intensity do not depend on the average beam size, but mainly on speckle size.