Reflection, Diffraction and Scattering at Low Grazing Angle of Incidence: Regular and Random Systems

When a monochromatic electromagnetic plane wave is incident on an infinitely extending surface with the translation invariance property, a curious phenomenon often takes place at a low grazing angle of incidence, at which the total wave field vanishes and a dark shadow appears. This paper looks for physical and mathematical reasons why such a shadow occurs. Three cases are considered: wave reflection by a flat interface between two media, diffraction by a periodic surface, and scattering from a homogeneous random surface. Then, it is found that, when a translation invariant surface does not support guided waves (eigen functions) propagating with real propagation constants, such the shadow always takes place, because the primary excitation disappears at a low grazing angle of incidence. At the same time, a shadow form of solution is proposed. Further, several open problems are given for future works. key words: reflection, diffraction by periodic surface, scattering by random surface, shadow theory. reciprocity, guided wave