Shadowing of an Inhomogeneous Plane Wave by an Edge

When an inhomogeneous plane wave or other type of evanescent field in a lossless medium strikes a large opaque object, the boundary of the shadow zone is displaced from the familiar geometric optical location for non-evanescent fields. This change is attributable to the complex propagation direction of evanescent waves. To study the mechanism of shadow formation, and indeed the significance of a shadow zone when the incident evanescent field may be weaker than diffracted fields generated by the obstacle, the problem of inhomogeneous plane diffraction by a perfectly conducting semi-infinite screen is investigated. By a careful asymptotic treatment and error analysis of the known exact solution, the location of the shadow boundary is determined, as is the transition region surrounding it wherein the field cannot be separated into incident and diffracted constituents. It is found that for strongly evanescent fields, the shadow boundary and transition zones differ markedly from those for a homogeneous plane wave. Effects of losses in the medium are also considered.