Fundamentals of the Physical Theory of Diffraction, 2nd Edition

9 Multiple Diffraction of Edge Waves: Grazing Incidence and Slope Diffraction

9.1 Statement of the Problem and Related References

Clearly, the theory developed in Chapter 8 can be utilized in the investigation of multiple diffraction at edges that are spaced apart. Only two special cases require an individual investigation.

The first case is a grazing incidence of edge waves on acoustically hard planar plates. In the asymptotic theory, the incident wave is approximated by an equivalent plane wave. However, a plane wave does not undergo diffraction at an infinitely thin plate under the grazing incidence, for the following reason. When this wave propagates in the direction parallel to the plate, its wave and amplitude fronts are perpendicular to the plate. As this incident field is constant in the direction normal to the plate, it automatically satisfies the boundary condition du/dn = 0 on the plate. Such a wave does not “see” the plate and propagates as if a free space is on its path. Because of this, the foregoing theory predicts a zero-diffracted field in this case. However, in the process of multiple diffraction, every diffracted wave is not plane. If its normal derivative du/dn is not a zero on the plate, it undergoes diffraction. Such a grazing diffraction is studied in Section 9.2.

The second case that also needs special treatment occurs when the scattering edge is located in the zero of the incident wave. This is the case for slope diffraction. One distinguishes a slope ...