Wedge Diffraction as an Instance of Radiative Shielding

Abstract

The celebrated Sommerfeld wedge diffraction solution is reexamined from a null interior field perspective. Exact surface currents provided by that solution, when considered as disembodied half-plane laminae radiating into an ambient, uniform space both inside and outside the wedge proper, do succeed in reconstituting both a specular, mirror field above the exposed face, and a shielding plane-wave field of a sign opposite to that of the incoming excitation which, under superposition, creates both the classical, geometric-optics shadow, and a strictly null interior field at the dominant, plane-wave level. Both mirror and shadow radiated fields are controlled by the residue at just one simple pole encountered during a spectral radiative field assembly, fixed in place by incidence direction $\phi_{0}$ as measured from the exposed face. The radiated fields further provide diffractive contributions drawn from two saddle points that track observation angle $\phi.$ Even these, more or less asymptotic contributions, are found to cancel exactly within the wedge interior, while, on the outside, they recover in its every detail the canonical structure lying at the base of GTD (geometric theory of diffraction). It is earnestly hoped that this revised scattering viewpoint, while leaving intact all details of the existing solution, will impart to it a fresh, physically robust meaning. Moreover, since this viewpoint confirms, admittedly in an extreme limit, the concept of field self-consistency (Ewald-Oseen extinction in more picturesque language), perhaps such explicit vindication may yet encourage efforts to seek exact solutions to scattering/diffraction by electromagnetically permeable (dielectric) wedges, efforts that harness integral equations with polarization/ohmic currents distributed throughout wedge volumes as sources radiating into an ambient, uniform reference medium.