THE USE OF SINGULAR INTEGRALS IN WAVE DIFFRACTION PROBLEMS WITH THE SOLUTION OF THE PROBLEM OF SCATTERING BY A DIELECTRIC WEDGE,
Abstract
The problem of diffraction by an infinite (lossless) dielectric wedge is solved, no matter what the angle of the wedge may be. The incident field is homogeneous and of degree -1, the equations governing the propagation of disturbances both inside the prism and in its surroundings, and the conditions to be enforced at the surface are all homogeneous. The diffracted field is then homogeneous and of degree -1 and represented as part of certain integrals of Cauchy type. The calculation of these functions involves applications of the theory of complex variables. A prism with two infinite refracting surfaces has a plane of symmetry. By considering separately the symmetric and the antisymmetric parts of the total field about this plane, the problem is reduced to one involving only one refracting surface. The situation examined is the more general involving two infinite wedges with one surface and the vertex in common and with the second surface of each wedge supporting definite homogeneous boundary conditions (involving first derivatives). The solution involves satisfying conditions at the interface, at the vertex and at the diffracted wave fronts, leaving boundary conditions at the second wall of each wedge to be satisfied simultaneously by a pair of non-singular Fredholm equations. The plane wave result is used as the base of further solutions. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1963
- Accession Number
- AD0430767
Entities
People
- Michael Papadopoulos
Organizations
- University of Wisconsin–Madison