In the calculation of the scattered fields for the radio communication in urban environment, the edge diffraction by the corners of the buildings contributes significantly. The accurate means of calculating the scattered fields by this lossy wedges are not available to date because of its non-separable nature having two different wavenumber inside and outside of the wedge, respectively. Maliuzhinets' solution for a impedance wedge is used in the calculation of edge diffracted fields by the highly lossly (i. e. almost conducting) wedge. It does not give the contributions of the refracted and the transmitted fields since it deals with the non-physical problem of impedance wedge. Heuristic solutions for the scattering by the lossy wedge are available. Their edge diffractions are obtained by properly multiplying the Fresnel reflection or transmission coefficients to the diffraction coefficients of the conduction wedge. They accoungted for the refracted and transmitted fields for which they assumed that the ray goes through the lossless dielectric wedge. Numerical FDTD method shows the possibility of calculating the edge diffracted fields for the lossy dielectric wedge in the region where the incident, the reflected, and the refracted fields are not present.
Rigorous formulation and its asymptotic solutions for the fields scattered by the lossless dielectric wedge and the composite wedge of dielectric and conducting are available. This employs the Kirchhoff's-integrals in the physical regions and the extinction theorem in the mathematically complementary regions. The extinction integral gives correction to the physical optics(PO) approximation which is obtained from the geometric optical(GO) solutions in the interfaces of the wedge via the Kirchhoff's integrals.
When the non-uniform plane wave is incident upon a plane boundary of the lossy dielectric half medium, the reflected and refracted fields are given. GO solutions for the lossy dielectric wedge may be obtained by this non-uniform plane wave tracing and its corresponding PO solutions may be obtained analytically as for the lossless dielectric wedge. The extinction integral vanishes if the exact boundary field are used. One may find the boundary fields asymptotically by adding the multipole line sources with unknown expansion coefficients at the tip of the wedge or the sheet currents expanded by Neumann series along the interface boundaries to GO boundary fields to make the extinction integral vanished. Numerical calculation of these expansion coefficients make the accurate calculation of the reflected, the refracted, and the edge diffracted fields possible inside as well as the outside of the lossy wedge up to its value of the loss tangent 10 for the multipole line sources and 0.03 for the sheet currents. The calculated edge diffracted fields are compared with those of impedance wedge and the heuristic solutiona.
