Scattering by a Dielectric Wedge for Oblique Incidence
Electromagnetic scattering of an incident plane monochromatic wave by dielectric or finitely conducting infinite cylinders of arbitrary cross section can be reduced to the solution of scalar Helmholtz equations in two dimensions for the components of the electric and magnetic fields parallel to the generator of the cylinder as functions of the coordinates in the plane perpendicular to the generator. In the single-source integral equation method, two unknown boundary functions are required for oblique incidence and arbitrary polarization . Sharp edges on the scatterer lead to divergent boundary functions for singular integral equations, a problem that is related to divergent fields components at the edge of a wedge . A rigorous solution of the scattering by an infinite dielectric wedge might yield the asymptotic behavior of the unknown function at the edge of the wedge, which could then be used near the edge in computations. Nonrigorous solutions  provide an asymptotic behavior for the fields equal to that of static fields, which is not necessarily supported by numerical experiments. The field behavior cannot be immediately applied to the boundary functions. Alternatively, hypersingular equations, , , can be derived for boundary functions that tend to a constant at the edge, but the difficulties with the divergent unknown function are shifted to integration difficulties due to the higher singularity of the kernel. The behavior of the unknown boundary functions near edges affects mainly the fields near the boundary, while the far fields are less sensitive to the details of the approximation, although computed images of a broad dielectric strip on a substrate can present anomalies due to these divergences. The behavior of arbitrary static fields near the edge of a wedge has also been determined as functions of the angle of incidence of the corresponding scattering problem . Numerical experiments for TE and TM modes generate fields near the edge of a finite wedge that agree only at times with the expected behavior , . These numerical experiments are now extended to oblique incidence. Scattered fields near the edge are compared to static fields in a transition between the TE and TM modes for arbitrary direction of incidence and polarization, for both singular and hypersingular integral equations. The behavior of the unknown boundary functions near the edge for singular integral equations is also shown.
January 1, 2002
PIERS 2002: Progress in Electromagnetics Research Symposium