Diffraction by, or diffusion into, a penetrable wedge

Abstract

Approximate expressions are obtained for the field produced when an electromagnetic plane wave is diffracted by an arbitrary angled dielectric wedge, whose refractive index is near unity. The solution is obtained from an application of the Kontorovich-Lebedev transform and a formal Neumann-type expansion. The diffraction problem is solved by firstly solving a related wedge diffusion problem and then using analytic continuation to obtain the solution for the diffraction problem. The results have applications in diffusion and wave propagation into a wedge.

An iterative approach to scattering by edges and wedges

“…However, we note that if the harmonic Z-dependence were e ik Z Z then the same form of reduced wave equation is obtained with k 2 replaced by k 2 À k 2 Z . The same approach will therefore be applicable, though care must be taken in the case of electromagnetic waves where the boundary conditions complicate things and different polarization states have to be uncoupled [5].…”

“…Thus, if we try to solve the problem of scattering by a semi-infinite plane with mixed boundary conditions (Rawlins [4]) we find that the solution is an integral over a kernel which itself can only be evaluated by performing another integration. Likewise if we try to solve the problem of scattering of light by a dielectric wedge then existing techniques (Rawlins [5]) can not even find the solution in that way. The best they can do is to reduce the problem to that of solving coupled integral equations in order to find a complicated kernel which will then have to be integrated numerically to find the full solution.…”

Electromagnetic fields in the presence of an infinite metamaterial wedge

“…Fields (E z , H r , H 4 ) are constructed from symmetric and antisymmetric parts (with respect to the planes 4Z0, Gp) and are represented by Kontorovich-Lebedev spectra. The continuity conditions of the fields E z , H r on the wedge face at 4Zb, together with the distribution given by Forristall & Ingram (1972), Osipov (1993) and Rawlins (1999) where v.p. in front of the integral sign denotes that the Cauchy principal value is to be taken.…”

“…We apply the scheme devised, detailed by Salem et al (2006) and inspired by the Neumann series expansion approach introduced by Rawlins (1999), to solve (2.2) numerically; now with k 1,2 switched back to real (complex) for the lossless (lossy) diffraction and scattering problem. A summary of the scheme is as follows:…”

“…The methods based on the Kontorovich-Lebedev transform (Lebedev 1965) have been successfully applied in the past to a number of problems of diffraction by wedges (Oberhettinger 1954;Forristall & Ingram 1971, 1972Rawlins 1972Rawlins , 1999Osipov 1993;Salem et al 2006). A strategy has been presented by Salem et al (2006) to solve the problem of diffraction by an ordinary material wedge.…”