Multiple diffraction of a line source field by a three-part thin transmissive slab

A uniform asymptotic high-frequency solution is presented for the problem of diffraction of a line source field by a three-part thin transmissive slab. After simulating the slab by a material plane with a set of approximate boundary conditions used recently by RAWLINS et al., the three-part boundary-value problem is transformed into a modified matrix Wiener-Hopf equation. By performing the factorization of the kernel matrix through the DANIELE-KHRAPKOV method, the modified matrix Wiener-Hopf equation is first reduced to a pair of coupled Fredholm integral equations of the second kind and then solved approximately by iterations. An interesting feature of the present solution is that the classical Wiener-Hopf arguments yield unknown constants which may be determined by means of the edge conditions

High frequency diffraction of cylindrical waves by perfectly conducting successive step discontinuities

The diffraction of high frequency cylindrical electromagnetic waves by step discontinuities is investigated rigorously by using the Fourier transform technique in conjunction with the mode matching method. The hybrid method of formulation gives rise to a scalar Wiener-Hopf equation of the third kind, the solution of which contains infinitely many constants satisfying infinite systems of linear algebraic equations