Dielectric-wedge fourier series

Diffraction of a magnetically polarized incident field by a dielectric wedge has been considered. The diffraction problem has been reduced to an integral equation which has been solved by iterations in the form of a converging series. The error of the nth-order iteration has been explicitly calculated. Furthermore, the chapter has introduced a new Fourier series of orthogonal Bessel-Hankel modes. These modes behave as Bessel functions near the tip of the wedge and are outgoing Hankel functions for large values of kr. The scattered magnetic field represented by the Fourier series satisfies the radiation condition at infinity and is finite at the tip of the wedge. The Fourier series has been constructed by a mapping of the far field onto the Fourier series. The error in approximating the exact solution of the diffraction problem by n terms of the Fourier series has been explicitly evaluated. The first term in the Fourier series behaves as the Bessel function Js(kgr) with rs being the static field singularity at the tip of the wedge. The theory has been tested numerically, and examples of field plots have been presented.