SCATTERING OF A PLANE WAVE BY A RECTANGULAR SEMI-INFINITE DIELECTRIC SLAB AND DIELECTRIC CYLINDER BY MODE MATCHING TECHNIQUE

Abstract

The dielectric slabs, dielectric wedges and dielectric rectangular cylinders represent a significant set of structures used in many practical systems. The par ari1etel'S of interest include field configuration (modes) that can be propagated and scattered by such structures. It is known that power carried by these structures depends upon the constitu tive parameters of the medium and the geometry of the structure. The studies carried out so far on the topic of propagation and scattering for these structures is generally due to the slab with very small thickness compared to the wavelength. The approximation solution for the t hick dielectric slab is not readily available. The reason is the complexity of the problems. The solutions of these problems result into complicated mathematical formulae which require efficient computational skill which was not available until the advent of fast computers. A solut ion for the two-dimensional diffr action problem of pl::\,ne electromagnetic waves by a thick dielectric slab is investigated thoroughly using Mode I\!Iatching (MM) technique, which is considered to be straightforward and underst andable, in conjunction v"ith the Method of Moment (MoM) considering t ransverse electric polarizations (TE) parallel to t he edge of the considered structure. To start wit h , tlw fields ill all regiolls are expanded in terms of mix spectrum of guided and radiated modes. In the free space, a continuous radiation mode expansion is used. The guided modes are finite in number while t here are infinite number of radiation modes. The condition for guided modes in the dielectric slab dictates eigenvalue equation. Only those eigenvalues axe retained which satisfy valid conditions of the problem. That is, the power is propagated within the slab and and decay exponentially in the free space. Then Mode NIatching technique is applied, incorporating t he orthogonal prop erties of the mixed spectrum of the modes in order to separate the guided and radiation components of the field. The discretization of radiation mode spectrum is achieved leading t o the numerically stable solution provided a sufficiently large number of points to convert the integral into finite summation. Method of Moment is employed to determine the reflection coefficients for free space radiation modes. Consequent ly mode amplitudes of all the even guided, odd guided and radiation modes are determined. The scattered far field is evaluat ed by the saddle point method. A numerical solution of this system is obtained, propagated and scat tered powers are evaluated in all regions, which includes the dielectric and free space regions, for various values of incident angles and slab thickness. The same method and sequence is employed for the other dielectric structures like wedge and rectangular cylinder.