UDC 621.372.853.1 : 621.396.677.73 Indexing Terms: Antennas, horn, Electromagnetic waves, scattering Scattering by a dielectric discontinuity in an H-plane sectoral horn Z. A. DELECKI, MSc* M. HAMID, PhD, FIEE, FIEEEt and A. Z. ELSHERBENI, PhD, MIEEE* * Dept of Electrical Engineering, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2 t University of Manitoba; on leave at the Dept of Electrical Engineering, University of Central Florida, Orlando, Florida 32816, USA t Dept of Electrical Engineering, University of Mississippi, Mississippi 38677, USA SUMMARY Scattering of an electromagnetic wave at a transverse discontinuity created by an imperfect dielectric in a long H- plane sectoral horn fed by parallel plate waveguide is solved by the method of transformation into an equivalent plane wave (TEPW). An analytical method of matching fields of both waveguides is developed in order to be consistent with the TEPW method. The results are compared with data based on classical and experimental methods. 1 Introduction Dielectrically loaded horn antennas have been experi- mentally investigated by a number of authors. 1 " 4 The simplest structure employing a horn antenna is an H-plane sectoral horn connected to parallel plate waveguide and embedded in a dielectric medium. In order to solve the scattering problem in such a structure the scattering at both the dielectric discontinuity and the waveguide junction must be considered. It is well known that such discontinuities have no exact solution due to the fact that regions associated with them cannot in most cases be described in a single coordinate system. Many researchers have contributed a great deal of work to determine analytically the scattering by such junctions. Among these are Stevenson, 5 Leonard and Yen, 6 Hamid, 7 Lewin, 8 Iskander and Hamid. 9 In spite of the fact that they have based their solutions on different concepts and theories, this question seems to be still open for an exhaustive treatment. The previous attempts discuss the case where in the interior of the horn (or sectoral waveguide) only outward propagating modes exist. The goal of this paper is to solve the problem of scattering at the dielectric discontinuity as well as the scattering at the waveguide junction discontinuity resulting in a single reflection coefficient to be monitored in the feed waveguide. The configuration of the dielectric loaded waveguide system under consideration is shown in Fig. 1. The parallel plate waveguide feeds the H-plane sectoral waveguide, which is assumed to be long and to have an arbitrary flare angle a. The fields diffracted at the outer edges of the sectoral waveguide do not interact with those existing on the transversely oriented internal dielectric surface due to the fact that the dielectric is assumedHossy and the sectoral waveguide is semi-infinite in length. It is further assumed that the waveguide supports a single TE p0 mode, where p = 1, 2, 3,..., in the forward direction (see Fig. 1). The effect of a discontinuous boundary at the junction causes a diffracted field with an infinite number of modes travelling in both directions of the junction. Journal of the Institution of Electronic and Radio Engineers, Vol. 58, No. 5, pp. 235-243, July/August 1988 2 Behaviour of the Electromagnetic Field in the Transition Region Considering that the parallel plate waveguide feeds the horn-like waveguide and that the tangential electric field across boundaries is continuous, the unknown total reflection coefficient F m may be found by substituting the solution of the Helmholtz equation in the parallel plate region Rj (with the undetermined reflection coefficient of interest) into the corresponding region of the sectoral waveguide. Let us take the solution of the Helmholtz equation for the electric field with provision that it is expressed in polar coordinates of the form 8 sin (1) where the index p denotes an arbitrary single mode supported by the parallel plate waveguide. In order to make use of equation (1) its partial derivatives must be found. Upon finding and substituting these into the Helmholtz equation expressed in polar coordinates we obtain, after lengthy routine calculations, the following partial differential equation for the unknown reflection coefficient F m valid for h, cos a , a 2 r 2 cos 0+ w + 2 mn ap tan mrr sin cos (j)— j ©1988 IERE