lnr. 1. Engng Sci. Vol. 27, No. 6, pp. 701-710, 1989 0020-7225/89 $3.00 + 0.00 Printed in Great Britain. All rights reserved Copyright 0 1989 Pergamon Press plc DIFFRACTION OF AN OBLIQUELY INCIDENT PLANE WAVE BY THE DISCONTINUITY OF A TWO PART THIN DIELECTRIC PLANE ALINUR BUYUKAKSOY’, GGKI-IAN UZGGREN* and A. HAMIT SERBEST3 1 Faculty of Electrical and Electronics Engineering, Technical University of Istanbul, 80626 Maslak, Istanbul, Turkey ’ Department of Electrical Engineering, Yildiz University, Istanbul, Turkey 3 Department of Electrical and Electronics Engineering, Cukurova University, Balcali, 01330 Adana, Turkey (Communicated by H. DEMIRAY) Ah&act-The problem of diffraction of an obliquely incident plane wave by the discontinuity occuring in the permittivity of a thin dielectric layer is investigated. The structure is simulated by a set of boundary conditions involving the normal components of the field and their normal derivatives. The related boundary value problem is then reduced to three scalar Wiener-Hopf equations and solved by standard techniques. Some numerical results are presented in the case of normal incidence. 1. INTRODUCTION The diffraction of electromagnetic waves by a two-part surface is an important topic in diffraction theory, because it constitutes a canonical problem for analyzing the scattering caused by an abrupt change in the material properties of a surface. The diffraction by a two part impedance plane and by the discontinuity formed by resistive and impedance half-planes have been treated by several authors [l-4]. As a part of this subject we consider in the present paper the diffraction of an obliquely incident plane wave by the discontinuity occuring on a plane composed by two parts with different dielectric permittivities. A non-magnetic thin dielectric slab is generally simulated by an infinitesimally thin resistive sheet supporting an electric current proportional to the common value of the tangential electric field at its surface [5]. Recently, it has been shown that the inclusion of a “modified conductive sheet” in addition to the resistive one provides a better simulation at oblique incidence when the incident electric vector has a component normal to the layer [6]. For a thin planar slab consisting of a homogeneous non-magnetic dielectric with thickness c and relative complex permittivity E, the boundary conditions are as follows: zyxwvutsrqponmlkjihgfedcba nX{nX[E+E-]}=-2RnX[H+-H-1 (14 nX{nX[H++H-]}=2R*nX[E+-E-]++-$E++E-] 0) Here R and R* stand for R= ‘ii? R*= zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQP iYE kt(E - 1) ’ kt(E - 1) with Z and Y being the intrinsic impedance and admittance of the surrounding medium, respectively. The (+) and (-) superscript to the value of the field on the upper and lower faces of the sheet whereas n denotes the unit normal vector directed outward from the upper surface. Note that in the case of normal incidence for H-polarization the boundary conditions in (la, b) reduce to those previously given by Leppington [7]. The problem of diffraction by a two-part dielectric plane at skew incidence will be considered by expressing the boundary conditions in (la, b) in terms of normal components of the field and their normal derivatives. This will enable us to reduce the mixed boundary-value problem into three scalar Wiener-Hopf equations which can be solved by standard techniques. 701