Edge diffraction by a two-dimensional composite wedge of conductor and lossless dielectric is obtained asymptotically for a plane wave incidence. When a plane electromagnetic wave is incident from the background medium upon a composite wedge of conductor and lossless dielectric, three Kirchhoff's integrals in three regions give the fields, respectively, in each region, if the exact boundary fields are known. Extinction theorem gives the null field in the complementary regions corresponding to the outside of each three region filled with the same medium of the original region, if the same boundary fields are used. This means that one may obtain the fields scattered by the composite wedge by solving the triple Kirchhoff's integrals in three regions of the composite wedge and another triple integrals of the extinction theorem in their complementary regions.
One may approximately solve this problem by assuming the geometrical optics (GO) fields along the interfaces, which gives the physical optics(PO) approximation. Another approximate primary solution better than PO may be obtained by using GO solutions along the dielectric interface and the known exact fields along the interfaces of the conducting wedge for approximate boundary fields.
Unknown correction sources which produce the correction fields may be added to these approximate boundary fields along the interface boundaries and these boundary fields should satisfy the integrals of the extinction theorem in their complementary regions. One may expand the correction sources along the boundaries by the complete Neumann series with unknown expansion coefficients and make its leading term at the edge satisfy the static edge condition of the composite wedge which is known. One may obtain these expansion coefficients by making the total asymptotic fields obtained analytically from the correction sources and the approximate primary fields zero in the complementary region numerically at the sampled field points.
With this limited number of expansion coefficients, the corrected solution satisfying the boundary conditions of the conducting wedge give close results with the exact solutions of the conducting wedge in two limits when the dielectric wedge becomes either the background medium or the conducting wedge. Edge diffracted patterns of the corrected solutions are shown to approach the exact pattern of the conducting wedge in those two limits. For the relative dielectric constant of the dielectric wedge larger than one, the edge diffracted pattern of the corrected solution is shown to satisfy the extinction theorem asymptotically in its complementary regions, which assures the validity of this solution. Numerically calculated asymptotic fields are shown for various values of dielectric constants, wedge angles, and incident angles and compared with the exact fields of those two limits.
