Diffraction of a plane wave by a right-angled penetrable wedge

The problem of electromagnetic diffraction (E-polarization) by two screens is analyzed. The screens are half-planes which form a right-angled wedge. The first half-plane is an electrically resistive sheet, and the second one is a perfectly magnetically conductive surface (ideal ferrite). The problem is formulated as a boundary-value problem for the Helmholtz equation with respect to the E-z-component of the electric field. On the conductive screen, the normal derivative of the function E-z vanishes. On the resistive half-plane, the function Ez is continuous and it is proportional to the jump of its normal derivative. The Sommerfeld integral representation is used to convert the problem to a difference equation of the second order. For a special value of the impedance parameter the problem reduces to two scalar Riemann-Hilbert (RH) problems on a segment with coefficients having a pole and a zero on the segment. The general solution to the RH problems is derived by quadratures. The RH problems are equivalent to the governing boundary-value problem when certain conditions are satisfied. These conditions are used to determine unknown meromorphic functions in the solution of the RH problems. Exact formulas for the reflected, transmitted, and diffracted waves are derived, and numerical results for the diffraction coefficient are reported.