Diffraction by right-angled penetrable wedges

Two problems of electromagnetic diffraction (B-polarization) by a right-angled penetrable wedge are analyzed. For both problems, one of the walls of the wedge is an electrically resistive half-plane. The second one is either a perfectly magnetically conductive half-plane (Problem A), or a perfectly electrically conductive half-plane (Problem B). The Sommerfeld integral representation is used to convert the problems to a difference equation of the second order. For a special value of the impedance parameter, the problems reduce 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.