Radiation from a planar waveguide with symmetrical flange

The problem of radiation from a planar waveguide with symmetrical flange is studied. This is one of the model problems of diffraction theory. The method of partial regions is used. In the first and second subregions the fields are presented in terms of Fourier integrals, and in the third subregion - in terms of the Sommerfeld-Maliuzhinets integral. After binding the fields on common subregion boundaries, the calculation reduces to the set of inhomogeneous functional Maliuzhinets equations, which are solved by Tuzhilin S-integrals. This allows for the initial problem to be formulated as the infinite set of algebraic linear equations relative to transformation coefficients of waveguide waves.