Diffraction of an electromagnetic wave in the gaps between plates

In the article, the problem of diffraction of a plane $TE$-polarized electromagnetic wave in the gaps between metal plates located in one plane is investigated. The diffraction problem is formulated in the form of a boundary-value problem for the Helmholtz equation with the “on metal” boundary conditions and a given asymptotic behavior on the edges of the screens. The solutions are searched for in the class of the waves propagating to infinity. The problem under consideration is reduced to an integral equation with a strong singularity of the kernel with respect to the trace of the electric field vector in the gap. The integral equation, in its turn, is reduced to an infinite system of linear algebraic equations with respect to the derived function expansion coefficients. Some singular integrals containing generalized Chebyshev polynoms are analytically calculated.