Diffraction by circular pin: Wiener-Hopf method

The paper considers the boundary value problem of the diffraction of a symmetric TE-wave by a semi-infinite pin located coaxially inside a circular waveguide. The problem is reduced to a system of singular integral equations, which is solved by the Wiener-Hopf method in the class of meromorphic functions. Based the factorized Bessel functions and the entire function, a technique for constructing a solution in the form of the Fourier component of the surface current density is developed. The Meixner condition is satisfied by shifting the zeros of the entire function. The correctness of the solution was verified using the stitching method. The solution also provides a limiting transition to a thin pin, where a semi-infinite pin and a hollow cylinder of the same radius are physically equivalent. In the case of the limiting transition, when the radius of the pin approaches the radius of the waveguide, the solution provides a complete reflection of the oncoming mode, which is the only mode of the waveguide propagating in the opposite direction.