Abstract
The boundary-value problem of TM-wave diffraction on a semi-infinite circular pin is studied using the mode-damping method derived from theWiener–Hopf analytical source. The solution is expressed as an infinite series, with subsequent terms obtained through a recurrence relation, ensuring systematic refinement of the approximation. Numerical verification based on the conservation of energy confirms the validity of the solution. As expected, the diffraction process generates a TEM wave in the coaxial region of the waveguide, which highlights the physical consistency of the approach. The analysis demonstrates that the proposed methodology achieves sufficient accuracy even at the first approximation, making it both efficient and reliable. Unlike conventional techniques, the presented method provides a mathematically rigorous framework that combines analytical tractability with numerical validation. Furthermore, the approach can be extended to diffraction problems involving volumetric axisymmetric structures, thereby broadening its applicability in electromagnetic wave analysis. The results contribute to the advancement of diffraction theory and provide a foundation for applications in antenna design, scattering studies, and modern wireless communication systems.