Analysis of open-ended circular waveguides using physical optics and incomplete Hankel functions formulation

The spatial distribution of the electromagnetic field excited in semi-infinite open-ended circular waveguides is analyzed using a physical optics (PO) and incomplete Hankel functions formulation. Using the incomplete Hankel functions, the PO surface integral employed to compute the field quantities is reduced to a simple line integral along the waveguide contour. Such a superposition integral, which describes the elementary field contributions having spherical and cylindrical character, is then evaluated in closed analytical form along the waveguide axis. It is shown that cylindrical waves are generated by the surface currents flowing on the waveguide walls, while the spherical waves are produced by the currents and charges excited at the waveguide truncation. Cylindrical and spherical waves are responsible for the field synthesis in terms of waveguided modes and scattered fields at the waveguide mouth. Numerical examples, demonstrating the accuracy of said field representation in the near- and far-field region of truncated circular waveguides, are finally provided.