Radiation from open-ended circular waveguides: A formulation based on the incomplete Hankel functions

An analytical formulation based on physical optics is employed to determine the field and the radiated power distribution by open-ended circular waveguides. Using the incomplete Hankel functions, the line integrals yielding the electromagnetic field are evaluated in closed analytical form along the waveguide axis. It is shown that cylindrical waves are generated by the surface currents. owing on the waveguide walls, while spherical waves are produced by the currents and charges excited at the waveguide truncation. Cylindrical and spherical waves are shown to be responsible for the field synthesis in terms of waveguide modes and scattered fields at the waveguide mouth. Numerical results concerning the spatial distribution of the electromagnetic field and associated power density are compared with previously published results, showing the advantage of the incomplete Hankel functions formulation. Finally, the uniform asymptotic representation of the incomplete Hankel function is shown to be suitable to compute the field distribution on the waveguide axis except for the TE11 and TM01 modes.