Wireless propagation in circular tunnels

We study models for propagation in circular tunnels. The excitation is either a circular magnetic or circular electric current loop. We produce expressions for the fields in terms of a Fourier transform over the axial variable. We then produce the modes in the lossy structure by contour integration techniques. We include numerical results for the field intensity both as a function of axial distance and as a function of radial distance for several frequencies, radii, and constitutive parameters of interest. We comment in particular concerning the specific form of the field both near to and far from the antenna source.