Absorbing and radiating cylinders as boundary-value problems*

Abstract

The exact Maxwell forms of the hybrid E and H fields and radiant-flux distributions in and outside of an absorbing cylinder of fixed length, when the cylinder is irradiated from below by E and H fields characteristic of particular modes, have been determined as a boundary-value problem in electromagnetic theory. The continuity of the tangential components of these E and H fields and the normal components of the radiant flux across the curved surface lead to the well-known Hondros equation, whose roots determine the propagation constants of the cylindrically guided waves. The simpler TE radiant fluxes above and inside the cylinder exhibit non-Fresnel-type periodic dependences on the length of the cylinder and the position of the observation plane inside the cylinder, which are functions of the material constants of both media, the frequency, the radius of the cylinder, and the TE mode being used. Approximate solutions, with cylinders of large radii, indicate the TE radiant fluxes at the curved surface of the cylinder and at the interface between the illuminated and unilluminated regions above the cylinder have continous normal components, discontinuous axial components, and reversed angular components. The reversals of the angular components are due to reversals of the directions of the radial electric fields associated with the Sommerfeld and Hondros nebenwellen, due to the charges and currents on these interfaces. Approximate as well as rigorous solutions are helpful in considering these problems; the primary difficulty in obtaining exact solutions is to find roots of the Hondros equation.