[Figure 1; see abstract in PDF for details].
It is a well-known fact that dielectric coated infinite metallic structures such as planes and wires can propagate "surface modes". We are here chiefly concerned with a two-dimensional case. There is no theoretical difficulty in extending our solution to three-dimensional structures.
We are dealing here with a grounded dielectric slab of permittivity ε and thickness a. (The case in which the electric wall is replaced by a magnetic one involves only slight modifications.) The half-space over the slab is a dielectric of permittivity 1.
E modes and H modes can propagate in the slab. They are the so- called "trapped waves". The number of modes is connected with ε and a.
As an example of the treatment of the general case, we shall suppose that a is small enough to propagate only one E mode. Extension to the H case or to the multimode case is obvious.
We then suppose (see Fig. 1) that only one mode is propagating, coming from z = +∞. This trapped wave will be diffracted by a semi infinite metallic sheet of zero thickness, which lies on x = d , z < 0. We are mainly interested in reflection and transmission coefficients for the trapped modes, the radiated power, and the far-field pattern
