Some extensions of the concept of complementary electromagnetic structures

The well known Booker´s concept of complementary electromagnetic structures is valid for plane, infinitely thin, perfectly conducting complementary screens situated in a homogeneous lossless medium. It is shown in the paper that the concept can be extended to include pairs of arbitrarily shaped dielectric and/or magnetic bodies, possibly lossy, of arbitrary values of complex permittivity and permeability, positioned symmetrically with respect to the plane of the structure. In this manner, further practical problems can be solved by reducing them to problems the solution of which is either known or can be obtained more easily. Particular attention is devoted to quasi-TEM transmission lines. The complementary concept is extended to include the surrounding medium as well. It is shown that many novel exact relationships can be derived between parameters of such complementary lines, which can aid in determining some parameters, the expressions for which are not known, in terms of known parameters.