On the theory of corrugated plane surfaces

An analysis is given of an electromagnetic system composed of a rectangular waveguide in tandem with a corrugated waveguide which feeds a flat, corrugated surface of arbitrary length terminated by a ground plane, whose length is also arbitrary. An improved procedure of field determination is used which combines Floquet´s theorem and the variational principle, thus revealing an additional requirement on the corrugation geometry. Factors influencing a match at the feed mouth, and satisfactory launching of the surface wave are discussed. The degree of suppression of the feed radiation is given in db as a function of the geometry of the system. Approximate radiation patterns are derived for two cases, (a) when the system is terminated by an infinite ground plane, and (b) when the system is terminated by a finite ground plane. For the latter case, an upper bound on the tilt angle of the main beam and a lower bound on its beamwidth result from an approximate theory. For both cases, the Hansen-Woodyard endfire relation is found to provide beam sharpening even when the feed radiation is considered. The presence of higher order surface modes, their effect, and their elimination are discussed. Comparison of the theory with experiment is reasonably good.