Smoothed half-infinite plane waves: Approaching to their optimum profiles

A concept of homogeneous, smoothed half-infinite plane waves is developed in the framework of a discontinuity-free decomposition of the field of a plane electromagnetic wave diffracted by a perfectly conducting half-infinite screen. It is shown that the entire diffracted field is broken down into the mentioned reflected and transmitted, smoothed half-infinite plane waves and edge quasi-cylindrical waves. In the planes of half-waists, the wavefronts of the smoothed waves are always rigorously plane, whereas their amplitude profiles are odd symmetrical in relation to respective half levels. The smoothed waves possess the phase-conjugate property relative to the planes of their half-waists and, in the first approximation, they are self-similar in the entire space. Also, the amplitude profiles at the half-waists of these waves are well reproduced within certain propagation distances. These and other properties of the smoothed half-infinite plane waves, a procedure for their approximate generation, and two simplest analytic profiles at their half-waists are considered in detail.