Structure of an edge-dislocation wave originating in plane-wave diffraction by a half-plane

Abstract

A new treatment of the well-known Sommerfeld solution of the problem of plane-wave diffraction from a perfectly conducting half-plane is reported. We show, in both theory and experiment, that the diffraction field (E-polarization) can be represented as a superposition of real physically existing waves, in contrast to geometrical and boundary waves postulated in Sommerfeld's representation. Our representation includes two pairs of wave components: one pair propagates along the direction of the incident wave, and the other in a mirror-reflected direction. Each wave pair consists of a plane-wave component with an amplitude half that of the incident wave and a nearly plane-wave component with an infinitely extended edge dislocation. On the basis of the proposed interpretation, all features of the half-plane diffraction are explained.

Wide-angle diffraction of the laser beam by a sharp edge

“…can be represented as the sum of two stable waves 1 almost everywhere behind the screen (see the discussion below) [11]:…”

“…2), except for a small region of a few tens of wavelengths in radius in close proximity to the edge and for diffraction angles exceeding a few tens of degrees. In these regions, one should take into account the field related to the component reflected from the screen [11]. The first term in Eq.…”

“…3) [12]. All the characteristic features of edge diffraction are related to exactly this singular wave [11]. In what follows this wave (related to diffraction and dislocation) is called the d-wave.…”

“…In this case, however, there remains a weak component which is related to the field reflected from the screen and can rigorously be taken into account[11].…”

MTPO based potential function of the boundary diffraction wave theory

“…Since the edge dislocation waves are continuous, it is possible to observe them separately as performed by Khizhnyak et al [22]. But they exist in the whole space and they pass through the obstruction as if there is no halfplane.…”