The Method of the Generalised Eikonal

Physical Interpretation of the Solution to the Problem of Diffraction on a Half-plane with Non-Ideal Boundary Conditions

“…A study of the behavior of the functions whose graphs are depicted in Figure 3 showed that as the parameter X changes from 0 to infinity, the shapes of curves GDC (5) and PODC (6) remain unchanged, while curves (4) and ( 9) shift from the curve (5) to curve (6). The angle φ is plotted horizontally.…”

“…The scattering diagrams (SD) modules are plotted vertically. The solid gray line is WHM solution fr(X, φ, φ0) (4}, circles are the GDC formula (5), triangles are the PODC formula (6), squares are the heuristic solution fh(R, T, φ, φ0) (9).…”

“…As X changes from 0 to ∞, the following changes occur: the expression fh(R, T, φ, φ0) (9) transforms from the formula fg(R, T, φ, φ0) (5) to the formula fg 0 (R, T, φ, φ0) (6), and the expression gh(R, T, φ, φ0) (17) transforms from the formula gf (R, T, φ, φ0) (14) to the formula gf 0 (R, T, φ, φ0) (15). This means that the greater the transparency of the object is, the more the formulas for the GDC approximation (5), ( 14) are transformed into formulas for the PODC approximation (6), (15).…”

“…The MFC application in order to obtain heuristic formulas describing the solution to the problem of diffraction on a semitransparent half-plane is based on the following algorithm [6,8,9]:…”

“…One of the fundamental components is the singular diffraction coefficient for a semi-infinite scatterer [6,8,9]. Obtaining heuristic formulas for two-dimensional semiinfinite scatterers, even in spite of the existence of rigorous solutions, is a topical problem [9].…”