Diffraction of plane and cylindrical waves by a metamaterial cylinder

Calculation of the near field for concave and convex-concave screens with a variable curvature in the presence of whispering-gallery modes

“…6, where the position of cylindrical wave source Q (points 1-3) is also shown. Evidently, for the aforementioned parame ters of the problem, scattering contour (13) has not only a variable curvature but also two points-{x = 0, y = 0} and {x = -60, y = 0}-where the curvature of the con tour is zero. Figure 7 illustrates the calculated spatial distribu tion of the absolute value of scattered field amplitude (Fig.…”

“…2a), but the amplitude of this field is smaller, a cir cumstance that can be attributed to the reduced amplitude of the edge ray field. Now, let us consider the case when the contour of the cross section of the scattering surface has a variable curvature and is described by formula (13). We use the following parameters of the contour: kA = 30, kT = 30, x b = -60, and x e = 30; cylindrical wave source Q is suc cessively located at the three points with the Cartesian coordinates {x 0 = -50, y 0 = -10} (point 1), {x 0 = -55, y 0 = -0} (point 2), and {x 0 = -5, y 0 = 0} (point 3).…”

“…This method is referred to as the method of extended boundary conditions. Its high efficiency has been demonstrated for a series of prob lems [10][11][12][13][14][15]. Recall that the method of extended boundary conditions is based on two ideas.…”

“…A new method is proposed in [13,14] for numerical solution of wave diffraction and scattering problems. According to this method, IEs of forms (4) and (7) are reduced to Fredholm IEs of the first kind with a smooth kernel.…”

“…Studies [12][13][14][15] are an exclusion, but, in these studies, only the field in the far zone of such screens (scattering pat tern) is investigated. Therefore, solution of such prob lems in a rigorous formulation and analysis of the near scattered field obtained on the basis of these solutions are of practical and theoretical interests.…”