Scattering of plane electromagnetic waves from a small inhomogeneity in a slightly curved layer (Q2567769)

The scattering problem of a plane short-wavelength elastic horizontally polarized (HP) shift wave from an inhomogeneous inclusion (IHG), which lies inside a slightly curved (SC) layer, is investigated. The inhomogeneous inclusion under consideration has the form of an infinite cylinder with a small-cross section of diameter \(d\) that is small in comparison with the wavelength \(\lambda\), i.e., \(d\ll\lambda\), and the incident plane electromagnetic wave is polarized parallel to the axis of the cylinder. The problem is solved in several steps. The field reflected from the layer without an IHG is formulated first in terms of the incident wave, and then the Green's function for the case without an IHG is constructed. In the third step, an integral equation having a small kernel is derived, and this integral equation is employed for finding the solution of the problem with an IHG inside the layer. Finally, the first approximation for the solution is determined by employing the method of successive approximations. It is proved that the small inhomogeneity radiates as a point source the intensity of which is proportional to the area of the cross-section of the inhomogeneity and to the jumps of the squared velocities in the layer and in the homogeneity.