On a method for solving problems of wave scattering by ``transparent'' obstacles (Q1595515)

The diffraction of an electromagnetic wave by a magnetoelectric body is considered. The method developed by the author [Dokl. Akad. Nauk 325, 273-279 (1992; Zbl 0790.45007) and Dokl. Akad. Nauk 337, 728-731 (1994; Zbl 0843.35069)] for solving problems of wave scattering by obstacles with impedance and ideal boundary conditions has been generalized to problems of wave scattering with conjugate conditions on the boundary of the scatterer (of a cylindrical form). The two-dimensional case is studied. Relations are obtained for the electromagnetic field on the boundary of the scatterer. The domain of regularity of the internal and external diffraction have nonempty intersection. The relations obtained can also be applied to determine the constants of wave propagation inside an optic fiber with a noncircular cross section.