Scattering of electromagnetic waves by a discrete octahedron from resonant spheres

A solution is given to the problem of scattering of electromagnetic waves by a discrete convex polyhedron – an octahedron of resonant magnetodielectric spheres based on a complex rhombic crystal lattice. Here we consider a case equivalent to the X-ray optics of crystals, when α / λ՛<<1 and can be α / λg ~ 1; d, h, l / λ՛ ~ 1, where α is the radius of the spheres; λ՛, λg are the lengths of the scattered wave outside and inside the spheres; d, h, l are constant lattices. The solution of the problem is obtained based on the Fredholm integral equations of electrodynamics of the second kind with nonlocal boundary conditions. The expressions found in this work for a metacrystal in the form of an octahedron can be used to study the fields scattered by the crystal in the Fresnel and Fraunhofer zones, as well as to study its internal field. The relations obtained in this work can find application in the study of the scattering of waves of various kinds by convex polyhedrons, the creation on their basis of new types of limited metacrystals, including nanocrystals with resonance properties, and in the study of their behavior in various external media. As well as in the development of methods for modeling electromagnetic phenomena that can occur in real crystals in resonance regions in the optical and X-ray wavelength ranges.