ИСТИНА

An acoustic field in a metamaterial can be represented as the sum of an incident field and all fields scattered by metamaterial elements. Complex scattering coefficients are introduced to describe these scattered fields. The scattering coefficients satisfy the general relationships between their phase and amplitude. Set of their values on the complex plane is the circle with the center of -2i and the radius of 2 in the absence of absorption, or the inner part of this circle, if absorption exists. The use of the scattering coefficients makes it possible to take into account the processes of the multiple scattering between separate elements of the metamaterial, rather than between every two points of the medium, which is typical for traditional scattering problems. This fact simplifies calculation of the acoustic field for a wide class of metamaterials. The limited set of the possible values of the scattering coefficients allows to consider solution of the inverse problem, i.e., to determine a design of a metamaterial element on base of the known scattering coefficients. However, the solution of this problem is unstable in a number of cases.