ИСТИНА

Acoustic metamaterials are artificial media, usually consisting of discrete elements smaller than a wavelength. The design of each element is designed in such a way that the medium has the specified wave properties. For example, with the help of metamaterials it is possible to observe negative refraction, superlens, hyperlens, concealment, and other effects of great practical importance. The task was set to design a metamaterial with desired properties. To solve it, an approach based on the scattering theory was proposed. It consisted of two stages. First, the zero field method was used to calculate the field in the medium. It is based on the multipole decomposition of the field scattered by each element of the metamaterial. In many cases, when the size of the metamaterial element is small relative to the wavelength, it is sufficient to take into account only a few terms of this expansion. The complex structure of a metamaterial element is reduced to just a few complex numbers - scattering coefficients. In addition, the set of values for each of these coefficients is limited. This can make the method efficient in terms of the amount of computation. The scattering coefficients and the position of the centers of the elements of the metamaterial were chosen so as to ensure the given wave properties of the medium. Secondly, it was required to propose a specific physically realizable design of a metamaterial element with a previously defined set of scattering coefficients. This is equivalent to solving the inverse scattering problem. It is shown that the well-established functional-analytical methods do not allow obtaining an acceptable result, since they have a limited resolution. Gradient optimization methods are free from this shortcoming, but do not guarantee the existence and uniqueness of the solution. For a design problem, non-uniqueness is not a drawback, but the question of the existence of a solution is important. To answer it, numerical simulation of acoustic field scattering on five-layer elastic cylinders of small radius was carried out. It is shown that by choosing materials and layer thicknesses, it is possible to provide any combination of monopole and dipole scattering coefficients.