Asymptotic Solution to Scattering Problem on a Set of Small Particles and Application to Creating the Materials with a Peculiar Refractive Index

Abstract

The asymptotic solution to the scattering problem on a set of small particles, supplemented into homogeneous material, is used for modeling the materials with the desired refractive index. The consideration concerns the case of acoustic scalar scattering and the solution to initial scattering problem is built using an asymptotic approach. The closed form solution is reduced for the scattering problem. This is significant advantage of approach because there is no need to solve the respective system of boundary integral equations. High accuracy of solving the scattering problem is achieved by choosing the optimal parameters of the domain with small particles. The approach allows obtaining an explicit formula for the refractive index of the resulting inhomogeneous material. The numerical calculations show the possibility to get the specific values of refractive index including its negative values.