Mathematical Modeling of Multi-Element Antenna Arrays with Chiral Metamaterials Substrates Using Singular Integral Equations

Abstract

In this paper, a physical model of the multi-element antenna arrays (MEAA) has been considered and a self-consistent numerical method for solving the problem of current distribution on the MEAA surface with chiral metamaterials substrate has been proposed. The algorithm of the input admittance matrix elements for chiral layer based on the conductive left and right-handed helices has been developed and elements of the matrix surface impedances for investigated structures have been found. A set of singular integral equations with a Cauchy kernel for calculating the current density on the surface of the MEAA has been derived. A numerical solution of the set is a well-posed in the sense of Hadamard. Calculations of current distribution on the MEAA surface, impedance characteristics of a three-element antenna array and the dependence of the isolation levels between emitters on the chirality parameter have been performed and analysed. It has been shown that the use of chiral substrates can substantially increase the isolation between emitters.