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.

Singular Integral Formulations for Electrodynamic Analysis of Metamaterial-Inspired Antenna Array

“…To determine surface impedance matrix elements in the antenna array the approach used in [12] first establishes the surface admittance matrix elements [ ] and then converts the matrix to its corresponding [ ] matrix, which takes a longer processing time. Unlike in [12] the proposed methodology used here avoids the complexity of this conversion step and therefore the additional computation processing. This is achieved by directly calculating the surface impedances matrix elements, the consequence of which is reduction in the computational time.…”

“…This is achieved by directly calculating the surface impedances matrix elements, the consequence of which is reduction in the computational time. Because the computational time in [12] was not reported it was necessary to benchmark the proposed technique against a commercial 3D full wave electromagnetic solver based on MoM. Moreover, the radiating elements in the proposed antenna array is metamaterial-inspired for realizing a wider operational bandwidth.…”

“…The surface impedance matrix elements in the xy-plane at = ℎ are specified by the surface impedances matrix of zone I ( > ℎ) (dielectric space) [ (1) ] and the matrix of zone II ( < ℎ) (MTM substrate layer) [ (2) ], and is defined by: (12)…”

“…± 0 2 ⃗ ⃗ + 2 (− 2 + 2 2 ) ⃗ − ∇ 2 ⃗ = 0 (10) It can be shown that by applying the electric and magnetic field derived in [12] into (9) and (10), we can determine the matrix elements of the surface impedance at the plane = ℎ resulting from zone II ( < ℎ) (MTM substrate layer). Elements of the matrix of surface impedance are given by:…”

“…Electrodynamic analysis of antennas and antenna arrays is typically carried out using commercial electromagnetic solvers such as CST Studio Suite® that employ finite integration technique (FIT), which is a discretization scheme for Maxwell's formulations in their integral form [11]. The use of this approach is associated with challenges associated with [12], namely, (i) inaccuracy of the constructed model, (ii) choice for optimum sampling rate used, and (iii) intensive demand on computational sources. The alternative method involves the use of method-of-moments (MoM) approach that involves solving Fredholm integral equations of the first kind to enable the determination of the impedance, spatial and polarization characteristics of the array with a high degree of accuracy using less computational effort.…”