Robust technique for the polarisability matrix retrieval of bianisotropic scatterers via their reflection and transmission coefficients

Abstract

A consistent algorithm for extracting the polarisability matrix of bianisotropic meta‐atoms directly from their reflection and transmission properties is introduced in this study. Considering a two‐dimensional periodic distribution of the scatterer under study, illuminated by properly‐polarised, normally‐incident, plane waves, the point‐dipole approximation is successfully applied in order to analytically compute the scattered field of the array in terms of the particle polarisabilities. Then, simulated or measured S‐parameters can be employed for the inversion of the resulting non‐linear system of equations, leading to the desired dynamic polarisability matrix and, especially, the magneto‐electric coupling term. Finally, the featured technique is applied to an assortment of important structures, frequently utilised for various metamaterial applications and the outcomes are extensively compared with previously existing techniques, thus verifying the merits of the novel approach.

Full Polarizability Matrix Extraction Formulas for Electrically Small Particles via Reflection/Transmission Coefficients

“…1 is replaced by a set of equivalent radiating surfaces. Following the averaging process described in [7,19,20], the currents of these surfaces can be expressed in terms of the induced dipole moments as…”

“…1, a set of induced dipole moments is derived, and subsequently, a set of scattered fields, whose computation at z = ±l leads to the reflection/transmition coefficients (or equivalently the S-parameters) of the 2D array. So, regarding the latter, if we use the evaluation scheme of [18][19][20], the induced dipole moments are given by…”

“…Based on the previous analysis, the desired polarizabilities can, now, be extracted in a way analogous to the techniques of [18][19][20]. Therefore, if (13) are inserted into (8), one arrives at…”

“…Firstly, an instructive technique for retrieving the polarizabilities of anisotropic scatterers in terms of closed-form expressions has been developed in [18]. Expanding this concept, the extraction of the polarizability matrix of omega-type bianisotropic structures through the reflection/transmission coefficients of two or, for simplicity, a single 2D particle array has been, respectively, proposed in [19]. Both approaches, however, involve the numerical solution of a nonlinear system of equations, which is not always easy to implement.…”

Evaluation of polarisability tensors of arbitrarily shaped highly conducting bodies

“…These methods can deal with scatterers of quite general shape and constitution but generally suffer from the necessity of removing the effect of the artificial periodic environment or the waveguide walls. This is done either by a suitable calibration process [32], [36], or by directly evaluating the interaction constants of the array [33]- [35]. The basic deficiency of the calibration procedure is the inaccesibility of precisely defined bianistropic standards.…”