Quick retrieval of effective electromagnetic metamaterial parameters by using a Multi-fidelity Surrogate Modelling approach

Abstract

Electromagnetic metamaterials (MMs) are artificial composites that exhibit exceptional physical characteristics. Their design, which relies on the retrieving of the effective medium parameters, is usually a very time-consuming process because of the high number of full-wave simulations involved in this task. To alleviate the related computational burden, we propose to use a Multi-fidelity Surrogate Modelling (MFSM) approach. Numerical results demonstrate that this methodology turns out to be promising for a quick evaluation of the scattering parameters from which the effective constitutive parameters of a MM are retrieved, as shown by two numerical examples.

Analytic Continuation, Phase Unwrapping, and Retrieval of the Refractive Index of Metamaterials from S-Parameters

“…where, for each z ∈ γ, the value assigned to the integer parameter p is the index q of the Riemann sheet S q (L) on which z lies. Relation (12) can be used to compute L(•) on γ(t) ≜ S 21 /(1 − S 11 R). Substituting ( 8) into (12), we have the following:…”

“…In the last decade, researchers have shown great interest in developing particular three-dimensional artificial materials, usually made up of a lattice of metallic resonant inclusions arranged in a dielectric host medium called metamaterials (MMs), given obtaining devices endowed with exceptional operating performances [4]. To characterize MMs, the so-called heuristic homogenization approach, developed for the first time in [5,6], is the procedure most commonly employed by practitioners and researchers in the field [7][8][9][10][11][12][13][14]. In this peculiar framework, it is assumed that an MM, within its operating frequency range, can be considered analogous to a homogeneous medium, called the effective medium, for which the electromagnetic properties are described by an effective electric permittivity ϵ e f f and magnetic permeability µ e f f [5,6].…”

Extraction of the Electromagnetic Parameters of a Metamaterial Using the Nicolson–Ross–Weir Method: An Analysis Based on Global Analytic Functions and Riemann Surfaces

“…In particular, the branch ambiguity issue, i.e., the lack of uniqueness in the evaluation of the effective refractive index, n e f f (ω) [18,19], turns out to be the most critical and problematic of all, even though all the conditions for the employment of the NRW method are fully satisfied [18,19]. In the literature, a number of techniques based on Kramers-Kronig (K-K) relations [20][21][22][23][24] and on the phase unwrapping approach [25][26][27][28] have been developed to counter this problem. Concerning the rationale behind the use of K-K relations, it is a direct consequence of the causality principle, which makes it possible to determine the real part of the effective complex refraction index without any ambiguity, Re[N e f f (ω)] = n e f f (ω), from the knowledge of its imaginary part, Im[N e f f (ω)] = κ e f f (ω) [29].…”