Method of Moment Analysis of Carbon Nanotubes Embedded in a Lossy Dielectric Slab Using a Multilayer Dyadic Green’s Function

Abstract

Modeling the electromagnetic response of carbon nanotube (CNT) reinforced composites is inherently a 3-D multiscale problem that is challenging to solve in real time for nondestructive evaluation (NDE) applications. This article presents a fast and accurate full-wave electromagnetic solver based on a multilayer dyadic Green’s function approach. In this approach, we account for the effects of the dielectric slab, where the CNTs are embedded, without explicitly discretizing its interfaces. Due to their large aspect ratios, the CNTs are modeled as arbitrary thin wires (ATWs), and the method-of-moment (MoM) formulation with distributed line impedance is used to solve for their coupled currents. The accuracy of the in-house solver is validated against the commercial MoM and the finite element method (FEM) solvers over a broad range of frequencies (from 1 GHz to 10 THz) and for a wide range of dielectric slab properties. Examples of 100 nm-long vertical and horizontal CNTs embedded in a 1 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> -thick lossy dielectric substrate are presented. The in-house solver provides more than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$50\times $ </tex-math></inline-formula> speed up while solving the vertical CNT and more than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$570\times $ </tex-math></inline-formula> speed up while solving the horizontal CNT than a commercial MoM solver over the GHz-to-THz frequency range.