Surface integral equation formulation for the analysis of left-handed metamaterials

Abstract

A surface integral equation (SIE) formulation is applied to the analysis of electromagnetic problems involving three-dimensional (3D) piecewise homogenized left-handed metamaterials (LHM). The resulting integral equations are discretized by the well-known method of moments (MoM) and solved via an iterative process. The unknowns are defined only on the interfaces between different media, avoiding the discretization of volumes and surrounding space, which entails a drastic reduction in the number of unknowns arising in the numerical discretization of the equations. Besides, the SIE-MoM formulation inherently includes the radiation condition at infinity, so it is not necessary to artificially include termination absorbing boundary conditions. Some 3D numerical examples are presented to confirm the validity and versatility of this approach on dealing with LHM, also providing some intuitive verifications of the singular properties of these amazing materials.

Comparison of Surface Integral Equations for Left-Handed Materials

“…to the analysis of LHM can be looked up in [18]. Their suitability for dealing with LHM will be tested next.…”

“…Surface integral equations (SIE) have been extensively used for solving scattering problems involving homogeneous or piecewise homogeneous dielectric objects [8][9][10][11][12][13][14][15]. Recent works have shown that their application may be extended to the homogeneous LHM analysis [16][17][18][19].…”

Parallel Implementation of Mlfma for Homogeneous Objects With Various Material Properties

“…JMCFIE is applicable to those objects with negative permittivity and/or permeability for the homogenization of metamaterials, provided that the roots when finding the wavenumber and intrinsic impedance are selected carefully [34]. In free space, negative parameters lead to a high-contrast object, whose iterative solution can be again challenging, especially if the object is lossless.…”

Fast surface integral equation formulations for large-scale conductors, metamaterials, and plasmonic problems

“…Looking for the extension of rigorous Maxwell integral equation solvers to these new demanded areas, our recent efforts were headed to extend the fast SIEMoM formulations to the analysis of composite piecewise homogeneous metamaterial and plasmonic objects [9][10][11][12][13]. Numerical examples will be presented confirming the validity and versatility of this approach for the accurate resolution of problems in the context of leading-edge nanoscience and nanotechnology applications.…”