ABSTRACT
This paper presents a discontinuous Galerkin (DG) integral equation (IE) method for the electromagnetic analysis of arbitrarily-shaped plasmonic assemblies. The use of nonconformal meshes provides improved flexibility for CAD prototyping and tessellation of the input geometry. The formulation can readily address nonconformal multi-material junctions (where three or more material regions meet), allowing to set very different mesh sizes depending on the material properties of the different subsystems. It also enables the use of h-refinement techniques to improve accuracy without burdening the computational cost. The continuity of the equivalent electric and magnetic surface currents across the junction contours is enforced by a combination of boundary conditions and local, weakly imposed, interior penalties within the junction regions. A comprehensive study is made to compare the performance of different IE-DG alternatives applied to plasmonics. The numerical experiments conducted validate the accuracy and versatility of this formulation for the resolution of complex nanoparticle assemblies.
ABSTRACT
The performance of most widespread surface integral equation (SIE) formulations with the method of moments (MoM) are studied in the context of plasmonic materials. Although not yet widespread in optics, SIE-MoM approaches bring important advantages for the rigorous analysis of penetrable plasmonic bodies. Criteria such as accuracy in near and far field calculations, iterative convergence and reliability are addressed to assess the suitability of these formulations in the field of plasmonics.
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.
ABSTRACT
The design of a hyperthermia applicator for heating biological tissues is presented in which the applicator consists of an array antenna surrounded by a perfect electrically conducting reflector. The heat hazard to superficial tissues is reduced by the introduction of a dielectric protecting layer over them. A method of moments formulation is applied to approximate the electric field within the biological medium and a closed form expression is presented for the electromagnetic coupling problem, which enables an optimisation procedure to be performed. The applicator enhances both penetration and focusing: deep tumours, close to the bone region, are heated and the percentage of biologically healthy tissue exposed to a specific absorption rate (SAR) hazard level diminishes by 53.8%.
