J. Rivero

Method-of-moments formulation for the analysis of plasmonic nano-optical antennas

We present a surface integral equation (SIE) to model the electromagnetic behavior of metallic objects at optical frequencies. The electric and magnetic current combined field integral equation considering both tangential and normal equations is applied. The SIE is solved by using a method-of-moments (MoM) formulation. The SIE-MoM approach is applied only on the material boundary surfaces and interfaces, avoiding the cumbersome volumetric discretization of the objects and the surrounding space required in differential-equation formulations. Some canonical examples have been analyzed, and the results have been compared with analytical reference solutions in order to prove the accuracy of the proposed method. Finally, two plasmonic Yagi-Uda nanoantennas have been analyzed, illustrating the applicability of the method to the solution of real plasmonic problems.

Comparison of surface integral equation formulations for electromagnetic analysis of plasmonic nanoscatterers

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.

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

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.

Solution of large-scale plasmonic problems with the multilevel fast multipole algorithm.

A surface integral equation together with the multilevel fast multipole algorithm is successfully applied to fast and accurate resolution of plasmonic problems involving a large number of unknowns. The absorption, scattering, and extinction efficiencies of several plasmonic gold spheres of increasing size are efficiently obtained solving the electric and magnetic current combined-field integral equation. The numerical predictions are compared with reference analytic results to demonstrate the accuracy, suitability, and capabilities of this approach when dealing with large-scale plasmonic problems.

SUPERCOMPUTER AWARE APPROACH FOR THE SOLUTION OF CHALLENGING ELECTROMAGNETIC PROBLEMS

Abstract|It is a proven fact that The Fast Fourier Transform(FFT) extension of the conventional Fast Multipole Method (FMM)reduces the matrix vector product (MVP) complexity and preservesthe propensity for parallel scaling of the single level FMM. In thispaper, an e–cient parallel strategy of a nested variation of the FMM-FFT algorithm that reduces the memory requirements is presented.The solution provided by this parallel implementation for a challengingproblem with more than 0.5 billion unknowns has constituted the worldrecord in computational electromagnetics (CEM) at the beginning of2009.1. INTRODUCTIONRecent years have seen an increasing efiort in the development of fastand e–cient electromagnetic solutions with a reduced computationalcost regarding the conventional Method of Moments. Among others,the Fast Multipole Method (FMM) [1] and its multilevel version, theMLFMA [2,3] have constituted one of the most important advances inthat context.This development of fast electromagnetic solvers has gone handin hand with the constant advances in computer technology. Dueto this simultaneous growth, overcoming the limits in the scalabilityof the available codes became a priority in order to take advantageof the large amount of computational resources and capabilities thatare available in modern High Performance Computer (HPC) systems.For this reason, works focused on the parallelization improvement ofthe Multilevel Fast Multipole Algorithm (MLFMA) [4{13] have gainedinterest in last years.Besides, the FMM-Fast Fourier Transform (FMM-FFT) deservesbe taken into account as an alternative to beneflt from massivelyparallel distributed computers. This variation of the single-level FMMwas flrst proposed in [14] as an acceleration technique applied to almostplanar surfaces. Later on, a parallelized implementation was applied togeneral three-dimensional geometries [15]. The method uses the FFTto speedup the translation stage resulting in a dramatic reduction ofthe matrix-vector product (MVP) time requirement with respect tothe FMM. Although in general the FMM-FFT is not algorithmically ase–cient as the MLFMA, it has the advantage of preserving the naturalparallel scaling propensity of the single-level FMM in the spectral (

COMPARISON OF SURFACE INTEGRAL EQUATIONS FOR LEFT-HANDED MATERIALS

A wide analysis of left-handed material (LHM) spheres with difierent constitutive parameters has been carried out employ- ing difierent integral-equation formulations based on the Method of Moments. The study is focused on the accuracy assessment of for- mulations combining normal equations (combined normal formula- tion, CNF), tangential equations (combined tangential formulation, CTF, and Poggio-Miller-Chang-Harrington-Wu-Tsai formulation, PM- CHWT) and both of them (electric and magnetic current combined fleld integral equation, JMCFIE) when dealing with LHMs. Relevant and informative features as the condition number, the eigenvalues dis- tribution and the iterative response are analyzed. The obtained results show up the suitability of the JMCFIE for this kind of analysis in con- trast with the unreliable behavior of the other approaches.

Optimization of invisibility cloaks by surface integral equation method

The surface integral equation (SIE) and the method of moments (MoM) are combined with a genetic algorithm (GA) for the design of multilayer invisibility shells. Thickness and material composition of the layers are simultaneously optimized to minimize the scattering cross section (SCS). The proposed procedure brings the possibility of easily including different shape and/or material constraints on the cloak design, which indeed is of great interest for manufacturing purposes.

Design of optical nanoantennas with the surface integral equation method of moments

Numerical computations using surface integral equation formulations solved by the method of moments are carried out in order to demonstrate that these techniques are useful tools for optical nanoantennas design. It is shown that almost frequency independent directivity patterns can be obtained over a large bandwidth for judiciously designed log-periodic nanoantennas.

MLFMA-FFT algorithm for the solution of challenging problems in electromagnetics

The development of fast and efficient algorithms to reduce the computational cost of the method of moments (MoM) has received a great attention in recent years. Among others, one of the most important advances was the development of the fast multipole method (FMM) [1] and its multilevel version, the MLFMA [2]. The FMM reduces the computational complexity from O(N2) -using an iterative resolution of the MoM-, to O(N3/2), and the multilevel versions have achieved O(N log N). So, while substantially more difficult to implement, the MLFMM has become the choice when solving large-scale electromagnetics scattering problems.

4-D interaction integrals between non-coplanar triangle pairs

In this paper we propose a scheme to treat, as a whole, the 4-D reaction integrals appearing in the Method of Moments. The approach is based on application of the surface divergence theorem to both source and test integrals, together with an appropriate integration reordering. The method is numerically validated for static and dynamic kernels arising in the Electric Field Integral Equation (EFIE), i.e., for kernels with 1/R singularities.