Optimization of Nanoparticle-Based SERS Substrates through Large-Scale Realistic Simulations

Surface-enhanced Raman scattering (SERS) has become a widely used spectroscopic technique for chemical identification, providing unbeaten sensitivity down to the singlemolecule level. The amplification of the optical near field produced by collective electron excitations plasmons in nanostructured metal surfaces gives rise to a dramatic increase by many orders of magnitude in the Raman scattering intensities from neighboring molecules. This effect strongly depends on the detailed geometry and composition of the plasmonsupporting metallic structures. However, the search for optimized SERS substrates has largely relied on empirical data, due in part to the complexity of the structures, whose simulation becomes prohibitively demanding. In this work, we use state-of-the-art electromagnetic computation techniques to produce predictive simulations for a wide range of nanoparticle-based SERS substrates, including realistic configurations consisting of random arrangements of hundreds of nanoparticles with various morphologies. This allows us to derive rules of thumb for the influence of particle anisotropy and substrate coverage on the obtained SERS enhancement and optimum spectral ranges of operation. Our results provide a solid background to understand and design optimized SERS substrates.Peer ReviewedPostprint (published version

DG-JMCFIE-EFIE formulation for multi-material complex radiation problems

The versatility of the Discontinuous Galerkin (DG) method [1, 2] to accurately deal with non-conformal meshes makes it a well-suited approach to address complex, multi-scale problems, greatly simplifying computer-aideddesign (CAD) generation and meshing processes. It also facilitates the implementation of domain decomposition (DD) approaches, improving iterative convergence for challenging realistic problems where small geometrical details are combined with large-scale smooth structures [1, 3]. This work presents the combination of the electric current (J) and magnetic current (M) combined field integral equation (JMCFIE) [4] and the electric field integral equation (EFIE) with the DG approach, for the electromagnetic analysis of homogeneous and piecewise homogeneous objects, including perfect electric conductor (PEC) surfaces and dielectric interfaces. With this formulation, the interfaces between different materials can be modeled independently, without the need to attend to any constraint in the multi-region junctions between them. Furthermore, because the JMCFIE includes both tangential and normal (or twisted) equations for the electric and magnetic fields, it leads to a well-posed matrix system. Properly applying the interior penalty term described in [1], the rather complex treatment at multi-material junctions can be avoided. A novelty of this formulation is that it can address nonconformal junctions using DG between interfaces concerning different regions with different materials, including the combination of PEC and dielectric junctions, where the imposition of normal continuity across the junction becomes particularly tedious and critical for accurate antenna analysis [5]. We will show the details of the proposed formulation and discuss its capability to solve various realistic antenna cases during the presentation, demonstrating the versatility of this approach in the application of DG techniques for the design of complex dielectric and metamaterial antennas

Comparison of surface integral equations for left-handed materials

A wide analysis of left-handed material (LHM) spheres with di®erent constitutive parameters has been carried out employ- ing di®erent 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 ¯eld integral equation, JMCFIE) when dealing with LHM's. 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.Ministerio de Ciencia e Innovación | Ref. TEC2008-06714-C02-01Ministerio de Ciencia e Innovación | Ref. TEC2008-06714-C02-02Ministerio de Ciencia e Innovación | Ref. CSD2008-00068Xunta de Galicia | Ref. INCITE08PXIB322250P

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 elec- tric andmagnetic 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

Improving condition number and convergence of the surface integral-equation method of moments for penetrable bodies

Most of the surface integral equation (SIE) formulations for composite conductor and/or penetrable objects suffer from balancing problems mainly because of the very different scales of the equivalent electric and magnetic currents. Consequently, the impedance matrix usually has high- or ill-condition number due to the imbalance between the different blocks. Using an efficient left and right preconditioner the elements of the impedance matrix are balanced. The proposed approach improves the matrix balance without modifying the underlying SIE formulation, which can be selected solely in terms of accuracy. The numerical complexity of this preconditioner is O(N) with N the number of unknowns, and it can be easily included on any existing SIE code implementation.Ministerio de Ciencia e Innovación | Ref. TEC2011-28784-C02-01Ministerio de Ciencia e Innovación | Ref. TEC2011-28784-C02-0

Multilevel fast multipole algorithm for fields

An efficient implementation of the multilevel fast multipole algorithm is herein applied to accelerate the calculation of the electromagnetic near- and far-fields after the equivalent surface currents have been obtained. In spite of all the research efforts being drawn to the latter, the electric and/or magnetic fields (or other parameters derived from these) are ultimately the magnitudes of interest in most of the cases. Though straightforward, their calculation can be computationally demanding, and hence the importance of finding a sped-up accurate representation of the fields via a suitable setup of the method. A complete self-contained formulation for both near- and far-fields and for problems including multiple penetrable regions is shown in full detail. Through numerical examples we show that the efficiency and scalability of the implementation leads to a drastic reduction of the computation time.Ministerio de Economía y Competitividad | Ref. MAT2014-58201-C2-1-RMinisterio de Economía y Competitividad | Ref. MAT2014-58201-C2-2-RGobierno Regional de Extremadura | Ref. IB1318

Accurate EMC engineering on realistic platforms using an integral equation domain decomposition approach

This article investigates the efficiency, accuracy and versatility of a surface integral equation (SIE) multisolver scheme to address very complex and large-scale radiation problems including multiple scale features, in the context of realistic electromagnetic compatibility (EMC)/electromagnetic interference (EMI) studies. The tear-and-interconnect domain decomposition (DD) method is applied to properly decompose the problem into multiple subdomains attending to their material, geometrical, and scale properties, while different materials and arbitrarily shaped connections between them can be combined by using the so-called multiregion vector basis functions. The SIE-DD approach has been widely reported in the literature, mainly applied to scattering problems or small radiation problems. Complementarily, in this article, the focus is placed on realistic radiation problems, involving tens of antennas and sensors and including multiscale ingredients and multiple materials. Such kind of problems are very demanding in terms of both convergence and computational resources. Throughout two realistic case studies, the proposed SIE-DD approach is shown to be a powerful electromagnetic modeling tool to provide the accurate and fast solution which is indispensable to rigorously accomplish real-life EMC/EMI studies.Agencia Estatal de Investigación | Ref. TEC2017-85376-C2-1-RAgencia Estatal de Investigación | Ref. TEC2017-85376-C2-2-

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.Ministerio de Ciencia e Innovación | Ref. TEC2011-28784-C02-01Ministerio de Ciencia e Innovación | Ref. TEC2011-28784-C02-0

HF broadband antenna design for shipboard communications: Simulation and measurements

The objective pursued in this work is to highlight the convenience of using electromagnetic simulation software as an alternative to the traditional scale model measurement when dealing with the design of HF antennas on real complex platforms. The experience was developed during the building process of a real vessel. A low and a medium band antennas (fan-wire type) were designed ad-hoc for this project. The HF broadband antennas’ study covered from the preliminary design stages to the final verification measurements completed onboard the ship. The experiment has demonstrated that more accurate results can be obtained when using an adequate electromagnetic simulation code, which, besides, brings important advantages in flexibility and usability. These advantages, inherent to the use of virtual models, hinge on the ability of the simulation tools to properly handle any modification of the vessel’s structure that might arise during the platform construction

Gold Nanostar-Coated Polystyrene Beads as Multifunctional Nanoprobes for SERS Bioimaging

Hybrid colloidal nanocomposites comprising polystyrene beads and plasmonic gold nanostars are reported as multifunctional optical nanoprobes. Such self-assembled structures are excellent Raman enhancers for bioapplications as they feature plasmon modes in the near-infrared "first biological transparency window". In this proof of concept study, we used 4-mercaptobenzoic acid as a Raman-active molecule to optimize the density of gold nanostars on polystyrene beads, improving SERS performance and thereby allowing in vitro cell culture imaging. Interestingly, intermediate gold nanostar loadings were found to yield higher SERS response, which was confirmed by electromagnetic modeling. These engineered hybrid nanostructures notably improve the possibilities of using gold nanostars as SERS tags. Additionally, when fluorescently labeled polystyrene beads are used as colloidal carriers, the composite particles can be applied as promising tools for multimodal bioimaging