Improved performance of numerical simulation algorithms for nanoscale electromagnetics (original) (raw)
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Numerical analysis of plasmon resonances in nanoparticles
IEEE Transactions on Magnetics, 2000
A novel technique for the numerical analysis of plasmon resonances by using fast multipole method (FMM) is presented. This approach is based on the solution of eigenvalue problem for boundary integral equations, which can be naturally implemented by using the fast multipole method. Numerical examples that highlight the efficiency of the fast multipole implementation are reported. Index Terms-plasmon resonance, nanoparticle, integral equation, fast multipole method. I. INTRODUCTION R ECENTLY, plasmon resonances in metallic nanoparticles
We develop the time-domain discrete dipole approximation (DDA), describing the temporal evolution of electric field in plasmonic nanostructures. The main equation is obtained by taking the inverse Fourier transform of the Taylor expansion of the frequency-domain DDA in terms of frequency deviation from the central frequency. Thus we assume that incident wavefronts of different frequencies accumulate relatively small phase difference when passing the particle. This assumption is always valid for nanoparticles much smaller than the wavelength. Being the time-domain method, the proposed approach also requires an analytic frequency dependence of electric permittivity, e.g. the Drude model. We present numerical results of application of the time-domain DDA to silver nanosphere, rod, and disk, which agree well with that obtained with its frequency-domain counterpart and the finite-difference time-domain method. Moreover, the time-domain DDA is the fastest of the three methods for incident pulses of several-femtoseconds width. Thus, it can effectively be applied for modeling the temporal responses of plasmonic nanostructures.
A Perspective on Plasmonics within and beyond the Electrostatic Approximation
Plasmonics, 2018
Plasmonic is an emerging branch of nanophotonics wherein the electromagnetic properties of nanoparticles are studied for variety of applications. The optics of nanoparticles is studied in terms of surface plasmon resonances and optical cross section. Initially the first principle approach has been used to study the plasmonic fundamentals known as electrostatic approach. Under this approach, various parameters are taken into account to observe the electromagnetic properties of plasmonic nanogeometries. This electrostatic model is only used to analyze the optical signature of smaller size plasmonic geometries. Therefore, for the estimation of optical properties of larger size nanoparticle numerical model (Discrete Dipole Approximation) has been used. The observed surface plasmon resonances could be useful in sensing field, SERS signal detection and thin film solar cell application.
Surface integral formulations for the design of plasmonic nanostructures
Journal of the Optical Society of America A, 2012
Numerical formulations based on surface integral equations (SIEs) provide an accurate and efficient framework for the solution of the electromagnetic scattering problem by three-dimensional plasmonic nanostructures in the frequency domain. In this paper, we present a unified description of SIE formulations with both singular and nonsingular kernel and we study their accuracy in solving the scattering problem by metallic nanoparticles with spherical and nonspherical shape. In fact, the accuracy of the numerical solution, especially in the near zone, is of great importance in the analysis and design of plasmonic nanostructures, whose operation critically depends on the manipulation of electromagnetic hot spots. Four formulation types are considered: the N-combined region integral equations, the T-combined region integral equations, the combined field integral equations and the null field integral equations. A detailed comparison between their numerical solutions obtained for several nanoparticle shapes is performed by examining convergence rate and accuracy in both the far and near zone of the scatterer as a function of the number of degrees of freedom. A rigorous analysis of SIE formulations and their limitations can have a high impact on the engineering of numerous nano-scale optical devices such as plasmon-enhanced light emitters, biosensors, photodetectors, and nanoantennas.
Scattering on plasmonic nanostructures arrays modeled with a surface integral formulation
Photonics and Nanostructures - Fundamentals and Applications, 2010
The surface integral formulation is a flexible, multiscale and accurate tool to simulate light scattering on nanostructures. Its generalization to periodic arrays is introduced in this paper. The general electromagnetic scattering problem is reduced to a discretizated model using the Method of Moments on the surface of the scatterers in the unit cell. The study of the resonances of an array of bowtie antennas illustrates the main features of the method. When placed into an array, the bowtie antennas show additional resonances compared to those of an individual antenna. Using the surface integral formulation, we are able to investigate both nearfield and far-field properties of these resonances, with a high level of accuracy.
Journal of the Optical Society of America A, 2013
In this paper we demonstrate that rigorous high-order perturbation of surfaces (HOPS) methods coupled with analytic continuation mechanisms are particularly well-suited for the assessment and design of nanoscale devices (e.g., biosensors) that operate based on surface plasmon resonances generated through the interaction of light with a periodic (metallic) grating. In this connection we explain that the characteristics of the latter are perfectly aligned with the optimal domain of applicability of HOPS schemes, as these procedures can be shown to be the methods of choice for low to moderate wavelengths of radiation and grating roughness that is representable by a few (e.g., tens of) Fourier coefficients. We argue that, in this context, the method can, for instance, produce full and precise reflectivity maps in computational times that are orders of magnitude faster than those of alternative numerical schemes (e.g., the popular "C-method," finite differences, integral equations or finite elements). In this initial study we concentrate on the description of the basic principles that underlie the solution scheme, including those that relate to analytic continuation procedures. Within this framework, we explain how, in spite of conventional wisdom to the contrary, the resulting perturbative techniques can provide a most valuable tool for practical investigations in plasmonics. We demonstrate this with some examples that have been previously discussed in the literature (including treatments of the reflectivity and band gap structure of some simple geometries) and extend this to demonstrate the wider applicability of the proposed approach.
Toward Ultimate Nanoplasmonics Modeling
ACS Nano, 2014
Advances in the field of nanoplasmonics are hindered by the limited capabilities of simulation tools in dealing with realistic systems comprising regions that extend over many light wavelengths. We show that the optical response of unprecedentedly large systems can be accurately calculated by using a combination of surface integral equation (SIE) method of moments (MoM) formulation and an expansion of the electromagnetic fields in a suitable set of spatial wave functions via fast multipole methods. We start with a critical review of volume versus surface integral methods, followed by a short tutorial on the key features that render plasmons useful for sensing (field enhancement and confinement). We then use the SIE-MoM to examine the plasmonic and sensing capabilities of various systems with increasing degrees of complexity, including both individual and interacting gold nanorods and nanostars, as well as large random and periodic arrangements of ∼1000 gold nanorods. We believe that the present results and methodology raise the standard of numerical electromagnetic simulations in the field of nanoplasmonics to a new level, which can be beneficial for the design of advanced nanophotonic devices and optical sensing structures.
2021
The finite difference time domain (FDTD) method is a grid-based, robust, and straightforward method to model the optical properties of metal nanoparticles (MNPs). Modelling accuracy and optical properties can be enhanced by increasing FDTD grid resolution; however, the resolution of the grid size is limited by the memory and computational requirements. In this paper, a 3D optimized FDTD (OFDTD) was designed and developed, which introduced new FDTD approximation terms based on the physical events occurring during the plasmonic oscillations in MNP. The proposed method not only required ~52% less memory than conventional FDTD, but also reduced the calculation requirements by ~9%. The 3D OFDTD method was used to model and obtain the extinction spectrum, localized surface plasmon resonance (LSPR) frequency, and the electric field enhancement factor (EF) for spherical silver nanoparticles (Ag NPs). The model’s predicted results were compared with traditional FDTD as well as experimental r...
3-DIMENSIONAL Eigenmodal Analysis of Plasmonic Nanostructures
Optics Express, 2012
We introduce a 3-dimensional electromagnetic eigenmodal algorithm for the theoretical analysis of resonating nano-optical structures. The method, a variant of the Jacobi-Davidson algorithm, solves the electric field vector wave, or curl-curl, equation for the electromagnetic eigenmodes of resonant optical structures with a finite element method. In particular, the method includes transparent boundary conditions that enable the analysis of resonating structures in unbounded space. We demonstrate the performance of the method. First, we calculate the modes of several dielectric resonator antennas and compare them to theoretically determined results. Second, we calculate the modes of a nano-cuboid and compare them to theoretically determined results. Third, we numerically analyze spherical nanoparticles and compare the result to the theoretical Mie solution. Fourth, we analyze optical dipole antenna configurations in order to assess the method's capability for solving technologically relevant problems.
Mathematical Analysis of Plasmonic Nanoparticles: The Scalar Case
Archive for Rational Mechanics and Analysis
Localized surface plasmons are charge density oscillations confined to metallic nanoparticles. Excitation of localized surface plasmons by an electromagnetic field at an incident wavelength where resonance occurs results in a strong light scattering and an enhancement of the local electromagnetic fields. This paper is devoted to the mathematical modeling of plasmonic nanoparticles. Its aim is threefold: (i) to mathematically define the notion of plasmonic resonance and to analyze the shift and broadening of the plasmon resonance with changes in size and shape of the nanoparticles; (ii) to study the scattering and absorption enhancements by plasmon resonant nanoparticles and express them in terms of the polarization tensor of the nanoparticle. Optimal bounds on the enhancement factors are also derived; (iii) to show, by analyzing the imaginary part of the Green function, that one can achieve super-resolution and super-focusing using plasmonic nanoparticles. For simplicity, the Helmholtz equation is used to model electromagnetic wave propagation.