Surface integral formulations for the design of plasmonic nanostructures (original) (raw)
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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.
IEEE Transactions on Antennas and Propagation, 2017
Surface integral equations, which are commonly used in electromagnetic simulations, have recently been applied to various plasmonic problems, while there is still no complete agreement on which formulations provide accurate and efficient solutions. In this work, we present the strong material dependencies of the conventional formulations, revealing their contradictory performances for different problems. We further explain the numerical problems in the constructed matrix equations, shedding light on the design of alternative formulations that can be more accurate, efficient, and stable than the existing ones. Based on our observations in the limit cases, we present a new formulation, namely a modified combined tangential formulation (MCTF), which provides stable solutions of plasmonic problems in wide ranges of negative permittivity values. The favorable properties of MCTF in comparison to other formulations are demonstrated not only on canonical problems but also on realistic cases involving nanowires.
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.
Method-of-moments formulation for the analysis of plasmonic nano-optical antennas
Journal of The Optical Society of America, 2011
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.
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.
A boundary integral equation method for plasmon resonances in metallic nanoparticles
CAS 2011 Proceedings (2011 International Semiconductor Conference), 2011
ABSTRACT Localized surface plasmon resonances (LSPRs) in metallic nanoparticles (NPs) are calculated by a boundary integral equation (BIE) method. The response to the incident electromagnetic field and the NP polarizability are shown to depend on eigenvalues and eigenfunctions of the integral operator associated with BIE. The NP polarizability is conveniently expressed as an eigenmode sum of analytic terms when the Drude model of metals is used. The proposed polarizability decomposition is proven to offer an analytical tool for the design of plasmonic nanostructures.
2018 International Applied Computational Electromagnetics Society Symposium (ACES), 2018
Quantum tunneling is observed between two nanostructures that are separated by a sub-nanometer gap. Electrons "jumping" from one structure to another create an additional current path. An auxiliary tunnel is introduced between the two structures as a support for this so that a classical electromagnetic solver can account for the effects of quantum tunneling. The dispersive permittivity of the tunnel is represented by a Drude model, whose parameters are obtained from the electron tunneling probability. The transient scattering from the connected nanostructures (i.e., nanostructures plus auxiliary tunnel) is analyzed using a time domain volume integral equation solver. Numerical results demonstrating the effect of quantum correction on the scattered fields are provided.
Integral Equation Formulation for Planar Plasmonic Structures With Finite Thickness in Layered Media
IEEE Photonics Journal, 2022
A detailed Volume Integral Equation (VIE) formulation for planar plasmonic nano structures with finite thickness in flat multi-layers medium is presented. The boundary condition along the localized metallic objects is expressed in terms of the unknown polarization current flowing through these objects in the form of an integral equation, which is solved using the Method of Moments (MoM). The Green's functions associated with a layered medium of practical importance are expressed in the spectral domain. The corresponding spatial domain Green's functions are obtained using the Discrete Complex Images Method (DCIM). Special treatment for the spectral function's asymptote at high spectral values is performed. The presented formulation is applied on different plasmonic structures immersed inside layered media. The structures include nano-rod and nano-patch excited by an incident plane wave. In addition, a simple band-stop filter based on quarter-wavelength stubs is considered. This filter is fed with a couple of plasmonic transmission lines. The obtained current distributions and S-parameters are compared with those obtained using a commercial full-wave electromagnetic simulator, namely CST Microwave Studio. A very good agreement is observed. The proposed integral equation formulation enjoys high degree of stability, numerical efficiency, and accuracy.
MLFMA-MoM For Solving The Scattering Of Densely Packed Plasmonic Nanoparticle Assemblies
IEEE Photonics Journal, 2015
In this paper, we present a judicious combination of two renowned surface integral equation (SIE)-based techniques, namely, the multilevel fast multipole algorithm (MLFMA) and the method of moments (MoM), which synergize into a hybrid method that allows to address the analysis of large densely packed particle assemblies in an efficient and accurate way. This hybridization takes advantage of the repetition pattern inherent to these kinds of structures. Basically, the repeated self-coupling problems are squarely solved throughout the factorization of their MoM impedance matrix, whereas the crosscouplings through the surrounding medium are expedited via the MLFMA in the framework of a global iterative scheme. Some results are presented here to demonstrate the suitability of the proposed hybrid method to address large-scale nanoparticle arrays in the framework of nanoplasmonic biosensing applications.