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# The Finite Element Method in Electromagnetics

01 Mar 1993-

TL;DR: The Finite Element Method in Electromagnetics, Third Edition as discussed by the authors is a leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagnetic engineering.

Abstract: A new edition of the leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagneticsThe finite element method (FEM) is a powerful simulation technique used to solve boundary-value problems in a variety of engineering circumstances. It has been widely used for analysis of electromagnetic fields in antennas, radar scattering, RF and microwave engineering, high-speed/high-frequency circuits, wireless communication, electromagnetic compatibility, photonics, remote sensing, biomedical engineering, and space exploration.The Finite Element Method in Electromagnetics, Third Edition explains the methods processes and techniques in careful, meticulous prose and covers not only essential finite element method theory, but also its latest developments and applicationsgiving engineers a methodical way to quickly master this very powerful numerical technique for solving practical, often complicated, electromagnetic problems.Featuring over thirty percent new material, the third edition of this essential and comprehensive text now includes:A wider range of applications, including antennas, phased arrays, electric machines, high-frequency circuits, and crystal photonicsThe finite element analysis of wave propagation, scattering, and radiation in periodic structuresThe time-domain finite element method for analysis of wideband antennas and transient electromagnetic phenomenaNovel domain decomposition techniques for parallel computation and efficient simulation of large-scale problems, such as phased-array antennas and photonic crystalsAlong with a great many examples, The Finite Element Method in Electromagnetics is an ideal book for engineering students as well as for professionals in the field.

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TL;DR: This paper describes Meep, a popular free implementation of the finite-difference time-domain (FDTD) method for simulating electromagnetism, and focuses on aspects of implementing a full-featured FDTD package that go beyond standard textbook descriptions of the algorithm.

Abstract: This paper describes Meep, a popular free implementation of the finite-difference time-domain (FDTD) method for simulating electromagnetism. In particular, we focus on aspects of implementing a full-featured FDTD package that go beyond standard textbook descriptions of the algorithm, or ways in which Meep differs from typical FDTD implementations. These include pervasive interpolation and accurate modeling of subpixel features, advanced signal processing, support for nonlinear materials via Pade approximants, and flexible scripting capabilities.

2,489 citations

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TL;DR: In plasmonics, the metal nanostructures can serve as antennas to convert light into localized electric fields (E-fields) or as waveguides to route light to desired locations with nanometer precision through a strong interaction between incident light and free electrons in the nanostructure.

Abstract: Coinage metals, such as Au, Ag, and Cu, have been important materials throughout history.1 While in ancient cultures they were admired primarily for their ability to reflect light, their applications have become far more sophisticated with our increased understanding and control of the atomic world. Today, these metals are widely used in electronics, catalysis, and as structural materials, but when they are fashioned into structures with nanometer-sized dimensions, they also become enablers for a completely different set of applications that involve light. These new applications go far beyond merely reflecting light, and have renewed our interest in maneuvering the interactions between metals and light in a field known as plasmonics.2–6
In plasmonics, the metal nanostructures can serve as antennas to convert light into localized electric fields (E-fields) or as waveguides to route light to desired locations with nanometer precision. These applications are made possible through a strong interaction between incident light and free electrons in the nanostructures. With a tight control over the nanostructures in terms of size and shape, light can be effectively manipulated and controlled with unprecedented accuracy.3,7 While many new technologies stand to be realized from plasmonics, with notable examples including superlenses,8 invisible cloaks,9 and quantum computing,10,11 conventional technologies like microprocessors and photovoltaic devices could also be made significantly faster and more efficient with the integration of plasmonic nanostructures.12–15 Of the metals, Ag has probably played the most important role in the development of plasmonics, and its unique properties make it well-suited for most of the next-generation plasmonic technologies.16–18
1.1. What is Plasmonics?
Plasmonics is related to the localization, guiding, and manipulation of electromagnetic waves beyond the diffraction limit and down to the nanometer length scale.4,6 The key component of plasmonics is a metal, because it supports surface plasmon polariton modes (indicated as surface plasmons or SPs throughout this review), which are electromagnetic waves coupled to the collective oscillations of free electrons in the metal.
While there are a rich variety of plasmonic metal nanostructures, they can be differentiated based on the plasmonic modes they support: localized surface plasmons (LSPs) or propagating surface plasmons (PSPs).5,19 In LSPs, the time-varying electric field associated with the light (Eo) exerts a force on the gas of negatively charged electrons in the conduction band of the metal and drives them to oscillate collectively. At a certain excitation frequency (w), this oscillation will be in resonance with the incident light, resulting in a strong oscillation of the surface electrons, commonly known as a localized surface plasmon resonance (LSPR) mode.20 This phenomenon is illustrated in Figure 1A. Structures that support LSPRs experience a uniform Eo when excited by light as their dimensions are much smaller than the wavelength of the light.
Figure 1
Schematic illustration of the two types of plasmonic nanostructures discussed in this article as excited by the electric field (Eo) of incident light with wavevector (k). In (A) the nanostructure is smaller than the wavelength of light and the free electrons ...
In contrast, PSPs are supported by structures that have at least one dimension that approaches the excitation wavelength, as shown in Figure 1B.4 In this case, the Eo is not uniform across the structure and other effects must be considered. In such a structure, like a nanowire for example, SPs propagate back and forth between the ends of the structure. This can be described as a Fabry-Perot resonator with resonance condition l=nλsp, where l is the length of the nanowire, n is an integer, and λsp is the wavelength of the PSP mode.21,22 Reflection from the ends of the structure must also be considered, which can change the phase and resonant length. Propagation lengths can be in the tens of micrometers (for nanowires) and the PSP waves can be manipulated by controlling the geometrical parameters of the structure.23

2,421 citations

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Rice University

^{1}TL;DR: This analysis demonstrates that the plasmon hybridization picture can be combined with numerical approaches to interpret the physical origin of the plasmons of highly complex nanostructures.

Abstract: Using the finite-difference time-domain method, we show that the plasmons of a nanostar result from hybridization of plasmons of the core and tips of the nanoparticle. The nanostar core serves as a nanoscale antenna, dramatically increasing the excitation cross section and the electromagnetic field enhancements of the tip plasmons. Our analysis demonstrates that the plasmon hybridization picture can be combined with numerical approaches to interpret the physical origin of the plasmons of highly complex nanostructures.

820 citations

### Cites methods from "The Finite Element Method in Electr..."

...Among others are the Discrete Dipole Approximation (DDA) [2], Multiple Multipole Program [3], the Boundary Element Method (BEM) [4], the Finite Element Method (FEM) [5] and Finite Difference Time Domain (FDTD) method [6] are the most popular....

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TL;DR: The limit of sensitivity in SERS is introduced in the context of single-molecule spectroscopy and the calculation of the ‘real’ enhancement factor, which illustrates the broad applications of this powerful technique.

Abstract: Surface-enhanced Raman spectroscopy (SERS) combines molecular fingerprint specificity with potential single-molecule sensitivity. Therefore, the SERS technique is an attractive tool for sensing molecules in trace amounts within the field of chemical and biochemical analytics. Since SERS is an ongoing topic, which can be illustrated by the increased annual number of publications within the last few years, this review reflects the progress and trends in SERS research in approximately the last three years. The main reason why the SERS technique has not been established as a routine analytic technique, despite its high specificity and sensitivity, is due to the low reproducibility of the SERS signal. Thus, this review is dominated by the discussion of the various concepts for generating powerful, reproducible, SERS-active surfaces. Furthermore, the limit of sensitivity in SERS is introduced in the context of single-molecule spectroscopy and the calculation of the 'real' enhancement factor. In order to shed more light onto the underlying molecular processes of SERS, the theoretical description of SERS spectra is also a growing research field and will be summarized here. In addition, the recording of SERS spectra is affected by a number of parameters, such as laser power, integration time, and analyte concentration. To benefit from synergies, SERS is combined with other methods, such as scanning probe microscopy and microfluidics, which illustrates the broad applications of this powerful technique.

706 citations

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12 Jul 2000TL;DR: Numerical Techniques in Electromagnetics is designed to show the reader how to pose, numerically analyze, and solve electromagnetic (EM) problems using a variety of available numerical methods.

Abstract: Numerical Techniques in Electromagnetics is designed to show the reader how to pose, numerically analyze, and solve electromagnetic (EM) problems. It gives them the ability to expand their problem-solving skills using a variety of available numerical methods. Topics covered include fundamental concepts in EM; numerical methods; finite difference methods; variational methods, including moment methods and finite element methods; transmission-line matrix or modeling (TLM); and Monte Carlo methods. The simplicity of presentation of topics throughout the book makes this an ideal text for teaching or self-study by senior undergraduates, graduate students, and practicing engineers.

662 citations