Book•
Microwave Engineering
01 Apr 1990-
About: The article was published on 1990-04-01 and is currently open access. It has received 10459 citations till now. The article focuses on the topics: Microwave engineering.
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TL;DR: It is demonstrated that, like their electronic counterparts, electromagnetic CESs can travel in only one direction and are very robust against scattering from disorder; it is found that even large metallic scatterers placed in the path of the propagating edge modes do not induce reflections.
Abstract: One of the most striking phenomena in condensed-matter physics is the quantum Hall effect, which arises in two-dimensional electron systems subject to a large magnetic field applied perpendicular to the plane in which the electrons reside. In such circumstances, current is carried by electrons along the edges of the system, in so-called chiral edge states (CESs). These are states that, as a consequence of nontrivial topological properties of the bulk electronic band structure, have a unique directionality and are robust against scattering from disorder. Recently, it was theoretically predicted that electromagnetic analogues of such electronic edge states could be observed in photonic crystals, which are materials having refractive-index variations with a periodicity comparable to the wavelength of the light passing through them. Here we report the experimental realization and observation of such electromagnetic CESs in a magneto-optical photonic crystal fabricated in the microwave regime. We demonstrate that, like their electronic counterparts, electromagnetic CESs can travel in only one direction and are very robust against scattering from disorder; we find that even large metallic scatterers placed in the path of the propagating edge modes do not induce reflections. These modes may enable the production of new classes of electromagnetic device and experiments that would be impossible using conventional reciprocal photonic states alone. Furthermore, our experimental demonstration and study of photonic CESs provides strong support for the generalization and application of topological band theories to classical and bosonic systems, and may lead to the realization and observation of topological phenomena in a generally much more controlled and customizable fashion than is typically possible with electronic systems.
2,383 citations
Book•
24 Feb 2012
TL;DR: This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software.
Abstract: This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Followingare chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.
2,372 citations
Cites background or methods from "Microwave Engineering"
...1, then the z-dependence of the electric field can be assumed to be of the form e−γz with γ = α + jβ a complex propagation constant (Pelosi et al., 1998; Pozar, 2005)....
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...The z-directed (axial) electric field corresponds to the TMmn (transverse magnetic) modes and has the form (Pozar, 2005) Ez = Bmn sin (mπx a ) sin (nπy b ) ....
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...The analytical expressions for the electric field components of a hollow rectangular guide with width a and height b are given by (Pozar, 2005)...
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...This is due to the fact that the displacement flux, D = eE, must be normally continuous at the dielectric interface (Pozar, 2005; Smith, 1997)....
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...Since waveguides are some of the most common structures in microwave engineering, especially in areas where high power and low loss are essential (Pozar, 2005), their analysis is still a topic of much interest....
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TL;DR: In this paper, the authors demonstrate a technique that allows direct electrical measurements of microwave-frequency dynamics in individual nanomagnets, propelled by a d.c. spin-polarized current.
Abstract: The recent discovery that a spin-polarized electrical current can apply a large torque to a ferromagnet, through direct transfer of spin angular momentum, offers the possibility of manipulating magnetic-device elements without applying cumbersome magnetic fields. However, a central question remains unresolved: what type of magnetic motions can be generated by this torque? Theory predicts that spin transfer may be able to drive a nanomagnet into types of oscillatory magnetic modes not attainable with magnetic fields alone, but existing measurement techniques have provided only indirect evidence for dynamical states. The nature of the possible motions has not been determined. Here we demonstrate a technique that allows direct electrical measurements of microwave-frequency dynamics in individual nanomagnets, propelled by a d.c. spin-polarized current. We show that spin transfer can produce several different types of magnetic excitation. Although there is no mechanical motion, a simple magnetic-multilayer structure acts like a nanoscale motor; it converts energy from a d.c. electrical current into high-frequency magnetic rotations that might be applied in new devices including microwave sources and resonators.
1,869 citations
TL;DR: In this article, the physical phenomenon of long-lifetime resonant electromagnetic states with localized slowly-evanescent field patterns was investigated to transfer energy efficiently over non-negligible distances even in the presence of extraneous environmental objects.
1,628 citations
TL;DR: In this article, the authors proposed an alternate perspective on the design and function of such materials that exploits the well-known L-C distributed network representation of homogeneous dielectrics.
Abstract: Recent demonstrations of negative refraction utilize three-dimensional collections of discrete periodic scatterers to synthesize artificial dielectrics with simultaneously negative permittivity and permeability. In this paper, we propose an alternate perspective on the design and function of such materials that exploits the well-known L-C distributed network representation of homogeneous dielectrics. In the conventional low-pass topology, the quantities L and C represent a positive equivalent permeability and permittivity, respectively. However, in the dual configuration, in which the positions of L and C are simply interchanged, these equivalent material parameters assume simultaneously negative values. Two-dimensional periodic versions of these dual networks are used to demonstrate negative refraction and focusing; phenomena that are manifestations of the fact that such media support a propagating fundamental backward harmonic. We hereby present the characteristics of these artificial transmission-line media and propose a suitable means of implementing them in planar form. We then present circuit and full-wave field simulations illustrating negative refraction and focusing, and the first experimental verification of focusing using such an implementation.
1,439 citations
Cites background or methods from "Microwave Engineering"
...using the standard procedure for 1-D periodic analysis of microwave networks [9], [10]....
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...533 mm to synthesize a characteristic impedance equal to that of a 400- m-wide microstrip line over the same substrate, for which standard quasi-static formulas exist [10]....
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