Showing papers on "Maxwell's equations published in 2010"
TL;DR: A new discretization scheme for Maxwell equations in two space dimension based on the use of bivariate B-splines spaces suitably adapted to electromagnetics and provides regular discrete solutions of Maxwell equations.
334 citations
Book•
16 Dec 2010TL;DR: The linear sampling method is the oldest and most developed of the qualitative methods in inverse scattering theory as mentioned in this paper, which is based on solving a linear integral equation and then using the equation s solution as an indicator function for the determination of the support of the scattering object.
Abstract: The linear sampling method is the oldest and most developed of the qualitative methods in inverse scattering theory. It is based on solving a linear integral equation and then using the equation s solution as an indicator function for the determination of the support of the scattering object. This book describes the linear sampling method for a variety of electromagnetic scattering problems. It presents uniqueness theorems and the derivation of various inequalities on the material properties of the scattering object from a knowledge of the far field pattern of the scattered wave. Also covered are the approximation properties of Herglotz wave functions; the behavior of solutions to the interior transmission problem, a novel interior boundary value problem; and numerical examples of the inversion scheme. Audience: This book is intended for mathematicians and engineers performing research in inverse electromagnetic scattering theory. It is also appropriate for an advanced graduate course on inverse problems. Contents: Preface; Chapter 1: Inverse Scattering in Two Dimensions; Chapter 2: Maxwell s Equations; Chapter 3: The Inverse Problem for Obstacles; Chapter 4: The Inverse Scattering Problem for Anisotropic Media; Chapter 5: The Inverse Scattering Problem for Thin Objects; Chapter 6: The Inverse Scattering Problem for Buried Objects; Bibliography; Index.
222 citations
TL;DR: A two-dimensional model coupling Maxwell equations with plasma fluid equations is used to describe the formation of patterns under conditions similar to recent experiments and for a wave electric field perpendicular to the simulation domain or in the simulationdomain.
Abstract: High power microwave breakdown at atmospheric pressure leads to the formation of filamentary plasma arrays that propagate toward the source. A two-dimensional model coupling Maxwell equations with plasma fluid equations is used to describe the formation of patterns under conditions similar to recent experiments and for a wave electric field perpendicular to the simulation domain or in the simulation domain. The calculated patterns are in excellent qualitative agreement with the experiments, with good quantitative agreement of the propagation speed of the filaments. The propagation of the plasma filaments is due to the combination of diffusion and ionization. Emphasis is put on the fact that free electron diffusion (and not ambipolar diffusion) associated with ionization is responsible for the propagation of the front.
166 citations
TL;DR: In this article, the authors apply the standard canonical quantization rules of quantum field theory to macroscopic electromagnetism and apply them to any linear, inhomogeneous, magnetodielectric medium with dielectric functions.
Abstract: Application of the standard canonical quantization rules of quantum field theory to macroscopic electromagnetism has encountered obstacles due to material dispersion and absorption. This has led to a phenomenological approach to macroscopic quantum electrodynamics where no canonical formulation is attempted. In this paper macroscopic electromagnetism is canonically quantized. The results apply to any linear, inhomogeneous, magnetodielectric medium with dielectric functions that obey the Kramers–Kronig relations. The prescriptions of the phenomenological approach are derived from the canonical theory.
163 citations
TL;DR: In this article, the authors address various aspects on estimating the magnetocaloric effect from magnetization measurements, and the use of a Maxwell relation in first-and second-order phase transitions, including (a) magnetization as a thermodynamic variable in an inhomogeneous situation (structural or chemical distributions, magnetic domains) and (b) non-equilibrium conditions (irreversibility) on first order phase transition, including mixed-phase conditions.
148 citations
TL;DR: A simple analysis of the problems involved in defining spin and orbital angular momenta for electromagnetic fields is presented and some of the remaining challenges are discussed.
Abstract: The association of spin and orbital angular momenta of light with its polarization and helical phase fronts is now well established The problems in linking this with electromagnetic theory, as expressed in Maxwell's equations, are rather less well known We present a simple analysis of the problems involved in defining spin and orbital angular momenta for electromagnetic fields and discuss some of the remaining challenges Crucial to our investigation is the duplex symmetry between the electric and magnetic fields
143 citations
TL;DR: In this article, the existence of a nontrivial solution to the non-linear Schrodinger-Maxwell equations in R 3, assuming on the nonlinearity the general hypotheses introduced by Berestycki and Lions, was proved.
Abstract: In this paper we prove the existence of a nontrivial solution to the nonlinear Schrodinger–Maxwell equations in R 3 , assuming on the nonlinearity the general hypotheses introduced by Berestycki and Lions.
139 citations
TL;DR: In this article, lower bounds on the quality factor (Q) of small electric and magnetic-dipole antennas were obtained for arbitrarily shaped volumes and excited by general sources or by global electric-current sources alone.
Abstract: General expressions are obtained for the lower bounds on the quality factor (Q) of electrically small electric- and magnetic-dipole antennas confined to an arbitrarily shaped volume V and excited by general sources or by global electric-current sources alone. The lower-bound expressions depend only on the direction of the dipole moment with respect to V , the electrical size of V , and the static electric and magnetic polarizabilities per unit volume of hypothetical perfectly electrically conducting and perfectly magnetically conducting volumes V . The lower bounds are obtained directly from the electromagnetic field expressions for Q with the help of current equivalence principles and the uncoupling of Maxwell's equations for electrically small volumes into quasi-electrostatic and quasi-magnetostatic fields.
138 citations
TL;DR: In this paper, the Abraham-Minkowski controversy was resolved within the framework of the classical theory of electrodynamics, without resorting to such complicating and ultimately unnecessary factors as pseudo-momentum, special surface forces, alternative energymomentums tensors, and hidden momenta, that have caused so much confusion for such a long period of time.
128 citations
TL;DR: In this article, the theory of monochromatic time-reversal mirrors (TRM) or equivalently phase conjugate mirrors is developed for electromagnetic waves, and a differential expression similar to the Lorentz reciprocity theorem is deduced.
Abstract: The theory of monochromatic time-reversal mirrors (TRM) or equivalently phase conjugate mirrors is developed for electromagnetic waves. We start from the fundamental time-symmetry of the Maxwell's equations. From this symmetry, a differential expression similar to the Lorentz reciprocity theorem is deduced. The radiating conditions on TRM are expressed in terms of 6-dimension Green's functions. To predict the time reversal focusing on antenna arrays, a formalism that involves impedance matrix is developed. We show that antenna coupling can dramatically modify the focal spot. Especially, we observe, that in some circumstances, sub-wavelength focusing on a bi-dimensional array may arise.
TL;DR: In this paper, the results of generalized Lorenz-Mie theories in spherical coordinates are modified from scalar results in the framework of the Bromwich method to vectorial expressions using vector spherical wave functions (VSWFs) in order to match the T-matrix formulation, and to express the T
TL;DR: In this article, a pedagogical introduction to magnetic fields in the early Universe is given, focusing on how to formulate electrodynamics in curved space time, defining appropriate magnetic and electric fields and writing Maxwell equations in terms of these fields.
Abstract: We give a pedagogical introduction to two aspects of magnetic fields in the early Universe. We first focus on how to formulate electrodynamics in curved space time, defining appropriate magnetic and electric fields and writing Maxwell equations in terms of these fields. We then specialize to the case of magnetohydrodynamics in the expanding Universe. We emphasize the usefulness of tetrads in this context. We then review the generation of magnetic fields during the inflationary era, deriving in detail the predicted magnetic and electric spectra for some models. We discuss potential problems arising from back reaction effects and from the large variation of the coupling constants required for such field generation (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
TL;DR: In this article, the authors used Numerical Maxwell Model in 3D Simulations (NMM3D) to study the backscattering coefficients, coherent reflectivities, and emissivities of soil surfaces using Gaussian random rough surfaces with exponential correlation functions.
Abstract: We used Numerical Maxwell Model in 3-D Simulations (NMM3D) to study the backscattering coefficients, coherent reflectivities, and emissivities of soil surfaces using Gaussian random rough surfaces with exponential correlation functions. The surface area used is 8 by 8 square wavelengths. A total of close to 200 cases are computed by varying rms height, correlation length, and soil permittivity. We consider a 40° incidence angle. For each case, 15 realizations of rough surface profiles are generated, and 30 solutions of Maxwell equations are computed because of two polarizations. The method for solving the Maxwell equations is based on the Method of Moments (MoM) with Rao-Wilton-Glisson (RWG) basis functions. The solutions are accelerated by the sparse matrix canonical grid method implemented on parallel computing. The rms height varies up to 0.126 wavelength. The results are compared with the Dubois formulation, Small Perturbation Method (SPM), Kirchhoff Approximation (KA), and Advanced Integral Equation Model (AIEM). The NMM3D results are also compared with VV and HH backscatter data of soil surfaces where ground truth rms heights and correlation lengths were both measured. Good agreement is found between the NMM3D results and experimental measurement data. Based on the computed cases, interpolation tables are derived that can be directly applied to L-band active and passive microwave remote sensing of soil moisture, such as for the upcoming Soil Moisture Active and Passive (SMAP) mission.
TL;DR: An interior penalty discontinuous Galerkin method is described with a conformal perfectly matched layer (PML) for solving the two first-order Maxwell's equations in the time domain.
Abstract: An interior penalty discontinuous Galerkin method is described with a conformal perfectly matched layer (PML) for solving the two first-order Maxwell's equations in the time domain. Both central and upwind fluxes are studied in this work. In both cases, the proposed method is explicit and conditionally stable. Additionally, a local time-stepping strategy is applied to increase efficiency and reduce the computational time. Finally, numerical examples are presented to validate the method.
TL;DR: The time harmonic Maxwell equations in a complex three-dimensional geometry are analyzed and effective equations for the scatterer and formulas for the effective permittivity and permeability are provided.
Abstract: We analyze the time harmonic Maxwell equations in a complex three-dimensional geometry. The scatterer $\Omega\subset\mathbb{R}^3$ contains a periodic pattern of small wire structures of high conductivity, and the single element has the shape of a split ring. We rigorously derive effective equations for the scatterer and provide formulas for the effective permittivity and permeability. The latter turns out to be frequency dependent and has a negative real part for appropriate parameter values. This magnetic activity is the key feature of a left-handed metamaterial.
TL;DR: Using smaller time steps precisely where smaller elements in the mesh are located, these methods overcome the bottleneck caused by local mesh refinement in explicit time integrators and resulting discrete time-marching schemes are fully explicit and thus inherently parallel.
TL;DR: In this paper, it was shown that the fish-eye lens in three dimensions has unlimited resolution for electromagnetic waves, and the fish eye has been known to be a perfect lens within the validity range of ray optics since 1854.
Abstract: Maxwell's fish eye has been known to be a perfect lens within the validity range of ray optics since $1854$. Solving Maxwell's equations, we show that the fish-eye lens in three dimensions has unlimited resolution for electromagnetic waves.
Book•
14 Jun 2010
TL;DR: In this paper, the authors present an approach to the problem of finding the minimum possible antenna quality factor in a set of antenna configurations with respect to a given number of antenna parameters.
Abstract: Preface. 1 Maxwell Equations. 1.1 Experimental Laws. 1.2 Maxwell Equations, Constitutive Relation, and Dispersion. 1.3 Theorems for Electromagnetic Fields. 1.4 Wavepackets. 2 Solutions of Maxwell Equations. 2.1 Linear Space and Linear Operator. 2.2 Classification of Partial Differential Equations. 2.3 Modern Theory of Partial Differential Equations. 2.4 Method of Separation of Variables. 2.5 Method of Green s Function. 2.6 Potential Theory. 2.7 Variational Principles. 3 Eigenvalue Problems. 3.1 Introduction to Linear Operator Theory. 3.2 Eigenvalue Problems for Symmetric Operators. 3.3 Interior Electromagnetic Problems. 3.4 Exterior Electromagnetic Problems. 3.5 Eigenfunctions of Curl Operator. 4 Antenna Theory. 4.1 Antenna Parameters. 4.2 Properties of Far Fields. 4.3 Spherical Vector Wavefunctions. 4.4 Foster Theorems and Relationship Between Quality Factor and Bandwidth. 4.5 Minimum Possible Antenna Quality Factor. 4.6 Maximum Possible Product of Gain and Bandwidth. 4.7 Evaluation of Antenna Quality Factor. 5 Integral Equation Formulations. 5.1 Integral Equations. 5.2 TEM Transmission Lines. 5.3 Waveguide Eigenvalue Problems. 5.4 Metal Cavity Resonators. 5.5 Scattering Problems. 5.6 Multiple Metal Antenna System. 5.7 Numerical Methods. 6 Network Formulations. 6.1 Transmission Line Theory. 6.2 Scattering Parameters for General Circuits. 6.3 Waveguide Junctions. 6.4 Multiple Antenna System. 6.5 Power Transmission Between Antennas. 6.6 Network Parameters in a Scattering Environment. 6.7 RLC Equivalent Circuits. 7 Fields in Inhomogeneous Media. 7.1 Foundations of Spectral Analysis. 7.2 Plane Waves in Inhomogeneous Media. 7.3 Inhomogeneous Metal Waveguides. 7.4 Optical Fibers. 7.5 Inhomogeneous Cavity Resonator. 8 Time-domain Theory. 8.1 Time-domain Theory of Metal Waveguides. 8.2 Time-domain Theory of Metal Cavity Resonators. 8.3 Spherical Wave Expansions in Time-domain. 8.4 Radiation and Scattering in Time-domain. 9 Relativity. 9.1 Tensor Algebra on Linear Spaces. 9.2 Einstein s Postulates for Special Relativity. 9.3 The Lorentz Transformation. 9.4 Relativistic Mechanics in Inertial Reference Frame. 9.5 Electrodynamics in Inertial Reference Frame. 9.6 General Theory of Relativity. 10 Quantization of Electromagnetic Fields. 10.1 Fundamentals of Quantum Mechanics. 10.2 Quantization of Free Electromagnetic Fields. 10.3 Quantum Statistics. 10.4 Interaction of Electromagnetic Fields with the Small Particle System. 10.5 Relativistic Quantum Mechanics. Appendix A: Set Theory. A.1 Basic Concepts. A.2 Set Operations. A.3 Set Algebra. Appendix B: Vector Analysis. B.1 Formulas from Vector Analysis. B.2 Vector Analysis in Curvilinear Coordinate Systems. Appendix C: Special Functions. C.1 Bessel Functions. C.2 Spherical Bessel Functions. C.3 Legendre Functions and Associated Legendre Functions. Appendix D: SI Unit System. Bibliography. Index.
TL;DR: In this paper, a model of the pattern formation and propagation under conditions close to recent experiments is presented, which provides a good qualitative and quantitative understanding of different features such as plasma front velocity, spacing between filaments, maximum plasma density in the filaments and influence of discharge parameters on the development of well-defined filamentary plasma arrays or more diffuse plasma fronts.
Abstract: During microwave breakdown at atmospheric pressure, a sharp plasma front forms and propagates toward the microwave source at high velocities. Experiments show that the plasma front may exhibit a complex dynamical structure or pattern composed of plasma filaments aligned with the wave electric field and apparently moving toward the source. In this paper, we present a model of the pattern formation and propagation under conditions close to recent experiments. Maxwell's equations are solved together with plasma fluid equations in two dimensions to describe the space and time evolution of the wave field and plasma density. The simulation results are in excellent agreement with the experimental observations. The model provides a physical interpretation of the pattern formation and dynamics in terms of ionization-diffusion and absorption-reflection mechanisms. The simulations allow a good qualitative and quantitative understanding of different features such as plasma front velocity, spacing between filaments, maximum plasma density in the filaments, and influence of the discharge parameters on the development of well-defined filamentary plasma arrays or more diffuse plasma fronts.
Journal Article•
TL;DR: In this paper, the existence of a ground state solution for the nonlinear Klein-Gordon-Maxwell equations in the electrostatic case was proved, and it was shown that such a solution can be obtained in the presence of a single generator.
Abstract: In this paper we prove the existence of a ground state solution for the nonlinear Klein–Gordon–Maxwell equations in the electrostatic case.
TL;DR: In this paper, the authors proposed to transform low-frequency Maxwell equations in the quasi-static or diffusive limit to a hyperbolic set of partial differential equations that give a representation of electromagnetic fields in a fictitious wave domain.
Abstract: The computer time required to solve a typical 3D marine controlled-source electromagnetic surveying (CSEM) simulation can be reduced by more than one order of magnitude by transforming low-frequency Maxwell equations in the quasi-static or diffusive limit to a hyperbolic set of partial differential equations that give a representation of electromagnetic fields in a fictitious wave domain. The dispersion and stability analysis can be made equivalent to that of other types of wave simulation problems such as seismic acoustic and elastic modeling. Second-order to eighth-order spatial derivative operators are implemented for flexibility. Fourth-order and sixth-order methods are the most numerically efficient implementations for this particular scheme. An implementation with high-order operators requires that both electric and magnetic fields are extrapolated simultaneously into the air layer. The stability condition given for high-order staggered-derivative operators here should be equally valid for seismic-wave simulation. The bandwidth of recovered fields in the diffusive domain is independent of the bandwidth of the fields in the fictitious wave domain. The fields in the fictitious wave domain do not represent observable fields. Propagation paths and interaction/reflection amplitudes are not altered by the transform from the fictitious wave domain to the diffusive frequency domain; however, the transform contains an exponential decay factor that damps down late arrivals in the fictitious wave domain. The propagation paths that contribute most to the diffusive domain fields are airwave (shallow water) plus typically postcritical events such as refracted and guided waves. The transform from the diffusive frequency domain to the fictitious wave domain is an ill-posed problem. The transform is nonunique. This gives a large degree of freedom in postulating temporal waveforms for boundary conditions in the fictitious wave domain that reproduce correct diffusive frequency-domain fields.
TL;DR: An efficient approach for computing high-order harmonic propagation based on the discrete dipole approximation based on computing the total field as the superposition of the driving field with the field radiated by the elemental emitters of the sample is presented.
Abstract: We present an efficient approach for computing high-order harmonic propagation based on the discrete dipole approximation. In contrast with other approaches, our strategy is based on computing the total field as the superposition of the driving field with the field radiated by the elemental emitters of the sample. In this way we avoid the numerical integration of the wave equation, as Maxwell's equations have an analytical solution for an elementary (pointlike) emitter. The present strategy is valid for low-pressure gases interacting with strong fields near the saturation threshold (i.e., partially ionized), which is a common situation in the experiments of high-order harmonic generation. We use this tool to study the dependence of phase matching of high-order harmonics with the relative position between the beam focus and the gas jet.
TL;DR: In this paper, a Hamiltonian framework is developed for a sequence of ultrashort optical pulses propagating in a nonlinear dispersive medium, and the integrals reflect time-averaged fluxes of energy, momentum, and photons transferred by the pulse.
Abstract: A Hamiltonian framework is developed for a sequence of ultrashort optical pulses propagating in a nonlinear dispersive medium. To this end a second-order nonlinear wave equation for the electric field is transformed into a first-order propagation equation for a suitably defined complex electric field. The Hamiltonian formulation is then introduced in terms of normal variables, i.e., classical complex fields referring to the quantum creation and annihilation operators. The derived $z$-propagated Hamiltonian accounts for forward and backward waves, arbitrary medium dispersion, and four-wave mixing processes. As a simple application we obtain integrals of motion for the pulse propagation. The integrals reflect time-averaged fluxes of energy, momentum, and photons transferred by the pulse. Furthermore, pulses in the form of stationary nonlinear waves are considered. They yield extremal values of the momentum flux for a given energy flux. Simplified propagation equations are obtained by reduction of the Hamiltonian. In particular, the complex electric field reduces to an analytic signal for the unidirectional propagation. Solutions of the full bidirectional model are numerically compared to the predictions of the simplified equation for the analytic signal and to the so-called forward Maxwell equation. The numerics is effectively tested by examining the conservation laws.
TL;DR: The aim of this work is to introduce a general and efficient set of vector functions associated with the edges and faces of a polyhedral primal grids or of a dual grid obtained from the barycentric subdivision of the boundary of the primal grid.
TL;DR: In this paper, a simulation of high power microwave breakdown of air at atmospheric pressure and 110 GHz is presented, based on finite-difference time domain solutions of the Maxwell equations coupled with a simple fluid description of the plasma growth and diffusion.
Abstract: Simulations of the dynamics of high power microwave breakdown of air at atmospheric pressure and 110 GHz are presented. The model reproduces well the formation and motion of filamentary plasma arrays observed experimentally with fast camera imaging. The numerical model is based on finite-difference time domain solutions of Maxwell equations coupled with a simple fluid description of the plasma growth and diffusion. The computational procedure is discussed in details along with numerical experiments, to show the sensitivity of the results to different numerical parameters.
TL;DR: A high-order non-dissipative discontinuous Galerkin (DG) method for solving Maxwell's equations on non-conforming simplex meshes is discussed, proved to be stable and conserves a discrete counterpart of the electromagnetic energy for metallic cavities.
TL;DR: This paper introduces a self-developed, three-dimensional parallel fully electromagnetic particle simulation code UNIPIC-3D, which can be used to simulate the high-power microwave devices, such as the relativistic backward wave oscillator, coaxial vircator, and magnetically insulated line oscillator.
Abstract: This paper introduces a self-developed, three-dimensional parallel fully electromagnetic particle simulation code UNIPIC-3D. In this code, the electromagnetic fields are updated using the second-order, finite-difference time-domain method, and the particles are moved using the relativistic Newton–Lorentz force equation. The electromagnetic field and particles are coupled through the current term in Maxwell’s equations. Two numerical examples are used to verify the algorithms adopted in this code, numerical results agree well with theoretical ones. This code can be used to simulate the high-power microwave (HPM) devices, such as the relativistic backward wave oscillator, coaxial vircator, and magnetically insulated line oscillator, etc. UNIPIC-3D is written in the object-oriented C++ language and can be run on a variety of platforms including WINDOWS, LINUX, and UNIX. Users can use the graphical user’s interface to create the complex geometric structures of the simulated HPM devices, which can be automatic...
TL;DR: In this article, the authors consider electromagnetic field quantization in an expanding universe and find that the covariant (Gupta-Bleuler) method exhibits certain difficulties when trying to impose the quantum Lorenz condition on cosmological scales.
TL;DR: A novel kind of multisymplectic method for three-dimensional (3-D) Maxwell's equations, which is not only efficient and simple in coding, but also has almost all the nature of mult Daisymplectic integrators.