Fields In Dispersive Media Research Articles

A Discontinuous Galerkin Time-Domain Method With Dynamically Adaptive Cartesian Mesh for Computational Electromagnetics

A discontinuous Galerkin time-domain (DGTD) method based on dynamically adaptive Cartesian meshes (ACM) is developed for a full-wave analysis of electromagnetic fields in dispersive media. Hierarchical Cartesian grids offer simplicity close to that of structured grids and the flexibility of unstructured grids while being highly suited for adaptive mesh refinement (AMR). The developed DGTD-ACM achieves a desired accuracy by refining non-conformal meshes near material interfaces to reduce stair-casing errors without sacrificing the high efficiency afforded with uniform Cartesian meshes. Moreover, DGTD-ACM can dynamically refine the mesh to resolve the local variation of the fields during propagation of electromagnetic pulses. A local time-stepping scheme is adopted to alleviate the constraint on the time-step size due to the stability condition of the explicit time integration. Simulations of electromagnetic wave diffraction over conducting and dielectric cylinders and spheres demonstrate that the proposed method can achieve a good numerical accuracy at a reduced computational cost compared with uniform meshes. For simulations of dispersive media, the auxiliary differential equation (ADE) and recursive convolution (RC) methods are implemented for a local Drude model and tested for a cold plasma slab and a plasmonic rod. With further advances of the charge transport models, the DGTD-ACM method is expected to provide a powerful tool for computations of electromagnetic fields in complex geometries for applications to high-frequency electronic devices, plasmonic THz technologies, as well as laser-induced and microwave plasmas.

Тензор энергии-импульса электромагнитного поля в средах с дисперсией

Тензор энергии-импульса электромагнитного поля в средах с дисперсией

Electromagnetic energy momentum in dispersive media

The standard derivations of electromagnetic energy and momentum in media take Maxwell's equations as the starting point. It is well known that for dispersive media this approach does not directly yield exact expressions for the energy and momentum densities. Although Maxwell's equations fully describe electromagnetic fields, the general approach to conserved quantities in field theory is not based on the field equations, but rather on the action. Here an action principle for macroscopic electromagnetism in dispersive, lossless media is used to derive the exact conserved energy-momentum tensor. The time-averaged energy density reduces to Brillouin's simple formula when the fields are monochromatic. The time-averaged momentum density for monochromatic fields corresponds to the familiar Minkowski expression $\mathbf{D}\ifmmode\times\else\texttimes\fi{}\mathbf{B}$, but for general fields in dispersive media the momentum density does not have the Minkowski value. The results are unaffected by the debate over momentum balance in light-matter interactions.

Joint time-frequency and finite-difference time-domain analysis of precursor fields in dispersive media

Superluminal group velocities, defined as group velocities exceeding the speed of light in vacuum, c, have been theoretically predicted and experimentally observed in various types of dispersive media, such as passive and active Lorentzian media, one-dimensional photonic crystals, and undersized waveguides. Though superluminal group velocities have been found in these media, it has been suggested that the pulse "front" and associated transient field oscillations, known as the precursors or forerunners, will never travel faster than c, and hence relativistic causality is always preserved. Until now, few rigorous studies of these transient fields in structures exhibiting superluminal group velocities have been performed. In this paper, we present the dynamic evolution of these earliest field oscillations in one-dimensional photonic crystals (1DPC), using finite-difference time-domain (FDTD) techniques in conjunction with joint time-frequency analysis (JTFA). Our study clearly shows that the precursor fields associated with superluminal pulse propagation travel at subluminal speeds, and thus, the arrival of these precursor fields must be associated with the arrival of "genuine information." Our study demonstrates the expected result that abnormal group velocities do not contradict Einstein causality. This work also shows that FDTD analysis and JTFA can be combined to study the dynamic evolution of the transient and steady state pulse propagation in dispersive media.

Thermal Fluctuations of a Quantized Electromagnetic Field in Weakly Absorbing Media

The quantum fluctuations of an electromagnetic field in thermally excited media are calculated using the quantum electrodynamical method of Γ operators and without invoking phenomenological elements. The drawbacks of the standard theory based on the fluctuation-dissipation theorem and on the Matsubara technique of temperature Green’s functions are indicated. The decisive role of the correct consideration of higher order photon-photon correlators and the inadmissibility of their approximation by products of lower order correlators are underlined. It is shown that, contrary to the accepted opinion, the quantum fluctuations of an electromagnetic field cannot be expressed via the refractive indices of media introduced into the theory for the calculation of mean fields. The results obtained are compared with those previously derived using the Matsubara technique for calculation of the Green’s functions of an electromagnetic field in dispersive media under conditions of thermodynamic equilibrium. The previous results are shown to be incorrect at least for media consisting of atoms or molecules with a discrete energy spectrum.

On the structure of self-compressing blobs of an electromagnetic field in dispersive media with cubic nonlinearity

We obtained an asymptotic solution of the nonlinear Schrodinger equation with dimension (3+1) that describes the behavior of an electromagnetic field near the singularity arising in the case of propagation of electromagnetic waves in a dispersive medium with cubic nonlinearity as a result of development of the modulation-self-focusing instability. According to the developed theory, there exists a finite volume of the medium occupied by the electromagnetic field in which the energy flux is directed toward the emerging singularity. The energy contained in this volume, which is the characteristic parameter of instability, turns out to be a finite value depending on the parameters of the medium and the value of the field against the background of which the singularity takes place. The above energy is much smaller than the energy per characteristic scale of the most rapidly increasing unstable perturbations of the field with uniform amplitude distribution. In the conclusion, we discuss the possibility of using the collapse phenomenon for the formation of electromagnetic-field pulses.

Extinction of light in dispersive media with high particle concentrations: applicability limits of the interference approximation

We investigated the limits of applicability of the interference approximation (ITA), which is often used to calculate light fields in dispersive media with high particle concentrations. We analyzed the conditions under which the use of the ITA leads to an error in calculation of the dispersive-medium extinction coefficient ∊ equal to 10%, 15%, and 25%. The analysis was carried out by comparing the values of ∊ calculated in the ITA with the results of the calculation of ∊ in a much more exact quasi-crystalline approximation (QCA). The validity of the QCA in estimating the error of the ITA is shown by comparing the values of ∊ calculated in the ITA and the QCA with experimental data [J. Opt. Soc. Am.72, 1317 (1982)]. Our investigation shows that the ITA can be used only at relatively small values of the particle size parameter x. When the relative refractive index of the particles is n≳1.8, the applicability of the ITA is limited to the case in which the particle size parameter x⩽xmax≈1.5. A decrease in n leads to an increase in xmax, and for nonabsorbing particles at n≲1.3,xmax is approximately proportional: 1/(n-1). An increase in the imaginary part of the relative refractive index of the particles κ leads to a decrease in xmax. The smaller the n, the greater the dependence of xmax on κ.

Time-domain Green dyadics for temporally dispersive, simple media

Time-domain fundamental solutions and Green dyadics for temporally dispersive, simple media are introduced. Second forerunner approximations to the electromagnetic fields from an electric point dipole in unbounded dispersive materials are obtained. Numerical results for two frequently used material models are presented. Moreover, surface integral representations of the electromagnetic fields in dispersive media are obtained, and, finally, surface integral equations are derived for impenetrable and permeable scatterers.

Invariance properties of random pulses and of other random fields in dispersive media.

This paper is concerned with one-dimensional random fields consisting of randomly distributed identical light pulses which propagate in a linear dispersive medium. It is shown that such fields are necessarily stationary and that their power spectra and their longitudinal coherence properties do not change on propagation. The invariance of the power spectrum and of the coherence properties are shown to apply more generally to any one-dimensional stationary field of any state of coherence, propagating in a linear dispersive medium. Some invariance properties of nondiffracting partially coherent fields in dispersive media and of partially coherent fields in lossless fibers are also discussed.

Self-modulation and nonlinear diffraction of strong light fields in dispersive media

The problem of space-time self-modulation of strong laser fields is solved by the method of successive approximations. The nonlinear diffractional and nonlinear dispersive transformations of beam width and pulse duration are studied with emphasis on the reciprocal effects of nonlinear diffraction and dispersion. The effect of incomplete initial time and space coherence on the space-time parameters of a laser field and the conversion of its coherent properties is examined.

Relativistic geometrical optics

We investigate the gravitational and electromagnetic fields on the generalized Lagrange space endowed with the metricgij(x, y) = γij(x) + {1 + 1/n2(x, y)}yiyj. The generalized Lagrange spacesMm do not reduce to Lagrange spaces. Consequently, they cannot be studied by methods of symplectic geometry. The restriction of the spacesMm to a sectionSν(M) leads to the Maxwell equations and Einstein equations for the electromagnetic and gravitational fields in dispersive media with the refractive indexn(x, V) endowed with the Synge metric. Whenn(x, V) = 1 we have the classical Einstein equations. If 1/n2=1−1/c2 (c being the light velocity), we get results given previously by the authors. The present paper is a detailed version of a work in preparation.

Transient Raman gain stimulated by a noise pump

Abstract We predict a strong transient Raman gain stimulated by a Gaussian noise field in dispersive media. Our theory is based on the method of successive approximations, the first of which is the Markovian approximation. It is shown that the transient behavior will take place near critical pump intensity both for “short” ( τ p > T 2 ) and “ultrashort” ( τ p T 2 ) laser pulses (τ p is the pump pulse duration, T 2 is the relaxation time of optical phonons). Solutions for average intensities of the Stokes wave and optical phonons are obtained for arbitrary form of the given pump pulse. We show that transient Raman gain allows to form a very steep leading edge of the Stokes pulse. The steady-state increments of the second approximation describe the effects of a strong noise field. We show that after the intensity of the pump has exceeded a value beyond which the framework of validity of the Markovian approximation does not hold anymore, the steady-state Raman gain is saturated. We give a review of experimental results and make estimations for conditions of observing transient scattering in the field of a noise pump. Methods of obtaining the powerful femtosecond pulses based on stimulated Raman scattering of broad-band excimer lasers and supercontinuum emission are suggested.

Time‐domain reciprocity theorems for electromagnetic fields in dispersive media

Time‐domain reciprocity theorems of the time‐convolution and the time‐correlation type for electromagnetic fields in linear, time‐invariant, and locally reacting media are discussed. Inhomogeneous, anisotropic, and arbitrarily dispersive, both active and passive, media are included. The analysis is entirely carried out in space‐time, without intermediate recourse to the frequency or the wave vector domain. The application to inverse source and inverse constituency (or inverse profiling) problems is briefly indicated.

Transient fields in dispersive media

The problem addressed in this paper is the determination of transmitted and scattered fields produced by a transient electromagnetic field incident on a three-dimensional body when the body and the surrounding medium are allowed to be dispersive. Instead of decomposing the pulse into its Fourier components, the solution is carried out in the time domain to take advantage of marching-in-time procedures. Maxwell’s equations are suitably modified, and the reduction of the problem to the solution of an integral equation for a single tangential vector field is adapted to dispersive media. A simple conductor and a collisionless plasma are studied as examples.

On the concept of reaction field for electromagnetic fields in dispersive media

The concept of reoction is introdoced for electromagnetic fields in dispersive media as a measure of the amount of the reactions of a radiation source on spatially distributed field detectors. It is found that the equations of the in the medium take the adjoint forms to those of the electromagnetic field. A reciprocity theorem having a clear-cut physical meaning is derived with the use of the concept of the reaction field. Some variational expressions are derived with the use of the reaction field.

Foundations of Electromagnetic Theory, 3rd Edition

This revision is an update of a classic text that has been the standard electricity and magnetism text for close to 40 years. The fourth edition contains more worked examples, a new design and new problems. Vector Analysis, Electrostatistics, Solution of Electrostatic Problems, The Electrostatic Field in Dielectric Media, Microscopic Theory of Dielectrics, Electrostatic Energy, Electric Current, The Magnetic Field of Steady Currents, Magnetic Properties of Matter, Microscopic Theory of Magnetism, Electromagnetic Induction, Magnetic Energy, Slowly Varying Currents, Physics of Plasmas, Electromagnetic Properties of Superconductors, Maxwell's Equations, Propagation of Monochromatic, Monochromatic Waves in Bounded Regions, Dispersion and Oscillating Fields in Dispersive Media, The Emission of Radiation, Electrodynamics, The Special Theory of Relativity. Intended for those interested in learning the basics of standard electricity and magnetism.

Electromagnetic field in dispersive media

Electromagnetic field in dispersive media