Solution Of Maxwell Equations Research Articles

Vortex Circular Dichroism: An experimental technique to assess the scalar/vectorial regime of diffraction.

In classical electrodynamics, light-matter interactions are modelled using Maxwell equations. The solution of Maxwell equations, which is typically given by means of the electric and magnetic field, is vectorial in nature. Yet it is well known that light-matter interactions can be approximately described in a scalar (polarization independent) way for many optical applications. While the accuracy of the scalar approximation can be theoretically computed, to the best of our knowledge, it has never been determined experimentally. Here, we introduce Vortex Circular Dichroism ( VCD), an optical measurement that has the required features to assess the vectoriality of diffraction. VCD is measured as the differential transmission (or absorption) of left and right circularly polarized vortex beams. We test the VCD measurement with two different systems: i) an experimental set of single circular nano-apertures drilled in a gold film with diameters ranging from 150 to 1950 nm; and ii) a theoretical set of golden spheres with the same diameters as the nano-apertures. We observe that in both systems, VCD > 0 for smaller diameters, VCD ≲ 0 for intermediate values and VCD ≈ 0 for larger values of the diameter. Furthermore, the simulations show that a diffraction process characterized by a VCD ≈ 0 ( VCD ≠ 0) is polarization-independent (polarization-dependent). As a result, we relate VCD ≠ 0 to a vectorial diffraction, and VCD ≈ 0 to a scalar one. Overall, our results show compelling evidence that it is possible to experimentally assess the scalar/vectorial regime of a diffraction process, and that the VCD technique possesses the required features to measure the vectoriality of diffraction processes involving plasmonic cylindrically symmetric structures.

First numerical evidence of the two-close frequency heating effect on electron cyclotron resonance ion sources

The two-close frequency heating (TCFH) is a new implementation of the well-known two frequency heating. In TCFH, the two frequencies differ around 200-300 MHz each other in order to establish two contiguous ECR resonance zones. TCFH has been proved to be a powerful technique to suppress plasma instabilities in Electron Cyclotron Resonance Ion Sources (ECRIS), as well as to improve their performances. Its beneficial effect, compared to the application of a single frequency, is always deduced from the extracted charge states distributions and from the detection of the plasma self-emission in the X-ray and microwave ranges. This paper presents the first approach to a numerical description of the two-close frequency effect, based on the relevant plasma parameters of the ECRIS setup operating at ATOMKI-Debrecen. Simulations have been performed by our PIC-Full Wave code, joining electron kinetics and FEM solution of Maxwell equations in a cold plasma model. Results on plasma electron density and energy distribution will be shown, together with a direct comparison with the already published data on X ray emission.

Sub-Micrometer Particles Remote Detection in Enceladus’ Plume Based on Cassini’s UV Spectrograph Data

Enceladus is the Saturnian satellite is known to have water vapor erupting from its south pole region called „Tiger Stripes”. Data collected by Cassini Ultraviolet Imaging Spectrograph during Enceladus transiting Saturn allow us to estimate water plume absorption from 1115.35–1912.50 Å and compare it to the Mie solutions of Maxwell equations for particles with a diameter in the range from 10 nm up to 2 µm. The best fit performed using Gradient Descent method indicates a presence of sub-micrometer particles of diameters: 120–180 nm and 240–320 nm consistent with Thermofilum sp., Thermoproteus sp., and Pyrobaculum sp. cell sizes present in hydrothermal vents on Earth.

Imaginary-shifted expression of Gaussian beams as rigorous solutions of Maxwell equations

Analytical and rigorous solutions of Maxwell equations for Gaussian beams have been derived, without using paraxial approximation. Vectorial formulation of high-order Gaussian beams including Laguerre–Gaussian-like beams and optical vortices were obtained. These analytical solutions are useful and effective for understanding the beam characteristics.

Polarization of electromagnetic pulses

We show the impossibility, for localized and exact solutions of the Maxwell equations, of perfect circular polarization in a fixed plane, or perfect linear polarization along a fixed direction. A measure of polarization of electromagnetic pulses is obtained by analogy with that useful in monochromatic radiation, and its limitations discussed. Using oscillatory solutions of the free-space Maxwell equations, for which all components of the electric and magnetic fields satisfy the wave equation, we construct explicit examples of TE pulses which are linearly polarized with an azimuthal electric field, TE+iTM pulses approximately linearly polarized along the propagation direction, and also approximately circularly polarized pulses. The latter have perfect circular polarization on the propagation axis.

Solutions of Maxwell equations for admissible electromagnetic fields, in spaces with simply transitive four-parameter groups of motions

All non-equivalent solutions of vacuum Maxwell equations are found for the case when space-time manifolds admit simply transitive four-parameter groups of motions [Formula: see text]. The potentials of the admissible electromagnetic fields admit the existence of the algebra of motion integrals of the Hamilton–Jacobi and Klein–Gordon–Fock equations which is isomorphic to the algebra of the group operators for the same group [Formula: see text].

Multiple cylindrically symmetric solutions of nonlinear Maxwell equations

In this paper, we study the following nonlinear time-harmonic Maxwell equations \begin{equation}\label{equation 0.1} \nabla\times(\nabla \times E)-\omega^2\varepsilon(x)E =P(x)|E|^{p-2}E+Q(x)|E|^{q-2}E, \end{equation} where $\varepsilon(x)$ is the permittivity of the material, $x\in\mathbb{R}^{3}$, $1< q< {p}/({p-1})< 2< p< 6$, $P(x),Q(x)\in C\left(\mathbb{R}^{3},\mathbb{R}\right)$. Under some special cylindrical symmetric conditions for $\varepsilon(x)$, $P(x)$ and $Q(x)$, we obtain infinite many cylindrically symmetric solutions of \eqref{equation 0.1} by using variational method and fountain theorems without $\tau$-upper semi-continuity.

From disformal electrodynamics to exotic spacetime singularities

We study different types of spacetime singularities which emerge in the context of disformal electrodynamics. The latter is characterized by transformations of the background metric which preserve regular (non-null) solutions of Maxwell equations in vacuum. Restricting ourselves to the case of electrostatic fields created by charged point particles along a line, we show that exotic types of singularities arise.

Numerical Simulation Method of Gyromagnetic Nonlinear Transmission Lines Based on Coupled Solution of Maxwell and LLG Equations

Numerical Simulation Method of Gyromagnetic Nonlinear Transmission Lines Based on Coupled Solution of Maxwell and LLG Equations

Revisiting canonical quantization of radiation: the role of the vacuum field

Canonical quantization has conventionally been adopted as a necessary procedure for the description of the quantum radiation field by analogy between quantum-mechanical oscillators and field oscillators. In this paper we provide the physical basis for the formal quantization of the radiation field interacting with matter in the presence of the vacuum field, taken here as a solution of classical Maxwell equations. Just as the canonical particle operators x^\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{x}$$\\end{document}, p^\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{p}$$\\end{document} have been shown to be the response functions of the particle to this field, here we derive the creation and annihilation operators a^†\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{a}^{\\dagger }$$\\end{document}, a^\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{a}$$\\end{document}, with [a^,a^†]=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[\\hat{a},\\hat{a}^{\\dagger }]=1$$\\end{document}, as an expression of the field’s response to this interaction. The results obtained shed new light on the physical meaning of the description of light in terms of operators and suggest that neither matter nor radiation are quantized in isolation.

Dispersive Propagation of Terahertz Pulses in a Plasmonic Fiber

The dispersion properties of surface plasmon polaritons (SPPs) during propagation on metal wires with a dielectric coating in the terahertz frequency range were investigated theoretically. An analytical expression was obtained for a pulsed electric field using the solution of Maxwell equations taking into account high-order dispersion terms. The influence of the dielectric coating on the distortion of the pulse shape was investigated. Unlike uncoated wire, the propagation of surface plasmon pulses along a coated wire is highly dispersive. It was shown that the coating leads to the appearance of a long-chirped signal with a propagation of only a few millimeters, i.e., when a terahertz pulse propagates along a coated wire, it acquires a long oscillatory tail, the frequency of which depends on time.

Subscriber location in radio communication nets

Our aim is to develop the method of location subscriber to be used in military communication nets. This method is based on frequency offset measurement. Analytic description of the Doppler effect creates one of such possibilities. In this paper, an original location subscriber method is presented. We showed the Maxwell equations solution in the case of a transmitter continually changing location in relation to a receiver. It makes possible to calculate exactly the value of the received signal parameters especially frequency offset. The methodology described in this paper shows that the Doppler frequency offset value can be used for radio signal sources location.

On Damping of Plasmons and Plasmon-Polaritons in Metallic Nanostructures and Its Influence onto Numerical Simulations

AbstractWe show that the damping of plasmons in metallic nanoparticles highly exceeds that caused by scattering of electrons on defects, phonons, and other electrons and on boundaries of particles. The radiation losses in far-field zone due to the Lorentz friction is especially high at nanometre scale of metal confinement (e.g. attains the maximum at ca. 100 nm diameter of particle, Au in vacuum). This causes a different e-m response of such size structures in comparison to conventional solution of Maxwell-Fresnel equations using the bulk dielectric function for metal. The strong discrepancy occurs also if plasmons are coupled in near-field zone to nearby-located absorbing medium, e.g. semiconductor substrate. This coupling cannot be accounted for by classical electrodynamic treatment (e.g. by numerical solution of Maxwell equations by finite element method for differential equation solution) and needs the application of quantum Fermi golden rule to estimate plasmon damping and related modifications of dielectric functions both of metallic nanoparticles and of absorbing medium. Similarly, the perfect cancellation of radiative losses of plasmon-polaritons in metallic nano-chains is beyond classical Maxwell equation modelling, as it reveals the perfect vanishing of Lorentz friction losses in chain segments by radiative contribution from other segments in near-, medium- and far-field zones. This demonstrates that nano-plasmonic effects cannot be reliably numerically modelled using material parameters from conventional packets referred to optical constants measured in bulk.

Dyson maps and unitary evolution for Maxwell equations in tensor dielectric media

The propagation and scattering of electromagnetic waves in dielectric media is of theoretical and experimental interest in a wide variety of fields. An understanding of observational results generally requires a numerical solution of Maxwell equations---usually implemented on conventional computers using sophisticated numerical algorithms. In recent years, advances in quantum information science and in the development of quantum computers have piqued curiosity about taking advantage of these resources for an alternate numerical approach to Maxwell equations. This requires a reformulation of the classical Maxwell equations into a form suitable for quantum computers which, unlike conventional computers, are limited to unitary operations. In this paper, a unitary framework is developed for the propagation of electromagnetic waves in a spatially inhomogeneous, passive, nondispersive, and anisotropic dielectric medium. For such a medium, generally, the evolution operator in the combined Faraday-Ampere equations is not unitary. There are two steps needed to convert this equation into a unitary evolution equation. In the first step, a weighted Hilbert space is formulated in which the generator of dynamics is a pseudo-Hermitian operator. In the second step, a Dyson map is constructed which maps the weighted-physical-Hilbert space to the original Hilbert space. The resulting evolution equation for the electromagnetic wave fields is unitary. Utilizing the framework developed in these steps, a unitary evolution equation is derived for electromagnetic wave propagation in a uniaxial dielectric medium. The resulting form is suitable for quantum computing.

Exact Solutions of Maxwell Equations in Homogeneous Spaces with the Group of Motions G3(VIII)

The problem of the classification of the exact solutions to Maxwell’s vacuum equations for admissible electromagnetic fields and homogeneous space-time with the group of motions G3(VIII) according to the Bianchi classification is considered. All non-equivalent solutions are found. The classification problem for the remaining groups of motion, G3(N), has already been solved in other papers. All non-equivalent solutions of empty Maxwell equations for all homogeneous spaces with admissible electromagnetic fields are now known.

Exact Solutions of Maxwell Equations in Homogeneous Spaces with the Group of Motions G3(IX)

This paper classifies the exact solutions of the Maxwell vacuum equations for the case when the electromagnetic fields and metrics of homogeneous spaces are invariant with respect to the motion group G3(IX). All the appropriate non-equivalent exact solutions of the Maxwell vacuum equations are found.

Analysis of Topologically Non-trivial Solutions of Maxwell Equations in de Sitter Spacetime

Analysis of Topologically Non-trivial Solutions of Maxwell Equations in de Sitter Spacetime

Vortex Circular Dichroism: An experimental technique to assess the scalar/vectorial regime of diffraction

Background: In classical electrodynamics, light-matter interactions are modelled using Maxwell equations. The solution of Maxwell equations, which is typically given by means of the electric and magnetic field, is vectorial in nature. Yet it is well known that light-matter interactions can be approximately described in a scalar (polarization independent) way for many optical applications. While the accuracy of the scalar approximation can be theoretically computed, to the best of our knowledge, it has never been determined experimentally. Here, we show that the vectoriality of diffraction can be probed with a new technique: Vortex Circular Dichroism(VCD). Methods: We measure the differential transmission of left and right circularly polarized vortex beams through a set of single circular nano-apertures with diameters ranging from 150 to 1950 nm. We observe that VCD > 0 for smaller diameters, VCD ≲ 0 for intermediate values and VCD ≈ 0 for larger values of the diameter. We also carry out Mie Theory simulations for spheres with the same diameters as the nanoholes and observe that the theoretical and experimental VCD values follow the same trend line. Results: We relate VCD ≠ 0 to a vectorial diffraction, and VCD ≈ 0 to a scalar one. This is corroborated by the simulations, which show that a diffraction process characterized by a VCD ≈ 0 (VCD ≠ 0) is polarization-independent (polarization-dependent). Conclusions: Overall, our results give a wealth of evidence that VCD allows for the experimental assessment of the scalar/vectorial regime of diffraction.

The quest of null electromagnetics knots from Seifert fibration

In this work we find new null electromagnetic fields that are exact solutions of Maxwell equations in vacuum and generalize the hopfion. The hopfion is an exact solution of Maxwell equations in vacuum in which all the field lines (both electric and magnetic) are topologically equivalent to closed and linked circles, forming a mathematical structure called Hopf fibration. Here we present a generalization to include other field lines topology, such as the Seifert fibration in which the field lines form linked torus knots. Included in this generalization are fields that ergodically fill torus surfaces.

Infinitely many cylindrically symmetric solutions of nonlinear Maxwell equations with concave and convex nonlinearities

Infinitely many cylindrically symmetric solutions of nonlinear Maxwell equations with concave and convex nonlinearities