Solving Maxwell Equations Research Articles

Liquid Crystalline Half‐Skyrmions and Their Optical Properties

AbstractLiquid crystals have intrigued physicists as a platform that facilitates direct visualization of topological concepts. Here, the theoretical and experimental studies demonstrating that a thin film of a chiral liquid crystal forms topological entities known as half‐Skyrmions, swirl‐like orientational order that spans the hemisphere of the order parameter space , are reviewed. They appear in the form of a hexagonal lattice or in an isolated manner, accompanied by topological line defects to satisfy topological constraints. Under an optical microscope, half‐Skyrmions appear as dark spots, and their hexagonal lattice yields a Kossel diagram comprising a hexagonal arrangement of circular arcs. These experimental observations are corroborated by numerical calculations of the orientational order based on the Landau‐de Gennes theory with an orientational order parameter of a second‐rank tensor, and construction of its optical images and Kossel diagrams by directly solving Maxwell equations for light wave. A thin film of a chiral liquid crystal thus provides an interesting system for the investigation of topological concepts, and spontaneous formation of a half‐Skyrmion lattice whose periodicity is of the order of the wavelength of visible light has a potential for photonics applications as well as poses a challenging problem on optics.

Core-cap heterodimer independent of polarization direction of excitation light

The plasmonic anisotropic nanostructure possesses the enhanced surface electric field and unique optical properties in near-infrared spectrum, thus it has potential applications in nano-optoelectronics and medical sensing. To obtain the best property, the excitation polarization normally needs to match the orientation of the structure. The strong polarization dependence, however, greatly limits the excitation efficiency. In this work, a patchy structure is introduced to release the dependence of polarization. In the proposed method here in this work, the lost properties due to unmatched polarizations are compensated for by the plasmonic resonance coupling between the patch and capped structure in the heterozygous dimer. By overlapping the two modes at the same wavelength, the absorption keeps rather stable undisturbed status during the variation of incident polarization. This work focuses on the theoretical exploration of the feasibility. Electromagnetic field in the interaction between light and heterozygous dimer is essential before extinction coefficient is calculated. The field of the model is obtained by solving Maxwell equations through using the finite element method. The numerical calculation presents a good understanding of the mechanism of the plasmonic interactions in the dimer, based on which the nanostructure with optimized configuration parameters can achieve the stable and high absorption in the near infrared wavelength.

Comparative Study of Electric Machines for Stirling Generator Application

The choice of a machine for an application and a given specification remains a complex problem. This will involve, for example, bringing together criteria such as: performance, space saving, economical, reliable, little acoustic noise and others. The best machine selection to fulfill all constraints is an important step for the project to be realized. This work focus on Stirling Engine based Generator and study all types of rotating machines that can be employed for maximum electric power production. Analytical electromagnetic models where developed for all types of rotating machines that satisfied minimum requirement for the project by solving Maxwell equations. The purpose is to develop the design model and combine electromagnetic and thermal study of the machines. Finite Element Method is used to compare the performances of the generators for the best choice. Results show that for applications not requiring bigger output power, the major criteria for the selection is the optimal magnetic induction created by the inducer in the stationary part of the machine. For application such as Stirling generators, permanent magnet (PM) machine satisfy many comparison criteria such as maximum power at low speed, torque density, high efficiency. Beyond exposing a selection method for a project, this work lay down a step-by-step method for engineers and scientists for the crucial stage of design and conception work

Casimir effect for magnetic media: Spatially nonlocal response to the off-shell quantum fluctuations

We extend the Lifshitz theory of the Casimir force to the case of two parallel magnetic metal plates possessing a spatially nonlocal dielectric response. By solving Maxwell equations in the configuration of an electromagnetic wave incident on the boundary plane of a magnetic metal semispace, the exact surface impedances are expressed in terms of its magnetic permeability and longitudinal and transverse dielectric functions. This allows application of the Lifshitz theory with reflection coefficients written via the surface impedances for calculation of the Casimir pressure between magnetic metal (Ni) plates whose dielectric responses are described by the alternative nonlocal response functions introduced for the case of nonmagnetic media. It is shown that at separations from 100 to 800~nm the Casimir pressures computed using the alternative nonlocal and local plasma response functions differ by less than 1\%. At separations of a few micrometers, the predictions of these two approaches differ between themselves and between that one obtained using the Drude function by several tens of percent. We also compute the gradient of the Casimir force between Ni-coated surfaces of a sphere and a plate using the alternative nonlocal response functions and find a very good agreement with the measurement data. Implications of the obtained results determined by the off-shell quantum fluctuations to a resolution of long-standing problems in the Casimir physics are discussed.

S11 Parameter Calculation of Frequency Selective Surface Based on Deep Learning

This paper proposes the FSS-CNN network model as a forward predictor, replacing the function of the Maxwell equation solver of commercial software. The predictor is different from the numerical optimization method, and the data-driven method based on machine learning (ML) can be expressed and generalize complex functions or data to discover unknown relationships between a large number of variables. In the frequency range of 2∼18GHz, the S11 parameter prediction of the corresponding metal pixel pattern can be easily realized by an accurate forward neural network model. The MSE reaches the level of less than 0.1 and the time consumption is less than 0.07s, which meets the requirements of fast, efficient and automatic calculation.

RF wave propagation simulation for ICRF antenna in EAST

ABSTRACT The propagation performance of radiofrequency (RF) waves excited by ICRF antenna in plasma has a great influence on the coupling effect. In this paper, the propagation characteristics of fast wave (FW) and slow wave (SW) under tokamak experimental condition are calculated, and the influence of angular frequency w 0, antenna power spectrum k// and tokamak total magnetic field B 0 is illustrated based on the typical operating parameters in EAST. By applying perfect matched layer (PML) boundary processing method to simulate single-pass absorption and using finite element method (FEM) to solve Maxwell equations in frequency domain, the propagation and coupling simulation of RF waves in cold plasma for EAST ICRF antenna in B-window were carried out to obtain the polarization characteristics of fields and the relationship between the coupling impedance and the gap length from antenna to the FW cut-off layer. The analysis results in this paper provide useful reference and guidance for the study of propagation coupling of ICRF waves in EAST and other magnetic confined fusion devices.

Convergence analysis of various factorization rules in the Fourier-Bessel basis for solving Maxwell equations using modal methods.

The choice of factorization rule can strongly affect the convergence of solutions to Maxwell equations based on the orthogonal expansion of electromagnetic fields. While this issue has already been investigated thoughtfully for the Fourier basis (plane-wave expansion), for other bases it has not yet received much attention. Although there are works showing that, in the case of the Fourier-Bessel basis (cylindrical-wave expansion), the use of an inverse factorization rule can provide faster convergence than Laurent's rule, these works neglect the fact that other rules are also possible. Here, I mathematically demonstrate four different factorization rules for solving Maxwell equations in cylindrical coordinates using the Fourier-Bessel expansion in both infinite and finite domains. I compare their convergence for a step-index fiber (which has a known exact solution and thus enables the absolute numerical error to be determined), as well as for several VCSEL structures. I show that the cylindrical-wave expansion differs from the plane-wave expansion and that the application of an inverse factorization rule for the electric field component perpendicular to the discontinuities can result in deterioration of numerical convergence. Finally, I identify the factorization rule that gives the fastest convergence of the modal method using the Fourier-Bessel basis.

2D NUMERICAL SIMULATION OF MAGNETIC FIELD IN LOW-VOLTAGE CIRCUIT BREAKER

Low Voltage Circuit Breakers is used for the switching process in power distribution and control system. This process is accompanied by the occurrence of the electric arc between the fixed and mobile contact pieces of the apparatus. The electric arc is introduced into the quenching chamber formed of ferromagnetic iron splitter plates, divided into short arcs and then the arc may extinguish after passing the current through zero. Behavior of the electric arc in the extinguishing chamber influences the performance of these devices, the ferromagnetic material leading to the improvement of these performances. This article presents the calculation of the magnetic field components in the extinguishing chamber of the low-voltage circuit breaker of the 2000 A, 690 V manufactured by Schneider Electric and to describe the physical phenomenon and mathematical calculation of the electric arc in LVCB. The Ansys Multiphysics program is used to determine the spectrum of magnetic field components. This program is based on the finite element method for solving Maxwell equations.

A Memory-Efficient Implementation of Perfectly Matched Layer With Smoothly Varying Coefficients in Discontinuous Galerkin Time-Domain Method

Wrapping a computation domain with a perfectly matched layer (PML) is one of the most effective methods of imitating/approximating the radiation boundary condition in Maxwell and wave equation solvers. Many PML implementations often use a smoothly-increasing attenuation coefficient to increase the absorption for a given layer thickness, and, at the same time, to reduce the numerical reflection from the interface between the computation domain and the PML. In discontinuous Galerkin time-domain (DGTD) methods, using a PML coefficient that varies within a mesh element requires a different mass matrix to be stored for every element and therefore significantly increases the memory footprint. In this work, this bottleneck is addressed by applying a weight-adjusted approximation to these mass matrices. The resulting DGTD scheme has the same advantages as the scheme that stores individual mass matrices, namely higher accuracy (due to reduced numerical reflection) and increased meshing flexibility (since the PML does not have to be defined layer by layer) but it requires significantly less memory.

Electric field simulation of Ag nanoparticles induced by Femtosecond laser in welding process

The electric field distribution of Ag nanoparticles under femtosecond laser is simulated by solving Maxwell equations in this article. The results show that with the same laser energy, the coupling electric field between adjacent nanoparticles becomes stronger and stronger as the spacing between nanoparticles decreases, while the enhancement factor decreases rapidly when the spacing between nanoparticles is less than 1 nm, because under this condition, its mechanism includes not only the coupling of two dipoles, but also the electron tunneling between two surfaces. Besides laser energy, the electric field of Ag nanoparticles is greatly affected by the nanoparticles size and their spatial distribution. With the same laser energy and spacing, the smaller the particle size, the higher the peak value of electric field intensity, but the faster the attenuation with distance. In the polarization direction of the laser, the enhancement factor of the electric field is more obvious. When the laser acts on several Ag nanoparticles, the electric field of nanoparticles in the range of spot size is quite different from that of the nanoparticles outside the spot.

Casimir effect for biaxial anisotropic plates with surface conductivity

The Casimir energy is constructed for a system consisting of two semi-infinite slabs of anisotropic material. Each of them is characterized by bulk complex dielectric permittivity tensor and surface conductivity on the free boundary. We found general form of the scattering matrix and Fresnel coefficients for each part of the system by solving Maxwell equations in the anisotropic media.

Reflection and transmission by large inhomogeneous media. Validity of born, rytov and beam propagation methods

The ability to model the backward and forward scattering by large inhomogeneous samples is of major importance especially for computational imaging applications. Unfortunately, when the sample dimensions exceed hundreds of wavelengths, a rigorous solving of the Maxwell Equations becomes difficult. In this work, we compare the scattered field estimated by a rigorous Maxwell equation solver, based on the discrete dipole approximation, with that given by several approached methods, Rytov, Born and a revisited Beam Propagation Method. We show on many examples, that BPM outperforms all the other techniques and accurately handles field distortion and moderate multiple scattering.

A multi-term spherical harmonic expansion of the Boltzmann equation for application to low-temperature collisional plasmas

The Boltzmann equation describes the evolution of the electron and ion distributions in a plasma over time through a six-dimensional phase space. For highly collisional plasmas, scattering collisions keep the distribution function nearly isotropic in velocity space with small perturbations created by the hydrodynamic and electromagnetic forces. For these plasmas, a spherical-harmonic expansion of the velocity-space distribution function is an effective technique for solving the Boltzmann equation. This paper examines each of the terms in the Boltzmann equation in detail to derive conditions where a spherical harmonic expansion is useful. Expressions for the matrix elements are presented which represent the projection of the various operators in the Boltzmann equation onto the spherical harmonics basis set. The resulting multiple-term spherical-harmonic expansion makes no assumptions about either the direction of the electric and magnetic fields or the magnitude of the spatial gradients and is appropriate for coupling with a Maxwell equation solver for the time- and spatially-dependent electromagnetic fields. When only the first two lowest-order terms are kept, it is shown that the resulting equations are very similar in form to the continuity and force-balance fluid equations. Additional kinetic terms appear in the continuity-like equation which are related to the changes in the energy distribution due to the electric field and collisions, including Ohmic heating. Two additional kinetic terms also appear in the force-balance-like equation. The collision term accounts for momentum-transfer during scattering collisions and the other accounts for the flow of energy in velocity space and is proportional to the derivative with respect to energy of the energy density.

Accurate Estimation of Frequency-Dependent Losses in High Voltage Test Transformers for the Assessment of Electric Discharge Powers

The work presented in this paper is related to the project GEMUDE (Genérateur Multifonction de Décharge Electrique) which aims to design a universal high-voltage generator for electrical discharge studies. To design this variable high voltage source that operates in the frequency range of 0 to 1 kHz, the assessment of transformer losses represents a crucial phase during the design process. These losses in the coils and iron core of the transformer are closely related to the frequency and nature of the materials used. This paper presents a comparative study of transformer losses using analytical methods and experimental calorimetry measurements. Steinmetz empirical formula is used to estimate magnetic core losses whereas coil losses are evaluated by solving Maxwell equations. The main goal is to control these losses to limit the internal temperature rise in the transformer through the implementation of an efficient cooling solution. The results obtained by the analytical method were satisfactory which confirm the feasibility of measuring the power absorbed by the various electrical discharge devices upstream of the high-voltage transformer. This is because it turns out that the power of the generator in charge is the total power of the electric discharge and the transformer losses. This method, termed Power Disparity Method (PDM). In this paper, it is an easy and reliable way as compared with high voltage measurement methods.

Analytical method for metal-insulator-metal surface plasmon polaritons waveguide networks.

Metal-insulator-metal (MIM) surface plasmon polaritons (SPPs) waveguides with side-coupled resonators have been widely studied through various approaches. However, few methods are both physically transparent and complete. Here, an analytical approach, which is based on the Green's function method, is developed in order to investigate electromagnetic wave transmission across SPPs MIM waveguide networks. The proposed method is applied in order to model different MIM-waveguide geometries with weakly-coupled side stubs, comparing to the geometries with strongly-coupled stubs. The weak coupling between the backbone and stubs is taken into account by the electromagnetic field leakage at metal-insulator interface. Analytical expressions for transmittance in cases of single stub and cavity are obtained straightforwardly. Our method shows excellent computational efficiency in contrast with solving Maxwell equations numerically.

Determination of 3D electrostatic field at an electron nano-emitter

Differential phase contrast in scanning transmission electron microscopy has been applied to image nanoscale electrostatic fields of a sharp tungsten electron emitter with an apex radius of about 20 nm and under field emission conditions. Assuming axial symmetry of the nano-emitter, we derived a method based on the inverse Abel transform to quantitatively reconstruct an axial slice of the 3D electrostatic field from a single projection measurement. The highest field strength of 2.92 V/nm is measured at the nano-emitter apex under the condition of a bias voltage of −140 V with respect to the grounded counter electrode located at about 650 nm from the apex, resulting in an emission current of more than 2 μA. The experimental results are compared with simulations based on a finite element numerical Maxwell equation solver. Quantitative agreement between experiment and simulation has been achieved.

Plasma magnetosphere of slowly rotating magnetized neutron star in branewold

The analytical expression for Goldreich-Julian (GJ) charge density at the polar cap of magnetized neutron star has been obtained in braneworlds for inclined neutron star through solving Maxwell equations and shown that the value of GJ charge density decreases with increasing the value of the brane charge. The analytical expressions for scalar potential and parallel electric field on the region greater than the polar cap region of the neutron star have also been obtained by solving Poisson equation in braneworlds.

A first-principles simulation method for ultra-fast nano-optics

We develop a computational approach for ultrafast nano-optics based on first-principles time-dependent density functional theory. Solving Maxwell equations for light propagation and time-dependent Kohn-Sham equation for electron dynamics simultaneously, intense and ultrashort laser pulse interaction with a dielectric nano-structure is described taking full account of nonlinear effects. As an illustrative example, irradiation of a pulsed light on silicon nano-sphere system is presented.

Time-dependent density functional theory for interaction of ultrashort light pulse with thin materials

We present a comprehensive theoretical description for an irradiation of an ultrashort light pulse normally on thin materials based on first-principles time-dependent density functional theory. As the most elaborate scheme, we develop a microscopic description solving Maxwell equations for light electromagnetic fields and the time-dependent Kohn-Sham equation for electron dynamics simultaneously in the time domain using a common spatial grid. We call it the microscopic Maxwell-TDDFT scheme. We test this scheme for silicon thin films of various thickness, from a few atomic layers to a few tens of nm. We show that the microscopic Maxwell-TDDFT scheme provides a satisfactory description incorporating the electronic structure of thin films in the first-principles level, multiple reflections of the electromagnetic fields at the surfaces, and nonlinear light-matter interaction when the incident light pulse is strong. However, the calculation becomes expensive as the thickness increases. We then consider two limiting cases of extremely thin and sufficiently thick films and develop approximate schemes. For the extremely thin case including two-dimensional atomic-layered materials, a two-dimensional macroscopic electromagnetism is developed: a two-dimensional susceptibility is introduced for a weak field, while time evolution equation is derived for an intense field. For sufficiently thick films, the microscopic Maxwell-TDDFT scheme is expected to coincide with a description utilizing ordinary macroscopic electromagnetism. We numerically confirm it comparing the calculated results: For a weak field, a comparison is made with a description using the bulk dielectric susceptibility. For a strong field, a comparison is made with a multiscale Maxwell-TDDFT scheme which the authors' group developed previously.

A simple absorbing layer for EM‐radiation from a beam‐plasma interaction system

In this paper, a problem of taking into account the electromagnetic radiation power in a numerical simulation of electron beam‐plasma interaction is considered. The numerical model is based on the particle‐in‐cell (PIC) method and the finite‐difference time‐domain (FDTD) scheme for solving Maxwell equations. As a boundary condition, it is proposed to use a simple layer of absorption, that is, artificial attenuation of an electromagnetic wave by multiplying the electromagnetic field in the boundary domain by a coefficient k < 1 depending on the distance to the boundary. The numerical experiments performed show that using such a layer for absorbing the electromagnetic radiation and for taking into account its power is efficient.