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Numerical Analysis of the Integral Equation Method for the Computation of the Electromagnetic Field in a Nonhomogeneous Medium
摘要： The article considers mathematical modeling of the electromagnetic field in a nonhomogeneous medium by the integral equation method. The case of high-contrast conducting media is studied in detail, with the conducting nonhomogeneity embedded in a poorly conducting medium. The analysis of the integral equation, in this case, has shown that the solution deteriorates when the conducting nonhomogeneity is inside a low-conductivity layer. It is shown that this effect can be overcome by Dmitriev’s method of elevated background conductivity. The contrast effect is most pronounced for the H-polarized two-dimensional electromagnetic field in a nonhomogeneous medium. The numerical experiment has accordingly been conducted for this particular case. The solution computed by the integral equation method with elevated background conductivity is compared with the solution computed by the finite-difference method. The results of the two methods show excellent fit.
关键词： integral equation method,electromagnetic sounding,nonhomogeneous medium,Maxwell equations
更新于2025-09-23 15:22:29
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The method of Fourier transforms applied to electromagnetic knots
摘要： The Fourier transform method can be applied to obtain electromagnetic knots, which are solutions of Maxwell equations in vacuum with non-trivial topology of the field lines and especial properties. The program followed in this work allows to present the main ideas and the explicit calculations at undergraduate level, so they are not obscured by a more involved formulation. We make use of helicity basis for calculating the electromagnetic helicity and the photon content of the fields.
关键词： Fourier transforms,helicity basis,Maxwell equations,electromagnetic knots,photon content
更新于2025-09-23 15:21:01
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[IEEE 2018 IEEE International Conference on Computational Electromagnetics (ICCEM) - Chengdu, China (2018.3.26-2018.3.28)] 2018 IEEE International Conference on Computational Electromagnetics (ICCEM) - High-Order Ultra-Weak Variational Formulation for Maxwell Equations
摘要： The ultra-weak variational formulation (UWVF) is a Trefftz method for solving time-harmonic wave problems. The combination of flexible meshing and the use of plane wave basis functions makes the UWVF well-suited for solving Maxwell problems in inhomogeneous media and in general geometries that can be tens or even hundreds wavelengths. In a single mesh, the number of basis functions can be adjusted element-wise based on the element size, material properties in the element and the requested level accuracy of the solution. Previous studies have shown that the UWVF method can use from 3 to 130 plane waves per element. In this study, the use of high-dimensional plane waves basis for the UWVF is investigated. The aim is to find a basis which would allow elements with h/λ ≈ 10 (where h is the length of the longest edge of the element and λ is the wavelength). Three methods for choosing the directions of the plane waves are compared in terms of accuracy of the UWVF approximation and the conditioning of the resulting matrix system. Results suggest that in a simple model problem the goal is achievable but requires over 500 plane wave basis functions per element for a tolerable accuracy.
关键词： Maxwell equations,Finite element method
更新于2025-09-23 15:21:01
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Numerical simulation of a coupled system of Maxwell equations and a gas dynamic model
摘要： It is known that both linear and nonlinear optical phenomena can be produced when the plasmon in metallic nanostructures are excited by the external electromagnetic waves. In this work, a coupled system of Maxwell equations and a gas dynamic model including a quantum pressure term is employed to simulate the plasmon dynamics of free electron fluid in different metallic nanostructures using a discontinuous Galerkin method. Numerical benchmarks demonstrate that the proposed numerical method can simulate both the high order harmonic generation and the nonlocal effect from metallic nanostructures. Based on the switch-on-and-off investigation, we can conclude that the quantum pressure term in gas dynamics is responsible for the bulk plasmon resonance. In addition, for the dielectric-filled nano-cavity, a coupled effective polarization model is further adopted to investigate the optical behavior of bound electrons. Concerning the numerical setting in this work, a strengthened influence of bound electrons on the generation of high order harmonic waves has been observed.
关键词： quantum pressure,Discontinuous Galerkin method,Maxwell equations,nonlocal effect,high order harmonic generation,gas dynamic model
更新于2025-09-23 15:19:57
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Numerically Implemented Impact of a Femtosecond Laser Pulse on Glass in the Approximation of Nonlinear Maxwell Equations
摘要： A finite-difference scheme is presented for the solution of the problem on the interaction of a femtosecond laser pulse with glass in the approximation of nonlinear Maxwell equations supplemented by equations of the hydrodynamic type for conduction electrons. The model takes into account all the basic physical processes involved in this interaction. An axially symmetric problem is considered. The construction of the scheme allows for the specifics of the problem, which ensures the efficiency of the developed method. The use of the scheme is illustrated by the results of modeling the interaction between glass and femtosecond laser pulses of an ordinary Gaussian shape with linear polarization and doughnut pulses with radial and azimuthal polarization. Significant differences in the dynamics of the interaction between glass and these three types of pulses are revealed.
关键词： aperture,nonlinear Maxwell equations,femtosecond laser pulse,Kerr effect,finite-difference scheme,implicit algorithms,plasma
更新于2025-09-23 15:19:57
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ANALYSIS OF A NON-INTEGER DIMENSIONAL TUNNEL AND PERFECT ELECTRIC CONDUCTOR WAVEGUIDE
摘要： Solutions to the Maxwell equations for a planar non-integer dimensional perfect electric conductor (NID-PEC) waveguide are obtained. The space within the guide is NID in direction normal to walls of the waveguide. Field behavior within the waveguide is noted for di?erent values of the parameter, D, describing dimension of the NID space. For D = 2, classical results are recorded. The discussion is further extended by treating propagation in a tunnel within unbounded dielectric medium. The space within tunnel is also NID in direction perpendicular to walls of the tunnel. For di?erent values of D ?eld behaviors are also presented. It has been noted that for D = 2 and taking very high values of permittivity ((cid:2) → ∞) classical results for PEC waveguide are recorded, whereas for (cid:2) → ∞, ?eld behavior within tunnel matches with NID-PEC waveguide.
关键词： TE/TM modes,Maxwell equations,PEC waveguide,Non-integer dimensional space,fractal medium
更新于2025-09-19 17:13:59
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[IEEE 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Munich, Germany (2019.6.23-2019.6.27)] 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - A Topologically Robust Formation of Broadband Vortices Propagating at the Speed of Light
摘要： We show that Flying Doughnuts, the exact propagating solutions of Maxwell equations in the form of single-cycle toroidal pulses have complex and robust fine topological structure of spectrally broadband vortices and extended areas of energy backflow. The study of the topology of electromagnetic waves provides insights into their fine-scale structure and can reveal information about their propagation dynamics. Typically, such studies are focused on vortices and polarization singularities of monochromatic light beams [1,2]. Here, we present a study of the singularities in the electromagnetic fields and Poynting vector of a single-cycle toroidal pulse, termed Flying Doughnut (FD). FD pulses are exact solutions of Maxwell's equations with known analytical form. Thus, such exotic forms of light are inherently stable under propagation and can be scrutinised at extraordinary level of detail. FDs propagate in free-space at the speed of light and their interactions with matter include non-trivial field transformations upon reflection from metallic and dielectric interfaces. The field configuration of the FDs is topologically similar to the toroidal dipolar excitations in matter, which allows to excite strong toroidal response and engage anapole modes (non-radiating configurations of electric and toroidal dipoles) in dielectric particles. It has been suggested that the longitudinal field components could be employed for the acceleration of charged particles.
关键词： toroidal pulses,anapole modes,broadband vortices,Maxwell equations,energy backflow,Poynting vector,Flying Doughnuts
更新于2025-09-16 10:30:52
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Time propagation of the coupled Maxwell and Kohn-Sham equations using the Riemann-Silberstein formalism
摘要： The coupled Maxwell and time-dependent Kohn-Sham equations are solved using the Riemann-Silberstein vectors to represent the electromagnetic fields. Momentum-space time propagation of the Riemann-Silberstein vectors are proposed and test calculations are presented to show the accuracy of the approach.
关键词： Kohn-Sham equations,Maxwell equations,momentum-space time propagation,electromagnetic fields,Riemann-Silberstein formalism
更新于2025-09-12 10:27:22
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Edge-plasmon assisted electro-optical modulator
摘要： An efficient electro-optical modulation has been demonstrated here by using an edge-plasmon mode specific for the hybrid plasmonic waveguide. Our approach addresses a major obstacle of the integrated microwave photonics caused by the polarization constraints of both active and passive components. In addition to subwavelength confinement, typical for surface plasmon polaritons, the edge-plasmon modes enable exact matching of the polarization requirements for silicon based input/output grating couplers, waveguides, and electro-optical modulators. A concept of the hybrid waveguide, implemented in a sandwichlike structure, implies a coupling of propagating plasmon modes with a waveguide mode. The vertically arranged sandwich includes a thin layer of epsilon-near-zero material (indium tin oxide) providing an efficient modulation at small length scales. Employed edge plasmons possess a mixed polarization state and can be excited with horizontally polarized waveguide modes. It allows the resulting modulator to work directly with efficient grating couplers and avoid using bulky and lossy polarization converters. A 3D optical model based on Maxwell equations combined with drift-diffusion semiconductor equations is developed. Numerically heavy computations involving the optimization of materials and geometry have been performed. Effective modes, stationary state field distribution, an extinction coefficient, optical losses, and charge transport properties are computed and analyzed. In addition to the polarization matching, the advantages of the proposed model include the compact planar geometry of the silicon waveguide, reduced active electric resistance R and a relatively simple design, attractive for experimental realization.
关键词： polarization constraints,hybrid plasmonic waveguide,drift-diffusion semiconductor equations,electro-optical modulation,edge-plasmon mode,indium tin oxide,epsilon-near-zero material,Maxwell equations
更新于2025-09-11 14:15:04
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Method of Integral Equations for the Three-Dimensional Problem of Wave Reflection from an Irregular Surface
摘要： The problem on the re?ection of the ?eld of a plane H-polarized three-dimensional electromagnetic wave from a perfectly conducting interface between media which contains a local perfectly conducting inhomogeneity is considered. To construct a numerical algorithm, the boundary value problem for the system of Maxwell equations in an in?nite domain with irregular boundary is reduced to a system of singular integral equations, which is solved by the approximation–collocation method. The elements of the resulting complex matrix are calculated by a specially developed algorithm. The solution of the system of singular integral equations is used to obtain an integral representation for the re?ected electromagnetic ?eld and computational formulas for the directional diagram of the re?ected electromagnetic ?eld in the far region.
关键词： directional diagram,integral equations,electromagnetic wave,Maxwell equations,numerical algorithm
更新于2025-09-11 14:15:04