Electromagnetic Wave Equation Research Articles

Momentary analysis of the electromagnetic radiation of gabbro rock under compressive stress

The phenomenon of electromagnetic radiation resulting from the application of pressure to rocks is caused by physical and chemical processes. Applying uniaxial pressure on gabbro rocks breaks the peroxy bonds and produces electron-hole pairs. These holes flow in the volume of gabbro rock under pressure and cause changes in electric charge, and as a result, generate variable electric and magnetic fields that vary with time and create electromagnetic signal. In this research work, by measuring the electric current of gabbro rock under pressure, its Fourier function is extracted, and the equations of the electric and magnetic fields of the sample and the energy and radiation equations of electromagnetic waves are calculated. Also, the relationship between these equations and the electric current equation is expressed. In addition, the amounts of absorption, transmission, and reflection of electromagnetic radiation of the rock can be analyzed during the application of pressure using the diagram of the radiant power of electromagnetic signal. The study of electromagnetic radiation can be useful for the development of electromagnetic radiation technology, can provide early warning about the risk of rock falls, and can reduce human injuries caused by the fall of places such as mines and tunnels.

Iterative addition of parallel non-local effects to full wave ICRF finite element models in axisymmetric tokamak plasmas

The current response of a hot magnetized plasma to a radio-frequency wave is non-local, turning the electromagnetic wave equation into an integro-differential equation. Non-local physics gives rise to wave physics and absorption processes not observed in local media. Furthermore, non-local physics alters wave propagation and absorption properties of the plasma. In this work, an iterative method that accounts for parallel non-local effects in 2D axisymmetric tokamak plasmas is developed, implemented, and verified. The iterative method is based on the finite element method and Fourier decomposition, with the advantage that this numerical scheme can describe non-local effects while using a high-fidelity antenna and wall representation, as well as limiting memory usage. The proposed method is implemented in the existing full wave solver FEMIC and applied to a minority heating scenario in ITER to quantify how parallel non-local physics affect wave propagation and dissipation in the ion cyclotron range of frequencies (ICRF). The effects are then compared to a reduced local plane wave model, both verifying the physics implemented in the model, as well as estimating how well a local plane wave approximation performs in scenarios with high single pass damping. Finally, the new version of FEMIC is benchmarked against the ICRF code TORIC.

Оптимизация оптического поглощения в спинтронных терагерцовых излучателях с использованием брэгговских отражателей

An optimized design of a spintronic terahertz emitter has been developed, based on a bilayer Co/Pt structure with an integrated distributed Bragg reflector. The incorporation of the Bragg mirror between the Co/Pt structure and the silicon substrate enhances optical absorption in the ferromagnetic layer, thereby amplifying spin current generation and, consequently, THz signal. A model was developed for calculating the optical absorption in the ferromagnetic layer of the spintronic emitter, taking into account the parameters of the Bragg mirror (layer thicknesses, period) based on the superlattice structure [TiO2/SiO2]N. This model is grounded on the solution of Maxwell's equations for electromagnetic waves using the COMSOL Multiphysics software. The effect of anti-reflective dielectric coatings on the level of optical absorption in the ferromagnetic layer was also analyzed. The study confirmed that using the optimized Bragg mirror is sufficient for achieving optimal absorption.

The electronic and electromagnetic Dirac equations

Maxwell’s equations and the Dirac equation are the first-order differential relativistic wave equation for electromagnetic waves and electronic waves respectively. Hence, there is a notable similarity between these two wave equations, which has been widely researched since the Dirac equation was proposed. In this paper, we show that the Maxwell equations can be written in an exact form of the Dirac equation by representing the four Dirac operators with 8×8 matrices. Unlike the ordinary 4×4 Dirac equation, both spin–1/2 and spin–1 operators can be derived from the 8×8 Dirac equation, manifesting that the 8×8 Dirac equation is able to describe both electrons and photons. As a result of the restrictions that the electromagnetic wave is a transverse wave, the photon is a spin–1 particle. The four–current in the Maxwell equations and the mass in the electronic Dirac equation also force the electromagnetic field to transform differently to the electronic field. We use this 8×8 representation to find that the Zitterbewegung of the photon is actually the oscillatory part of the Poynting vector, often neglected upon time averaging.

Electromagnetic duality and discrete symmetries for dyon in macroscopic media

This paper investigates discrete symmetries for dyon and the invariance of Maxwell’s field equations in the macroscopic media (material medium). Using advanced mathematical approaches, the paper derived electromagnetic duality and a unique form of Poynting theorem for dyon in macroscopic media. Here, we demonstrate that the combination of parity [Formula: see text], charge conjugation [Formula: see text], and time reversal [Formula: see text] symmetry: [Formula: see text], is an exact symmetry for dyon in macroscopic media. Furthermore, a comprehensive analysis of the electromagnetic wave equation for dyons in conducting media is also derived. These findings contribute significantly to the understanding of dyon behavior in electromagnetic fields.

Physics‐Informed Machine Learning for Inverse Design of Optical Metamaterials

Optical metamaterials manipulate light through various confinement and scattering processes, offering unique advantages like high performance, small form factor and easy integration with semiconductor devices. However, designing metasurfaces with suitable optical responses for complex metamaterial systems remains challenging due to the exponentially growing computation cost and the ill‐posed nature of inverse problems. To expedite the computation for the inverse design of metasurfaces, a physics‐informed deep learning (DL) framework is used. A tandem DL architecture with physics‐based learning is used to select designs that are scientifically consistent, have low error in design prediction, and accurate reconstruction of optical responses. The authors focus on the inverse design of a representative plasmonic device and consider the prediction of design for the optical response of a single wavelength incident or a spectrum of wavelength in the visible light range. The physics‐based constraint is derived from solving the electromagnetic wave equations for a simplified homogenized model. The model converges with an accuracy up to 97% for inverse design prediction with the optical response for the visible light spectrum as input, and up to 96% for optical response of single wavelength of light as input, with optical response reconstruction accuracy of 99%.

Understanding Frequency Response of Induction Motor Winding through Electromagnetic Wave Equations

Understanding Frequency Response of Induction Motor Winding through Electromagnetic Wave Equations

Dispersion Equations of Transverse Electromagnetic Waves Narrowly Localized Near the Interface between the Media with Different Graded-Index Profiles

"Combinations of three pairs of contacting media with linear, exponential, and parabolic profiles of dielectric permittivity are described theoretically. Three new types of narrowly localized transverse electric waves propagating along the interfaces between the considered graded-index media are found. The exact dispersion equations for each type of the waves determining the effective refractive index in dependence on optical and geometric characteristics are obtained. The influence of the thicknesses of the graded-index layers on dispersion equation solutions is analyzed. It is found that the effective refractive index increases with an increase in the thickness of the gradedindex layers in all considered combinations of the contacting media. The thickness of the parabolic graded-index profile has the least significant effect on the effective refractive index, compared to the linear and exponential ones. "

EM wave propagation within plasma-filled rectangular waveguide using fractional space and LFD

This paper aims to investigate the propagation of the electromagnetic (EM) within the rectangular waveguide that is filled with plasma. A rapid Cherenkov free electron laser ( C-FEL) beam was injected into the plasma to excite its natural oscillations and, therefore, an EM wave was generated. We focused on TM-mode propagation through this waveguide. Exact solutions of the EM wave equation have been found using both the Laplacian operator in the fractional D-dimensional space and the local fractional derivative (LFD). The fractional solutions have been converted into classical results to simulate the usual behavior of the waves. It has been found that the well-known Bessel, Neumann, and Mittage–Leffler functions are observed and their propagation is directly proportional to fractional parameters.

Characterization of Excitation Effects and Data Interpretation of Combined Time-Domain Multiwaveform Transmission Currents

With the development of electronic technology, time-domain electromagnetic (TDEM) transmitters are now capable of emitting various waveforms such as trapezoidal, triangular, and semi-sinusoidal waveforms, as well as their combinations. However, the application of multi-waveform combination detection methods is still immature, and modeling methods are required to analyze the characteristics of different waveforms and complete data interpretation. Based on the Crank-Nicolson finite difference time-domain (CN-FDTD) method for discretizing the electromagnetic wave equations, the current waveform can be converted into current surface density for source-included calculations, enabling high-precision modeling of the responses to different current waveforms. The responses to multiple transmission current waveforms were compared and analyzed using various models, and the results showed that selecting targeted excitation parameters based on the characteristics of the target can improve detection sensitivity. We applied the multi-waveform combination detection method to the actual exploration in the field, obtained the pure secondary field response by subtracting the primary field of the actual current waveform from the measured data, converted the responses of different transmission current waveforms into step wave responses by deconvolution method, and performed resistivity imaging. The results of modeling and data interpretation demonstrate the effectiveness of the multi-waveform combination detection method in improving geological exploration accuracy, and promoted the development of fine-scale geophysical exploration.

Curved spacetime as a dispersive multiferroic medium for an electromagnetic wave: Polarization and magnetization vectors in the Schwarzschild spacetime

We study one of the interesting properties of the electromagnetic wave propagation in the Schwarzschild background spacetime in the framework of general relativity (GR). The electromagnetic wave equation has been derived from vacuum general relativistic Maxwell’s equations. It is shown that the solutions for the electromagnetic field can be expanded in the spherical harmonic functions and all components of the electromagnetic fields can be expressed in terms of two radial profile functions. These radial profile functions can be expressed in terms of the confluent Heun function. The calculated behavior of the electric and magnetic susceptibilities near the event horizon appears to be similar to the susceptibilities of multiferroic materials near phase transition. The Curie temperature of this phase transition appears to coincide with the Hawking temperature.

Electromagnetic Waves in Cosmological Spacetime

We consider the propagation of electromagnetic waves in the Friedmann–Lemaître–Robertson–Walker metric. The exact solutions for plane and spherical wave are written down. The corresponding redshift, amplitude change, and dispersion are discussed. We also speculate about the connection of the electromagnetic wave equation to the Proca equation and its significance for the early Universe.

Deriving an Electric Wave Equation from Weber’s Electrodynamics

Weber’s electrodynamics presents an alternative theory to the widely accepted Maxwell–Lorentz electromagnetism. It is founded on the concept of direct action between particles, and has recently gained some momentum through theoretical and experimental advancements. However, a major criticism remains: the lack of a comprehensive electromagnetic wave equation for free space. Our motivation in this research article is to address this criticism, in some measure, by deriving an electric wave equation from Weber’s electrodynamics based on the axiom of vacuum polarization. Although this assumption has limited experimental evidence and its validity remains a topic of debate among researchers, it has been shown to be useful in the calculation of various quantum mechanical phenomena. Based on this concept, and beginning with Weber’s force, we derive an expression which resembles the familiar electric field wave equation derived from Maxwell’s equations.

Modulation of electromagnetic waves in a relativistic degenerate plasma at finite temperature

We study the modulational instability (MI) of a linearly polarized electromagnetic (EM) wave envelope in an intermediate regime of relativistic degenerate plasmas at a finite temperature (T≠0) where the thermal energy (KBT) and the rest-mass energy (mec2) of electrons do not differ significantly, i.e., βe≡KBT/mec2≲ (or ≳) 1, but the Fermi energy (KBTF) and the chemical potential energy (μe) of electrons are still a bit higher than the thermal energy, i.e., TF>T and ξe=μe/KBT≳1. Starting from a set of relativistic fluid equations for degenerate electrons at finite temperature, coupled to the EM wave equation and using the multiple scale perturbation expansion scheme, a one-dimensional nonlinear Schödinger (NLS) equation is derived, which describes the evolution of slowly varying amplitudes of EM wave envelopes. Then, we study the MI of the latter in two different regimes, namely, βe<1 and βe>1. Like unmagnetized classical cold plasmas, the modulated EM envelope is always unstable in the region βe>4. However, for βe≲1 and 1<βe<4, the wave can be stable or unstable depending on the values of the EM wave frequency, ω, and the parameter ξe. We also obtain the instability growth rate for the modulated wave and find a significant reduction by increasing the values of either βe or ξe. Finally, we present the profiles of the traveling EM waves in the form of bright (envelope pulses) and dark (voids) solitons, as well as the profiles (other than traveling waves) of the Kuznetsov–Ma breather, the Akhmediev breather, and the Peregrine solitons as EM rogue (freak) waves, and discuss their characteristics in the regimes of βe≲1 and βe>1.

On Nanobubble Dynamics under an Oscillating Pressure Field during Salting-out Effects and Its DLVO Potential

We have investigated the origin, stability, and nanobubble dynamics under an oscillating pressure field followed by the salting-out effects. The higher solubility ratio (salting-out parameter) of the dissolved gases and pure solvent nucleates nanobubbles during the salting-out effect, and the oscillating pressure field enhances the nanobubble density further as solubility varies linearly with gas pressure by Henry's law. A novel method for refractive index estimation is developed to differentiate nanobubbles and nanoparticles based on the scattering intensity of light. The electromagnetic wave equations have been numerically solved and compared with the Mie scattering theory. The scattering cross-section of the nanobubbles was estimated to be smaller than the nanoparticles. The DLVO potentials of the nanobubbles predict the stable colloidal system. The zeta potential of nanobubbles varied by generating nanobubbles in different salt solutions, and it is characterized by particle tracking, dynamic light scattering, and cryo-TEM. The size of nanobubbles in salt solutions was reported to be higher than that in pure water. The novel mechanical stability model is proposed by considering both ionic cloud and electrostatic pressure at the charged interface. The ionic cloud pressure is derived by electric flux balance, and it is found to be twice the electrostatic pressure. The mechanical stability model for a single nanobubble predicts the existence of stable nanobubbles in the stability map.

Accelerating magnetotelluric forward modeling with deep learning: Conv-BiLSTM and D-LinkNet

Magnetotelluric forward modeling is important for exploring underground electromagnetic anomalies. Although directly solving the electromagnetic wave equation has high accuracy, its computational cost is usually unaffordable for large-scale models. A neural network (NN) can increase the computation of the magnetotelluric forward modeling; however, its numerical accuracy is limited owing to the use of a simple network structure and small-scale training data sets. We have increased the computational efficiency of the magnetotelluric forward modeling by deep learning based on cyclic NN and full convolution NN models. First, we have extracted the basic characteristics of the 2D-magnetotelluric forward modeling, which were important for selecting and optimizing the network. Then, we have developed two forward network models: convolutional bidirectional long short-term memory (Conv-BiLSTM) and LinkNet with pretrained encoder and dilated convolution (D-LinkNet). Next, we have constructed data sets of large-scale multiple anomalies. Finally, we have tested our models using various examples. Existing methods only consider a single anomaly and have low accuracy; in contrast, our methods can handle multianomaly models because they have strong generalization, even though the training is based on models with two or three anomalies. Numerical experiments find that the average accuracy of the Conv-BiLSTM and D-LinkNet forward network models was 87.5% and 95.3%, respectively. Compared with D-LinkNet, the Conv-BiLSTM network model has lower accuracy but higher computational efficiency. Our deep-learning schemes can significantly reduce the computational burdens of the magnetotelluric forward modeling, and thus allow us to perform swift inversions of multianomaly models.

Mathematical modeling of electromagnetic radiations incident on a symmetric slit with Leontovich conditions in an-isotropic medium

This article presents the rigorous analysis of the an-isotropic medium affecting the diffraction process of EM-signals of high frequency by a symmetric slit of finite width. Leontovich boundary conditions for the present model are taken into consideration to show the existence of impedance. The ionosphere having non-thermal plasma contains the geomagnetic field which turns the medium into an an-isotropic medium. The well-known Helmholtz equation for electromagnetic (EM) waves is formulated through Maxwell’s equations with consideration of dielectric permittivity tensor for an an-isotropic medium due to non-thermal plasma. The Fourier transform is employed for the equations formulated for this model and then a pair of Wiener–Hopf equations (coupled form) is devised. These Wiener–Hopf equations are then tackled and an asymptotic method is used to achieve the target. Results for the isotropic medium can be obtained by assigning the values to permittivity elements controlling the medium. Graphical results are sketched for better visualization of the separated field for the an-isotropic medium and isotropic medium as well.

On the Majorana representation of the optical Dirac equation

We consider the representations of the optical Dirac equation, especially ones where the Hamiltonian is purely real-valued. This is equivalent, for Maxwell’s equations, to the Majorana representation of the massless Dirac (Weyl) equation. We draw analogies between the Dirac, chiral and Majorana representations of the Dirac and optical Dirac equations, and derive two new optical Majorana representations. Just as the Dirac and chiral representations are related to optical spin and helicity states, these Majorana representations of the optical Dirac equation are associated with the linear polarization of light. This provides a means to compare electron and electromagnetic wave equations in the context of classical field theory.

Studies on Maxwell Equations, Electromagnetic Wave Equations and Functions in Cosmological Special Relativity Theory

Studies on Maxwell Equations, Electromagnetic Wave Equations and Functions in Cosmological Special Relativity Theory

Dispersion equation for electromagnetic waves in a Dicke system

The self-organization process in a Dicke model is studied with taking into account electromagnetic field states. The interaction between two-level emitters provided by the field results in generating field waves of increasing amplitudes. The picture of superradiance development in a prolonged system can be described in terms of electromagnetic field in continuous medium formed by emitters. The generalized induction in the Dicke system is introduced on the basis of the material equation for charge current obtained using the Bogolyubov reduced description method. The dispersion equation for waves and its solutions are derived and analyzed. Non-singular expressions for material coefficients are proposed and used for calculating the wave characteristics.