Plane Electromagnetic Wave Research Articles

Calculation of single-layer dielectric coatings for antireflection 
 in a given range of angles of incidence

In this work, the problem of antireflection a single-layer magneto-dielectric system is formulated when a plane electromagnetic wave passes through it in the range of angles of incidence, and necessary and sufficient conditions for the existence of solutions to this problem are obtained

Vector-Field Visualization of the Total Reflection of the EM Wave by an SRR Structure at the Magnetic Resonance

Metamaterials are artificially structured composite media with a unique electromagnetic (EM) response that is absent from naturally occurring materials, which appears counterintuitive and aggravates traditional difficulties in perceiving the behavior of EM waves. The aim of this study was to better understand the interaction of EM waves with metamaterials by virtual visualizing the accompanying physical phenomena. Over the years, virtual visualization of EM wave interactions with metamaterials has proven to be a powerful tool for explaining many phenomena that occur in metamaterials. In this study, we performed virtual visualization of the interaction of an EM plane wave with a split-ring resonator (SRR) metamaterial structure, employing CST Studio software for modeling and comprehensive simulations of high-frequency EM fields of 3D objects. The SRR structure was designed to have its magnetic resonance at the frequency f = 23.69 GHz, which is of interest for antennas supporting wireless microwave point-to-point communication systems (e.g., in satellite systems). Our numerical calculations of the coefficients of absorption, reflection, and transmission of the EM plane wave incident on the SRR structure showed that the SRR structure totally reflected the plane EM wave at the magnetic resonance frequency. Therefore, we focused our research on checking whether the results of numerical calculations could be confirmed by visualizing the total reflection phenomenon on the SRR structure. The performed vector-field visualization resulted in 2D vector maps of the electric and magnetic fields around the SRR structure during the wave period, which demonstrated the existence of characteristic features of the total reflection phenomenon when the EM plane interacted with the studied SRR, i.e., no EM field behind the SRR structure and the standing electric and magnetic waves before the SRR structure, thus, confirming the numerical calculations visually. For deeper understanding the interaction of the EM plane wave with the SRR structure of reflection characteristics at the magnetic resonance frequency f = 23.69 GH, we also visualized the SRR structure response at the frequency f = 21 GHz, i.e., at the so-called detuned frequency. As expected, at the detuned frequency, the SRR structure lost its metamaterial properties and the obtained 2D vector maps of the electric and magnetic fields around the SRR structure during the wave period showed the transmitted EM wave behind the SRR structure and no EM (fully) standing waves before the SRR structure. The visualizations presented in this study are both unique educational presentations to help understand the interaction of EM plane waves with the SRR structure of reflection characteristics at the magnetic resonance and detuned frequencies.

ОПЕРАТОРНИЙ МЕТОД В ЗАДАЧІ ПРО ДИФРАКЦІЮ ПЛОСКОЇ ЕЛЕКТРОМАГНІТНОЇ ХВИЛІ НА КІЛЬЦЕВІЙ ЩІЛИНІ В ПЛОЩИНІ АБО НА КІЛЬЦІ

Purpose: The problem of a plane electromagnetic wave diffraction by an annular slot in the perfectly conducting zero thickness plane is considered. As a dual problem, the problem of diffraction by a perfectly conducting zero thickness ring is also considered. The paper aims at developing the operator method for the axially symmetric structures placed in free space. Design/methodology/approach: The problem is considered in the spectral domain. The scattered field is expressed in terms of unknown Fourier amplitudes (spectral functions). The annular slot is given as a unity of two simple discontinuities, namely of a disk and a circular hole in the plane, which interact with each other. The Fourier amplitude of the scattered field is sought as a sum of two amplitudes, the Fourier amplitude of the field of currents on the disk and Fourier amplitude of the field of currents on the perfectly conducting plane with circular hole. The operator equations are written for these amplitudes, which take into account the electromagnetic coupling of the disk and the hole in the plane. The equations use the reflection operators of a single isolated disk and a single hole in the plane. They are supposed to be known and can be obtained for example by the method of moments.The reflection operators can have singularities. After transformations, the equations are obtained, which are equivalent to the Fredholm integral equations of second kind and they can be solved numerically. Findings: The operator equations relative to the Fourier amplitudes of the field scattered by the discussed structure are obtained. The far zone scattered field for an annular slot and a ring for different values of parameters are studied. Conclusions: The rigorous solution of the problem of the electromagnetic wave diffraction by an annular slot in the plane and by a circular ring is obtained. The problem is reduced to the Fredholm integral equations of second kind. The far field distribution for different parameters is studied. The developed approach is an effective instrument for a number of problems of antenna technique to be solved. Key words: circular hole; disk; annular slot; ring; operator method; diffraction

The structure of the curvature tensor of plane gravitational waves

Plane gravitational waves in the Riemann space of General Relativity is considered. The criterion of plane gravitational waves is used based on the analogy between plane gravitational and electromagnetic waves. The Theorem is proved that the action of the Lie derivative on the plane wave curvature 2-form in the direction of the vector generating the invariance group of this wave in the Riemann space is equal to zero. It is justified that the gravitational waves can be used to transmit information in the Riemann space.

An impedance approach to the response of matter

At the dawn of the research on waveguides the propagation by electrical conduction through transmission lines was compared with the general transmission theory of plane electromagnetic waves. After the invention of lasers we wonder whether the impedance concept can allow a seamless shift from the geometric rendering of received electromagnetic signals to the understanding of simple arguments on power transfer. Perhaps, the impedance concept could help noticing the occurrence of radiation-matter interactions and give hints as to how some phenomena could be enhanced by exposing matter to specific non-ionizing radiations.

Phase Statistics of Light/Photonic Wave Reflected from One-Dimensional Optical Disordered Media and Its Effects on Light Transport Properties

Light wave reflection intensity from optical disordered media is associated with its phase, and the phase statistics influence the reflection statistics. A detailed numerical study is reported for the statistics of the reflection coefficient |R(L)|2 and its associated phase θ for plane electromagnetic waves reflected from one dimensional Gaussian white-noise optical disordered media, ranging from weak to strong disordered regimes. The full Fokker–Planck (FP) equation for the joint probability distribution in the |R(L)|2−(θ) space is simulated numerically for varying length and disorder strength of the sample; and the statistical optical transport properties are calculated. Results show the parameter regimes of the validation of the random phase approximations (RPA) or uniform phase distribution, within the Born approximation, as well as the contribution of the phase statistics to the different reflections, averaging from nonuniform phase distribution. This constitutes a complete solution for the reflection phase statistics and its effect on light transport properties in a 1D Gaussian white-noise disordered optical potential.

Modified Theory of Physical Optics Approach to Diffraction by an Interface between PEMC and Absorbing Half-Planes

The scattering of electromagnetic plane waves by an interface, located between perfect electromagnetic conductor and absorbing half-planes is investigated. The perfect electromagnetic conductor half-plane is divided into perfect electric conductor and perfect magnetic conductor half-screens. The same decomposition is done for the absorbing surface. Then four separate geometries are defined according to this approach. The scattered fields by the four sub-problems are obtained with the aid of the modified theory of physical optics. The resultant scattering integrals are combined in a single expression by using key formulas, defined for the perfect electromagnetic conductor and absorbing surfaces. The scattering integral is asymptotically evaluated for large values of the wave-number and the diffracted and geometric optics fields are obtained. The behaviors of the derived field expressions are analyzed numerically.

Morphology-Dependent Resonances in Two Concentric Spheres with Variable Refractive Index in the Outer Layer: Analytic Solutions

In many applications constant or piecewise constant refractive index profiles are used to study the scattering of plane electromagnetic waves by a spherical object. When the structured media has variable refractive indices, this is more of a challenge. In this paper, we investigate the morphology dependent resonances for the scattering of electromagnetic waves from two concentric spheres when the outer shell has a variable refractive index. The resonance analysis is applied to the general solutions of the radial Debye potential for both transverse magnetic and transverse electric modes. Finally, the analytic conditions to determine the resonance locations for this system are derived in the closed form of both modes. Our numerical results are provided with discussion.

A 4-Bit Multistate Frequency-Selective Surface With Dual-Band Multifunction Response

In this letter, a novel 4 b multistate frequency-selective surface is proposed. Four p-i-n diodes are used to maneuver multifunction behavior of the structure with seven different functional states. The 4 b binary state operations 0000, 1100, 0011, and 1111 offer transverse electric (TE)/transverse magnetic (TM) waves both transmit, TE transmit/TM shield, TM transmit/TE shield, and TE/TM both shield, respectively, at 2 GHz frequency. The passband at 2 GHz frequency has <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$-\text{10}$</tex-math></inline-formula> dB fractional bandwidth of 117%. The binary states 1101 and 1110 are symmetric, which select the TE wave transmit/TM wave shield to the passband at 3.45 GHz frequency with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$-\text{10}$</tex-math></inline-formula> dB fractional bandwidth of 49%, whereas binary states 1011 and 0111 allow the TM wave to transmit at 3.45 GHz and shield the TE wave. The four symmetric binary states 0101, 0110, 1010, and 1001 provide transmission band at 3.45 GHz frequency for dual-polarized plane wave incidence. The transmission of both the passbands can be shielded by selecting the binary state equal to 1111. An equal circuit model is used to elaborate the contribution of different passive structural elements in terms of lumped components. A prototype of the structure is fabricated, and transmission coefficients for different states at normal and oblique incidence of the electromagnetic plane wave are measured, which verifies the simulated responses of the structure.

Comparison of numerical integration methods for calculating diffraction of a plane electromagnetic wave by a rectangular aperture

We discuss features of the calculation of a Fraunhofer integral by traditional quadrature numerical integration methods and a special collocation Levin method when calculating the diffraction of a plane electromagnetic wave by a rectangular aperture. For the quadrature numerical integration methods, a criterion for the assessment of the integration step is derived depending on the screen size and required calculation accuracy. Advantages of the use of the special collocation Levin method in comparison with the traditional quadrature numerical integration methods are shown.

Reflection and transmission of electromagnetic pulses at a planar dielectric interface: Theory and quantum lattice simulations

There is considerable interest in the application of quantum information science to advance computations in plasma physics. A particular point of curiosity is whether it is possible to take advantage of quantum computers to speed up numerical simulations relative to conventional computers. Many of the topics in fusion plasma physics are classical in nature. In order to implement them on quantum computers, it will require couching a classical problem in the language of quantum mechanics. Electromagnetic waves are routinely used in fusion experiments to heat a plasma or to generate currents in the plasma. The propagation of electromagnetic waves is described by Maxwell equations with an appropriate description of the plasma as a dielectric medium. Before advancing to the tensor dielectric of a magnetized plasma, this paper considers electromagnetic wave propagation in a one-dimensional inhomogeneous scalar dielectric. The classic theory of scattering of plane electromagnetic waves at a planar interface, separating two different dielectric media, leads to Fresnel equations for reflection and transmission coefficients. In contrast to plane waves, this paper is on the reflection and transmission of a spatially confined electromagnetic pulse. Following an analytical formulation for the scattering of a Gaussian pulse, it is deduced that the maximum transmission coefficient for a pulse is n2/n1 times that for a plane wave; the incident and transmitted pulses propagate in dielectric media with refractive indices n1 and n2, respectively. The analytical theory is complemented by numerical simulations using a quantum lattice algorithm for Maxwell equations. The algorithm, based on the Riemann–Silberstein–Weber representation of the electromagnetic fields and expressed in terms of qubits, is an interleaved sequence of entangling operators at each lattice site and unitary streaming operators, which transmit information from one site to an adjacent lattice site. Besides substantiating results from the theory for Gaussian pulses, numerical simulations show their validity for non-Gaussian pulses. Apart from their time-asymptotic forms, the simulations display an interplay between the incident, reflected, and transmitted pulses in the vicinity of the transition region between two dielectric media.

Deep learning-based design of broadband GHz complex and random metasurfaces

We are interested in exploring the limit in using deep learning (DL) to study the electromagnetic (EM) response for complex and random metasurfaces, without any specific applications in mind. For simplicity, we focus on a simple pure reflection problem of a broadband EM plane wave incident normally on such complex metasurfaces in the frequency regime of 2–12 GHz. In doing so, we create a DL-based framework called the metasurface design deep convolutional neural network (MSDCNN) for both forward and inverse designs of three different classes of complex metasurfaces: (a) arbitrary connecting polygons, (b) basic pattern combination, and (c) fully random binary patterns. The performance of each metasurface is evaluated and cross-benchmarked. Dependent on the type of complex metasurfaces, sample size, and DL algorithms used, the MSDCNN is able to provide good agreement and can be a faster design tool for complex metasurfaces than the traditional full-wave EM simulation methods. However, no single universal deep convolutional neural network model can work well for all metasurface classes based on detailed statistical analysis (such as mean, variance, kurtosis, and mean-squared error). Our findings report important information on the advantages and limitations of current DL models in designing these ultimately complex metasurfaces.

Degeneracy of light scattering and absorption by a single nanowire

We theoretically and numerically prove that under an electromagnetic plane wave with linear polarization incident normally to a single nanowire, there exists a power diagram that could indicate scattering properties for any system configurations, material parameters, and operating wavelength. We demonstrate the distinct power distribution boundary in absorption, scattering, and extinction for a generalized nanowire with any partial wave modes dominant. In the boundary, each dominant scattering coefficients remain constant, and its energy performance would display superabsorbers or superscatterers. Interestingly, for a system with larger partial wave modes dominant, the occupied domain in the power diagram could completely cover that with lower ones. Hence, a system with different levels of partial wave modes can display the same power results, reflecting the degeneracy. This degenerate property could release more degrees of freedom in design of energy harvesting devices and sensors. We demonstrate several systems based on realistic materials to support our findings.

Scattering of a finite length anisotropic medium cylinder

Based on the conservation of electromagnetic energy, a theoretical model of equating the electromagnetic anisotropic medium to the electromagnetic isotropic medium is established. The correctness of this proposed model is verified, and how to use the model is presented. The equivalent permittivity of an anisotropic medium cylinder is researched by using the proposed model. It is found that the equivalent permittivity increases with the increase of the volume of the cylinder, and the electromagnetic mechanism of this phenomenon is presented. The analytical expression of the scattered field of an anisotropic cylinder being irradiated by a plane electromagnetic wave with a general direction is studied. It is found that the geometrical size of the finite length and the angle between the electromagnetic wave propagation direction and the symmetry axis of the cylinder have a great effect on the scattering of the anisotropic medium cylinder.

Understanding energy propagation during reflection of an evanescent electromagnetic wave

Reflection of plane electromagnetic waves at a planar surface separating two media is typically discussed at length in undergraduate texts. However, a similar analysis for the case of evanescent electromagnetic waves, although illustrative and interesting, is rarely discussed. In this paper, we present such an analysis for the reflection of an evanescent wave at a plane dielectric surface and highlight the important conceptual difference in the energy flow for this case compared to that of a plane wave. It is generally emphasized that an evanescent wave does not propagate energy away from the surface emanating these waves. We show that in the case of an evanescent wave, the pair of incident and reflected waves together propagates energy if the imaginary part of the reflectivity is non-zero. Further, the real part of the reflectivity can be greater than unity in the case of an evanescent wave without violating energy conservation. Connection of these properties to the existence of surface modes, Čerenkov radiation, and a quantum analogue are elucidated in the paper.

Matrix Exponential Method Exploiting Field-Splitting Technique for Calculating Electromagnetic Response of Rotating Bodies: 2-D Configuration

We put forward a numerical method, which the matrix exponential and the field-splitting technique underlie, to solve the problem of the interaction between electromagnetic (EM) wave and rectangular rotating bodies. In such a method, the general results are obtainable in the time domain within the laboratory frame. The detail of deriving the discretized governing equation of EM fields in each computational cell jointly occupied by the rotating and surrounding media is given. A numerical test concerning the modulation effect of a rotating square dielectric on the incident EM plane wave is carried out for validation. Furthermore, the proposed method is applied to a rotating system comprising multiple separate bodies. Without loss of generality, a 2-D case is solely stressed.

A Novel Processing for CNT-Reinforced Mg-Matrix Laminated Composites to Enhance the Electromagnetic Shielding Property

The microstructure, electrical conductivity, and electromagnetic interference (EMI) shielding effectiveness (SE) of CNTs/Mg Matrix composites prepared by accumulative roll bonding (ARB) were systematically investigated to understand the effects of CNTs on the electromagnetic interference shielding effectiveness property of magnesium. A model based on the shielding of the electromagnetic plane wave was used to theoretically discuss the EMI shielding mechanisms of ARB-processed composites. The experimental results indicated that the methods were feasible to prepare laminated composites. The SE of the material increased gradually with the increase of electrophoretic deposition time. When the electrophoretic deposition time reached 8 min, the value of SE remained 87–95 dB in the frequency range of 8.2–12.4 GHz. The increase in SE was mainly attributed to the improvement in the reflection and multiple reflection losses of incident electromagnetic wave due to the increased amounts of CNTs and interfaces. The methods provided an efficient strategy to produce laminated metal matrix composites with high electromagnetic shielding properties.

ANIMATION OF PLANE ELECTROMAGNETIC WAVES IN VACUUM USING WINPLOT SOFTWARE

In this work, the Winplot software was used to animate plane electromagnetic waves in a vacuum. The target audience was a class of 18 undergraduates in Physics and was applied at the Federal University of Acre, campus Rio Branco, in Brazil. The activity was carried out in a computer lab and conducted through a script with detailed instructions. The results were satisfactory, where participants got more than 60.0% right of four of the six investigative questions. In evaluating the activity, 88.9% considered it a good method to visualize the propagation of electromagnetic waves and 77.0% classified the activity as excellent or good. The application of the activity allowed a dynamic view of the propagation of plane electromagnetic waves in a vacuum, which could contribute to the teaching of such content.

Analysis of plasma sheath propagation attenuation based on ray tracing

AbstractBased on the complex Snell's law of lossy media, a ray tracing method is proposed to study the propagation attenuation characteristics of electromagnetic (EM) waves in plasma sheaths. The plasma sheath is modelled as layered media. This method considers the complex ray characteristics of inhomogeneous plane EM waves, tracks the propagation rays of EM waves in each layer of media, and calculates the propagation attenuation of EM waves in each layer of media according to the propagation direction of the complex rays. The attenuation during numerical cumulative propagation is the total attenuation of EM waves through the plasma sheath. By comparing the results with that obtained from the WKB method, the accuracy of the ray tracing algorithm is proved. The results of the propagation attenuation of a blunt cone model are calculated by the proposed method, and the effects of different parameters on the EM wave propagation attenuation in the plasma sheath are analysed at different heights, velocities, incident angles, and incident positions. Studying the propagation characteristics of EM waves in the plasma sheath is of importance in application for radar target tracking, blackout communication, and other issues.

Vacuum Birefringence in a Field of a Plane Electromagnetic Wave

Vacuum Birefringence in a Field of a Plane Electromagnetic Wave