Problem Of Electromagnetic Wave Diffraction Research Articles

Influence of spatial dispersion in metal on optical characteristics of a magnetoplasmonic layered nanoparticle cluster

In the current work, the diffraction problem of a plane electromagnetic wave on a cluster of two layered nanocylinders consisting of a magnetoplasmonic core and a gold shell is considered. The arising effects of spatial dispersion in the gold shell are taken into account within the framework of the generalized nonlocal optical response theory. Based on the discrete source method scheme, an analysis of the influence of the mutual arrangement of particles, their deformation, and the effect of spatial dispersion on the behaviour of the absorption cross-section and the near-field enhancement factor is conducted. It is shown that the position of the plasmon resonance can be shifted to the transparency region of biological tissues by varying the distance between particles and the core material. It has been established that taking into account spatial dispersion in the gold shell leads to a decrease in intensity and a slight shift of the plasmon resonance position to the shortwave region, without going beyond the tissue transparency region.

ELECTRODYNAMIC ALGORITHM FOR CALCULATING AN ANTENNA ARRAY BASED ON AN INTEGRAL REPRESENTATION FOR A COMMON REGION FIELD

The article is devoted to the study of a new approach in the integral equation method. The solution of the electrodynamic problem is carried out based on conditional selection of the common region in the entire area of electromagnetic field definition. In our previous publications, we proposed an integral equation method based on the selection of a penetrating region for solving the problem of electromagnetic wave diffraction on a periodic structure. The legality of using the proposed approach and its equivalence with the previously proposed approach are shown. In this article, the calculation of an infinite antenna array scanning in the H-plane is carried out. The numerical convergence of the proposed approach for reflection coefficients R10 with increasing order of truncation of the system of linear algebraic equations was studied. It was found that the modulus of the reflection coefficient coincides with the exact solution at M = 1 and subsequently does not change with the growth of M. While the phase of the reflection coefficient changes with the growth of M and when M˃11, the difference between the phase value of the exact solution and the calculated value is less than 1%. That is, for the case of scanning in the H-plane, good convergence of the problem solution was obtained for all scanning angles. The aim of the work is to show that for a certain class of problems of applied electrodynamics, it is possible to apply the integral equation method based on the selection of a common region. The methodology consists in the conditional allocation of a common region in the entire area of electromagnetic field determination and the application of the integral equation method. The scientific novelty is that we have shown the correctness of using a new approach based on the selection of the field of the common region for the calculation of periodic structures in the H-plane. The conclusions can be formulated as follows. It is shown that two approaches can be used to calculate the antenna array in the H-plane: the first based on the selection of the integral representation for the full field of the penetrating region, the second based on the selection of the integral representation for the full field of the common region.

Refinement of the Heuristic Solution for the Problem of TE-Polarized Electromagnetic Wave Diffraction on a Half-Plane with Two-Sided Impedance Boundary Conditions

A technique for obtaining refined heuristic solutions for problems with electromagnetic wave diffraction by scatterers with non-ideal boundary conditions is proposed. Based on the method of fundamental components for the problem of TE-polarized wave diffraction on a “semitransparent” half-plane with two-sided impedance boundary conditions, an improved heuristic solution for the scattered field is obtained by replacing the primary heuristic formula. A quantitative and qualitative assessment of the accuracy of the heuristic relationship is carried out as well as a physical interpretation of the rigorous solution based upon them. A classification of heuristic solutions is proposed according to the purpose of their application in practical problems.

A technique for obtaining analytical heuristic solutions in problems of diffraction on two-dimensional semi-infinite objects with non-ideal boundary conditions

A technique for obtaining analytical heuristic solutions in two-dimensional problems of electromagnetic wave diffraction on semi-infinite objects with non-ideal boundary conditions is proposed. The essence of the technique is that the values of the phenomenological coefficients contained in the heuristic formulas are found numerically, minimizing the discrepancy between the heuristic solution and the verification one. For the case of diffraction on a half-plane with two-sided impedance boundary conditions, an additional analytical solution of the corresponding problem is obtained. It is based on the requirement that the reciprocity principle be satisfied. The coincidence of the phenomenological adjusting coefficients found numerically for the same problem with those that were previously found analytically proves the effectiveness of the proposed technique.

Maxwell Equations in Anisotropic Half-Space and Integral Equations of Problem of Electromagnetic Wave Diffraction by Screen

Maxwell Equations in Anisotropic Half-Space and Integral Equations of Problem of Electromagnetic Wave Diffraction by Screen

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

МЕТАРЕЗОНАТОР ФАБРІ‒ПЕРО, ЯКИЙ ПІДТРИМУЄ РЕЗОНАНСНИЙ РЕЖИМ НА ЗАМКНЕНИХ МОДАХ

Purpose: Investigation of the electrodynamic properties of a Fabry-Perot metaresonator formed by two parallel perfectly conducting, two-dimensionally periodic, two-element screens of finite thickness with rectangular holes. The resonator is excited by a plane linearly polarized electromagnetic wave. The basic cell of each of the screens used as the metaresonator mirrors contains two lengths of rectangular waveguides of different transverse sections. Design/methodology/approach: An operator method for solving the 3D problems of electromagnetic wave diffraction by multielement two-dimensionally periodic structures is used in the study. The computation algorithm uses the partial domain technique and the method of generalized scattering matrices. Findings: As follows from the results of the numerical modeling made, the magnitude of the plane wave reflected from the metaresonator turns to zero at fixed frequencies lying below the cutoff frequencies for the rectangular waveguide sections embedded in the resonator mirrors. The effect of the total electromagnetic wave transmission through the metaresonator at the first lower frequency is characterized by a strong localization of the electromagnetic field in the resonator volume. The reason is excitation of the metaresonator by the exponentially descending field penetrating inside the resonator through the evanescent holes at the resonance frequency. The second low-frequency resonance of the total electromagnetic wave transmission through the metaresonator is associated with the trapped-mode resonance, which is observed in multielement two-dimensionally periodic structures. This case is characterized by a strong localization of the electromagnetic field from both sides near the metaresonator mirror surfaces. Conclusions: The unique electrodynamic properties of the metaresonator can find application in the devices for measuring the electrophysical parameters of composite materials with high losses. The effect of strong localization of the electromagnetic field both in the resonator volume and near the mirror surfaces can be used for monitoring the gaseous substances in crowded places. Key words: two-dimensionally periodic screen; rectangular waveguide; Fabry-Perot metaresonator; reflection factor; evanescent waveguide; trapped-mode resonance

Calculation method of the radar cross section of the complex shape object located on the surface with an arbitrary reflection coefficient

Relevance. Currently, an important problem is the electromagnetic wave scattering modeling on the complex shape objects located on some underlying surface (this may be military equipment on bitumen/ grass, surface objects directly on the water). Such tasks are important when designing new inconspicuous equipment. The purpose of the work. Consider the existing and suggest improvements in the method solving of the problem of electromagnetic wave diffraction on the complex shape object, which is located on some underlying surface. In this case, the change in the electromagnetic parameters of the underlying surface should not lead to the need to re-calculate the field scattered from the object. Materials and methods. The diffraction problem is solved for the complex shape object, which is located on the underlying surface. The surface can be characterized by dielectric (and magnetic) permeability, complex reflection coefficient or surface impedance. In order to determine the resulting field for an object located on an arbitrary surface, the scattering problem is solved for cases when the object is located above an ideally conducting surface and above an ideal magnetic. Results. A modeling technique for the scattering of the electromagnetic waves by the complex shape objects located above an underlying surface is proposed. Numerical experiments have been caried out in order to demonstrate the effectiveness of this technique. Conclusion. It is shown that the method proposed in the article allows to effectively calculate the contribution of different underlying surfaces in the resulting scattered field of the complex shape objects that are located on it. You do not need to simulate directly for an object over a specific surface each time. It is enough to carry out only three simulations: for an object in free space, and also when ideal conductor and ideal magnetic are used as the underlying surface. Formulas that allow to calculate the field scattered by this object for an arbitrary underlying surface are obtained.

Solving the Problem of Electromagnetic Wave Diffraction by a Flat Screen Using CUDA

Solving the Problem of Electromagnetic Wave Diffraction by a Flat Screen Using CUDA

On Generalized Solutions of the Problems of Electromagnetic Wave Diffraction in the Open Space

On Generalized Solutions of the Problems of Electromagnetic Wave Diffraction in the Open Space

Analytical Inversion of the Operator Matrix for the Problem of Diffraction by a Cylindrical Segment in Sobolev Spaces

A vector problem of electromagnetic-wave diffraction by a cylinder is described by a system of two two-dimensional integro-differential equations. After expanding the unknown functions and the right-hand sides in Fourier series, the problem reduces to systems of one-dimensional equations. Analytical inversion of the principal operator of one-dimensional systems in Sobolev spaces is considered. Theorems on the boundedness and bounded invertibility of the principal operator are proved. The inverse operator is represented by series and in closed form: the elements of the inverse matrix are integral or integro-differential operators.

Electromagnetic field of the circular magnetic source in biconical section

The problem of axially-symmetric electromagnetic wave diffraction from the perfectly conducting biconical scatterer formed by the finite cone placed in the semi-infinite conical region is solved rigorously using the mode-matching and analytical regularization techniques. The problem is reduced to the infinite systems of linear algebraic equations (ISLAE) of the second kind. The obtained equations admit the reduction procedure and can be solved with a given accuracy for any geometrical parameters and frequency. The numerical examples of the solution are presented. The analysis of the source location influences on the far-field pattern for different geometrical parameters of the bicone is carried out.

Plasmon Resonances in Square and Rectangular Noble Metal Nanoplates

Abstract—The article considers the two-dimensional diffraction problem of a TM-type plane electromagnetic wave on a cylindrical silver or gold structure, the contour of the cross section of which is a square or rectangle. In the wavelength range $$300\,\,{\text{nm}} < \lambda < 900\,\,{\text{nm}}$$ a rigorous numerical method is used calculate the spectra of the scattering cross section and scattering patterns. The influence of losses of the medium, the geometric dimensions of the structure, and the angle of incidence of a plane wave on the scattering cross section and scattering pattern is studied. It has been shown that the real losses of gold make it impossible for multipole resonances to exist at plate sizes substantially less than the wavelength. In the case of a silver plate, the position of the dipole and the presence of multipole resonances depends both on the length and thickness of the plate and on the angle of incidence of the plane wave.

Infinite Sets of Linear Algebraic Equations in the Problems of Diffraction of Electromagnetic Waves by the Non-Coordinate Periodic Media Interfaces

The diffraction problem of plane electromagnetic wave by the non-coordinate periodic media interface is reduced to an infinite set of linear algebraic equations for Floquet coefficients of scattered field. Two-dimensional case of diffraction problem is considered in detail. In the three-dimensional case, special attention is paid to problems of program implementation of algorithms of approximate solving of ISLAE.

Research of influence a physical carrier on the characteristics for four-element circular antenna array

The main problem arising in the development of mobile-based antenna arrays is the problem of taking into account the influence of the carrier body on the characteristics of such an antenna array. Pilotless vehicle are one of the most popular directions of modern aviation development. It is aimed to consider a quite simple in design four-element annular antenna array and to analyze the influence on the bearing direction finding characteristics of such a mobile carrier which is a pilotless vehicle. Theoretical consideration of the carrier body effect on the bearing direction finding errors is usually reduced to the problem of electromagnetic waves diffraction on conducting objects. Comparison of some absolute bearing direction finding errors obtained by the phase correlation method for the cases of placing the antenna array in free space and on the array carrier is given. The results of the calculation of the root-mean-square values dependence on the frequency, averaged over all the analyzed angles of the radio wave direction of arrival, are presented. The dependences of the root-mean-square value on the azimuth angle of the radio wave direction of arrival for the cases of the antenna array placement on the carrier body and in the free space averaged for all the analyzed signal frequencies were calculated.

On the Solvability of the Problem of Electromagnetic Wave Diffraction by a Layer Filled with a Nonlinear Medium

The problem of diffraction of a polarized electromagnetic wave by a layer filled with a nonlinear medium is considered. The layer is located between two half-spaces with constant permittivities. Two widely used types of nonlinearities: saturation nonlinearity and Kerr nonlinearity are considered. It is proved that the results on the solvability of the problems in these cases are qualitatively different: in the case of saturation nonlinearity, there are conditions under which the diffraction problem has a unique solution and, in the case of Kerr nonlinearity, the diffraction problem always has an infinite set of solutions. Analytical and numerical methods for solving this kind of problems are developed. Numerical results are presented.

On Generalized Solutions of Problems of Electromagnetic Wave Diffraction by Screens in the Closed Cylindrical Waveguides

In this article we propose to use special classes of the generalized functions in order to state the correct statement of some diffraction problems of electromagnetic waves by thin conducting screens in the cylindrical waveguides with conducting walls. As the generalized solutions, such mappings are considered which assign a linear functional defined on the linear shell of the set of the functions satisfying the corresponding boundary conditions to every value of longitudinal space coordinate. The traces of the solutions on the cross-section of the cylindrical domain are interpreted in the generalized sense. The infinite sets of linear algebraic equations are derived immediately from the generalized boundary conditions. We show that it is advisable to use the boundary conditions for the normal components of the electromagnetic field.

An integral equation technique for the analysis of phased array antenna with matching step discontinuities

Applying the integral equation method of overlapping partial domains and the Schwartz alternating method to solving an electromagnetic wave diffraction problem is considered in this paper. The infinite rectangular waveguide phased array antenna scanning in H plane which waveguides have step matching discontinuities is represented. The whole field definition domain is sliced into three overlapping partial domains. The system of integral representations for unknown Ey components of the electrical field vector in each domain is set up using Greenʼs functions. Unknown functions in each domain are presented as orthogonal eigenfunction series. Using Galerkinʼs procedure, the system of integral representations is reduced to the system of linear equations for unknown expansion coefficients. For Schwartz method the system of integral representation is solved using iterative methods. The dependences of the reflection coefficient magnitude and phase on the value of scan angle are obtained. The comparison of obtained results for particular cases with known ones is performed.

Software package for calculating the reflectance profile of axisymmetrically-shaped targets in resonant and high frequency wavelength ranges

To develop software for solving the problem of electromagnetic wave diffraction at an object and calculate its scattering cross section, it is proposed to apply one of the most accurate, stable and common methods today - the integral equation method, confining its use to considering the targets with an axisymmetric surface shape, which often happens in practice. The study deals with a wide range of practical issues related to the application of the integral equation method for solids of revolution, with the main attention being paid to the conditions necessary for obtaining results with known-high accuracy. We present the software in which the proposed method is implemented, and give the results of calculations.

Wave Flow and the Resonant Decrease in the Radiation Visibility of Extensive Corrugated Diffusers

In this paper, the problem of electromagnetic wave diffraction by extensive conducting bodies with uniform cross sections and continuous curvature boundaries is studied. Corrugated cylinders are considered as diffusers. A resonant decrease in the radiation visibility of such bodies was discovered.