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—The article studies the effect of the electromagnetic field of wireless communications on a human inside a car in the frequency ranges of 450, 900, and 1800 MHz, corresponding to the operational range of police radios and modern mobile phones. A comparative analysis of the influence of the Earth’s surface under the car is presented. The results of numerical calculations using the Method of Auxiliary Sources show the presence of resonance phenomena and a high reactive field inside the car, which leads to an undesirable increase in the level of absorbed energy in human tissues.

The study aims to determine the buried dielectric object under the ground based on the frequency characteristics of the object. To achieve that goal, a minimum reflection angle - Brewster angle is found when there is no object in the region of interest. Then, the electromagnetic propagation with the obtained angle is employed when the object exists. The reflected field reveals the resonances of the object and by comparison, the physical properties of the unknown object can be predicted. To achieve this goal using computer simulation, the Method of Auxiliary Source (MAS) is employed.

An algorithm for optimal antenna synthesis using the Method of Auxiliary Sources is proposed. The physical meaning of the analyticity of the wave fields, which underlies the algorithm, as well as the method itself, is discussed. The physical meaning of reactive fields and the role of the singularities of the analytic continuation of a given far field in solving the problem are discussed. The results of numerical experiments are presented, confirming the theoretical ideas.

The algorithm for finding the optimal antenna for a given pattern, based on the Method of Auxiliary Sources, is used for the case of an adaptive phased array. The solution to this problem suggests finding the singularities of the analytical continuation of a given far field and placing sources with varying complex amplitudes in them. This allows to obtain the desired variable radiation pattern, with a minimum number of sources, with a minimum reactive field, and with a minimum size of the antenna's array. The results of numerical experiments for obtaining an optimal antenna with a periodically changing directional pattern are presented.

A numerical algorithm is proposed to localize field singularities with the aid of the method of auxiliary sources using functions that describe converging and diverging waves. Effect of field singularities of particular pattern is studied in the problem of synthesis of an optimal antenna. It is shown that a desired pattern with minimum reactive field is obtained when the sources are located at such singularities. Results of numerical and real experiments are presented to prove the correctness of the proposed algorithm.

With great sorrow, we write this memoriam for Prof., D.Sc. Nikolai Nikolayevich Voitovich, who passed away on July 11, 2020. This mournful event is a great loss for all scientists working in the field of electrodynamics, especially for his colleagues, students and friends in various countries. Prof. N. N. Voitovich was an outstanding scientist and pedagogue, who stood at the origins of electrodynamics and mathematical physics and who made an invaluable contribution into diffraction scattering, wave propagation, theory of oscillations, spectra, resonance systems, as well as their application to new objects, such as nanoplasmonics. Prof. N. N. Voitovich was an organizer and chairman of the IEEE Ukraine Section (West) MTT/ED/AP/EP/SSC Societies Joint Chapter, and organizer and permanent participator of the International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave (DIPED).

In this article, the diffraction of the electromagnetic wave by the building with two rooms is considered. The rooms have doors and windows with lossy dielectric walls. The electromagnetic properties of the building as an opened coupled resonator system are investigated at different source locations and several frequencies including 5G band. The problem is solved by using the Method of Auxiliary Sources. The near electric field distributions are calculated and analyzed.

In this article there is investigated the character of the singularities’ distribution corresponding to the analytical continuation of the field reflected by the front part of the perfect electric conductor sphere illuminated by the electromagnetic waves point source. The analysis of these singularities show, that they represent the distorted image of the incident wave source and are distributed on the caustic surface. The discrete character of the singularities, when the ratio of the sphere radius and the incident wave length is finite, is explained by the Fresnel zone method. The numerical experiments performed to determine the scattered field’s singularities confirm theoretical reasoning based on geometrical optics and Fresnel’s zone method.

During solution of the practical problems related to the construction of the field radiators or receivers, the important problem is to “match” them with the free space. The bad matching leads to the formation of the undesired reactive field in the near zone of the corresponding antenna. The investigations show that, the best matching can be achieved by putting the sources in the points of singularities of the far field’s analytical continuation. By this could be achieve the minimalarea of the reactive field. If the sources, which describes the far field, are distributed outside the singularities, then in the near zone the reactive field with the high amplitude is created, which doesn’t make such a radiator optimal. In the given work the sources are distributed initially outside the singularity points. The goal is to study main properties of the excited reactive field and to study the far field formation mechanism, when the sources of the radiation are singularities points out.

The paper presents a memorial to the outstanding FSU scientist, world-known specialist in the electromagnetic wave theory, Prof. Boris Z. Katsenelenbaum, who passed away more than four years ago on the 96th year of his life. The fields of his scientific investigations, his significant contribution to the organization and existence of the DIPED Seminar/Workshop, the memories about him of his friends and colleagues are highlighted.

The Method of Auxiliary Sources MAS) used for the 2D scattered electromagnetic field analytical continuation’s singularities distribution and character determination.Smooth bounded perfect cylindrical conductor surface is considered as a scatterer. The idea of the MAS application for this problem related to the holography principle and is based on the properties of field’s analyticity and uniqueness of its analytical continuation up to the singularities. After the theoretical foundations of the problem, several results of numerical experiments are presented.

Mobile phones’ radiation influence on a homogenous human model located inside a car is studied in this research. One of the novelty of proposed research is earth surface influence consideration under the car on EM field formation inside it. The inner field and its amplification by the car’s walls that in some cases act like a resonator are studied. The problem was solved numerically using the Method of Auxiliary Sources. Numerical simulations were carried out at the 450, 900, 1800 [MHz] standard communication frequencies. Obtained results showed the presence of resonant phenomena inside the car.

The results of the efficiency study of the Method of Auxiliary Sources (MAS), applied to the problem of electromagnetic wave diffraction by infinitely thin and perfectly conducting unclosed surfaces, are presented in this paper. Planar, corrugated, hemispherical, and half-open surfaces are discussed. The numerical implementation details, allowing the determination of the induced currents on the different sides of the open surface, are discussed. The numerical results obtained with the MAS are compared to those, obtained with the help of the Method of Moments. It is demonstrated that the MAS has some advantages over other methods, is efficient, and trustworthy for the simulation of such problems. This is confirmed by comparing certain numerical results with the real experiment data.

The Method of Auxiliary Sources (MAS) is used to study the torus form concave-convex hollow metallic voluminous resonator. Such resonators have wide application in high frequency radio-electronics. Using the proposed method it is possible to find ail eigen frequencies of the voluminous resonators and study the structure of the eigen resonant fields.

The aim of this research is to investigate the influence of EM radiation, emitted by base station antenna, on a human homogenous model located in a car and study possible resonant fields inside it considering ground existence. The standard frequencies: 450, 900, 1800 [MHz] are selected for numerical experiments. The problems are studied using a user friendly program package base on the Method of Auxiliary Sources (MAS). The results of the numerical simulations are presented and analyzed below.

This paper presents the human EM exposure simulation study considering the presence of a hand, holding the handset. The inhomogeneous child model was used to simulate thermal response of head tissues exposed to RF energy at 900 MHz, 1900 MHz and 3700 MHz frequencies. The goal of proposed research is to study how the head and hand (fingers) positions (being in a near field of phone's antenna) can influence on the SAR pick values and temperature rise in the head tissues, caused by absorption of EM field energy. 1mm and 10mm distances have been studied from the handset to the child's head model. Numerical simulations are carried out using finite-difference time domain (FDTD) method. Obtained results are presented and analyzed below.

The method of auxiliary sources is applied to solve problems of electromagnetic wave diffraction by certain metal-dielectric structures that are finite 3D periodic lattices embedded in an ordinary dielectric. On the basis of the structures under study, the possibilities of designing antenna devices with a desired pattern and the rotating polarization are considered. A software packet is developed for computer simulation of such structures. The software is oriented to performing the corresponding computational experiments.

The main aim and the novelty of the proposed research is to study Mobile phone EM exposure thermal influence for the inhomogeneous woman models in case of different hand (finger) positions, holding the mobile phone, at 900 MHz, 1900 MHz and 3700 MHz frequencies. The motivation of this work is the necessity to consider influence of the hand, its position and position of the handset upon the near field for proper understanding of the exposure nature. Numerical simulations are carried out using finite-difference time domain (FDTD) method to estimate the specific absorption rate (SAR) and temperature rise caused by absorption of EM field energy in the human tissues. The obtained results are presented and analyzed below.

This paper presents the utilization of the Method of Auxiliary Sources (MAS) to localize active source positions of radiation by a desired predefined pattern or measured near-field distribution. The active sources position is based on the uniqueness of the wave field's analytical continuation along its propagation and, by means of the converging and diverging wave's function, localizes the positions of the field's singularities. Determining the coordinates of these active source locations with appropriate polarization and placing in these locations the field sources as a corresponding current, we can restore complete near-field distribution or a desired field pattern. The objective of this paper is to study the nature of the near-field regions (reactive and radiative zones), as well as transition zones in some particular cases. This paper presents the source localization methodology along with simulation and measurement results. The proposed methodology is used for directive antenna synthesis to realize a desired pattern with minimal side lobes and reactive fields, and also could be used efficiently for far-field prediction or EMI source localization by near-field scanning.

In the previous work [1] there was shown the efficient application of the Method of auxiliary sources (MAS) for the problems of Eigen frequencies and electromagnetic resonator's Eigen Fields. The calculations for numerical results were conducted for 2D case, when the resonator is bounded by the cylindrical surface. There was shown the efficiency of the proposed method in comparison to the traditional method, based on the numerical solution of the linear algebraic equations homogenous system. In the given work there is considered the 3D case with the examples of the spherical and elliptical resonators. There is investigated the error of the solution and the boundary condition satisfaction. The short description of the corresponding theory is given below. After that there is considered some numerical results of volume resonators' excitation in order to determine their Eigen frequencies and Eigen fields.

This paper presents creation of the optimal size directive gain antenna which radiates a desired predefined pattern. Theory of this study based on the Method of the Auxiliary Sources (MAS) was published in previous paper and briefly reminding the basic ideas of the approach results of the experimental measurements on created real prototype antenna are discussed. In practice during the antenna syntheses and its design very crucial problem is to minimize the size if the aperture which depends on the directive gain. We introduce the volume antenna which could minimize diameter of the aperture. Comparatively easy to construct and simply for feeding system with another positive radiations qualities like minimal side lobes and reactive fields makes interesting to use offered methodology. Eventually, for predicted antenna geometry using the MAS together with real experiments additionally to verify validity and correctness of approach the EMC Studio simulation used. All results are in a good agreement.

This paper presents the human exposure simulation study considering the presence of a hand, holding the handset, and some resonant effects due to the presence of the room walls. The motivation for this research is the necessity to consider influence of the hand on the field in the near zone for proper understanding of the exposure nature. It is known that for some frequencies rooms in the ferroconcrete buildings are resonant for EM field. The standing waves may be created with field values several times higher than value of the incident field. One of the parameters to consider for resonant effects study is the variable wall transparency. We have investigated several cases when a human with a cell phone is located inside and outside of a room and also the case when the EM source is the base station antenna. The problem is solved using the Method of Auxiliary Sources with a user friendly program package, created for numerical experiments for this particular problem. Several cases of the human location and building wall's transparency parameters are considered during the calculations. The numerical experiment results are presented and analyzed.

In this article there is considered a new approach for Active Sources Localization (ASL) based on the measured or given data of the field's distribution on some surface. The task belongs to the solution of the inverse scattering problem based on the Method of Auxiliary Sources (MAS). Inherently, proposed approach is using fundamental property of the scattered field — the uniqueness of the wave field's analytical continuation along and backwards its propagation. In the paper we discuss about two approaches for solution state problem. The positions of the active source are determined by means of the converging and diverging wave's function. The program package is created based on both approach and the numerical experiments are realized. The results of simulation show the efficiency of this new proposal.

A new approach of remote sensing for buried bodies by means of reflected pulses is presented in this article. This method is based on the concept of a scattered field’s analytical continuation (Zaridze et al. in IEEE Trans Antennas Propag 50(1):50–58, 4). Soil properties were deduced using data processing and these properties analyzed. Computer simulation results of both holographic and combined holographic/photographic methods for immersed body visualizations are presented. Several ways to simplify the experimental measurements are also presented. All of these research efforts are directed towards creating a software package for high resolution image recognition devices.

A novel numerical model to simulate thermal response of human body tissues exposed to RF energy is presented in this article. It is based on a new algorithm for the construction of a realistic blood vessel network, a new model of blood flow velocity distribution and an approach to solve the bio-heat equation in human tissue with variable and initially unknown blood temperature distribution. The algorithm generates a discrete 3D representation of both arterial and venous vascular networks and a continuous blood velocity vector field for arbitrary enclosed geometries required to represent the complex anatomy of human body and blood flow. The results obtained in this article by applying the developed method to realistic exposure conditions demonstrates relative difference in thermal response of the exposed tissue compared to results obtained by conventional bio-heat equation with constant blood perfusion and temperature. The developed technique may provide more accurate and realistic modelling in thermal dosimetry studies of human body RF exposure.

The influence of specific absorption rate averaging schemes on the spatial correlation between mass-averaged specific absorption rate and radio-frequency-induced steady-state temperature-rise distributions in the “Visible Human” body model exposed to plane waves in the 30–800 MHz frequency range is investigated through finite-difference time-domain modeling. The averaged specific absorption rate is computed on the basis of the IEEE Std. C95.3-2002 specific absorption rate mass-averaging algorithm, employing 1-g and 10-g averaging tissue masses and several air-inclusion factors. The analysis reveals that the 10-g average specific absorption rate yields larger global correlation with the corresponding radio-frequency-induced temperature-rise distribution for the considered plane-wave exposures, while the dependence on the air-inclusion factor features a distinctive threshold behavior.

By means of the scattered field singularities localization, optimal antenna synthesis problem solution with predefined pattern directivity is considered. Using the analytical continuation of the scattered field, along and backwards its propagation, could be determined the positions of their singularities. Determining the coordinates of these singularity points with appropriate polarization and placing in these points the field sources as a corresponding currents, we get the desired directional pattern. Numerical realization of described above algorithm showed ability to determine the positions of the scattered field singularities of the given pattern and the possibility to find optimal distribution of the currents, which creates the predefined far field's pattern.

The Method of Auxiliary Sources (MAS) is efficiently used in the synthesis problem of antenna with the given far field pattern, by means of the radiated field's fundamental singularities determination. The paper is the continuation and the generalization to the 3D cases our previous publications. As it is known, the same directivity pattern, at the given frequency, could be obtained with the different current distribution on different antenna surface. The problem is reduced to the finding of the more or less optimal current distribution, which is unique. This means the minimal values of the: currents, reactive near field values and also the best matching between antenna and radiation. In the given work is confirmed that the optimal currents' distribution is related to the fundamental singularities of the radiated field.

The method of auxiliary sources is used in the spectral problem for 2D and 3D electromagnetic resonators. Instead of traditional solution methods, based on the search of nonzero roots of homogenous equation system, in this work the problem is reduced to the solution of the nonhomogeneous system which simplifies the solution of the stated problem. Considering the diffraction problem on concrete objects and calculating the frequency characteristic for them, the resonant frequencies are determined, corresponding to their eigen values, at which the inner resonant field is excited as a standing wave. The obtained results confirm the efficiency of the proposed algorithm.

A mobile communication system base station's radiation interaction with a human model inside of a building is studied in this article. The inner field and its amplification by the building as a resonator are studied. The problem is solved using the Method of Auxiliary Sources with a program package, created for numerical experiments. Several cases of the human location and building wall's transparency parameters are considered and the numerical experiment results are presented.

The main goal of this work is the construction of a special electronic devices and equipment — for perimeter physical protection. The objective of this paper is consideration of the methods, permitting quick patrolling, easy intruder detection and revealing approximation of the undesirable person to the guarded perimeter. In this paper we introduce frequency analysis of the two wire system in an open environment, where the measurements have been conducted.

Plane EM wave diffraction phenomenon for the layered structure of the infinite 2D periodic lattices using the Method of Auxiliary Sources (MAS) is studied. There are considered the cases when this structure in embedded in the free media and also inside of the dielectric layer. The lattice elements represent open and closed conductors with the small electric radius, which have the resonant properties. As a result of the multiple resonances, these structures should have interesting complex materials properties. The existence of several resonant layers will amplify these phenomena.

The motivation of this paper is to study the influence of the background EM field (at wireless connection frequencies) on the human body. We have investigated the EM field's distribution in the closed, semi-open and open geometries with the presence of the human model. We studied the EM wave field's nature for some big scenarios considering interaction with an object like a human body. Besides, we have an interest in dependence of the radiated pattern on the user's position, mobile position and window location for the studied geometry. We consider several cases with different positions of the EM source, and different transparency coefficients for the surfaces of the semi-closed geometries. A special attention in the paper is paid to the modeling methodology of surface transparency variations. An algorithm based on MAS method applied to the semi-open geometries is described in this paper. Because of resonance phenomena on some frequency and surface transparency the strength of the standing EM field becomes extremely high and this is the cause of the high SAR values. Results of calculations are presented in the paper mainly for different wireless connections frequencies.

The method of auxiliary sources is applied to solve problems of electromagnetic wave diffraction by finite 2D and 3D periodic metal-dielectric structures. The goal of this work is to get multiple resonance effects in such structures when these structures have complex materials properties. On the basis of the structures under study, 3D lattice with negative refractive index is modeled. The possibilities of designing antenna devices with a desired pattern, the rotating polarization and electronically operate the radiation direction are considered.

Computer simulation of electrostatic discharge (ESD) for simplified objects is described and compared to measured transient fields of human/metal ESD. The simulation algorithm uses the method of moments in time domain, coupled with nonlinear arc resistance model. Transient currents and fields are analyzed from the electromagnetic compatibility (EMC) point of view. Validation of the numerical simulation is done by comparison to experimental data. The simulated structure models the human/metal ESD in its peak current and field values and their derivatives reasonably well.

The extension of the Method of Auxiliary Sources (MAS) to large body scattering problems is investigated. Approximations leading to correct predictions of scattering field with minimum numerical cost are examined. After interpreting the involved physical phenomena associated with scattering field singularities, highly efficient MAS algorithms are developed. Furthermore, the same approach leads to a source visualization technique, which is of exceptional interest. As result of this analysis, an efficient "target" visualization method for large body scatterers, is proposed.

The study of the electromagnetic wave diffraction on the thin, perfectly conductor surfaces using the Method of Auxiliary Sources (MAS) is presented in this paper. Plane, corrugated and rounded plate cases are considered. Details of numerical realizations are discussed. Comparison of the numerical results obtained using MAS and Method of Moments (MOM) are given, from which the advantage of the MAS is for this cases is shown.

In this paper is considered the synthesis of antennas with flat pattern in certain angle which has circular polarization of radiation. This antenna is based on complex materials and represents the dielectric body in which the resonance admixture elements lattice is embedded. Here is considered numerical simulation of this problem using the Method of Auxiliary Sources (MAS) [1]

The primary objective of this paper is consideration of the several methods, permitting quick and easy mapping of the sensors position during near field measurements. Measured field's data (amplitudes and phase) in high resolution image reconstruction experimental devices must be mapped in the computer Cursor Position (CUP). The main goal is construction of a high-speed device for measurement and recording to the amplitude and phase information of the reflected electromagnetic wave over a two-dimensional surface appropriate to the exact space coordinates.

In this paper we suppose to discuss recent results of study influence of Electromagnetic (EM) exposure of mobile phones radiation on the user. This is the part of topic: “Developing a Thermal Exemptions Rationale for Low-Power Transmitters”. Particularly, we present results of computer simulation of the users head exposure via radiation of electrically small and resonant length antennas. Compare and contrast threshold power with temperature increase in tissue and SAR. Investigate the relationship between temperature rise with SAR and between temperature rise and bandwidth/efficiency.

Primary intent of this study is development of realistic vascular structure and simulation of the blood perfusion in capillary. It is needed for precise thermal analysis using the modified bio-heat equation to provide better prediction of thermal response of tissues exposed to RF energy then in conventional Pennes model [1]. Particularly, motivation of this paper is to use previously presented modified bioheat equation [2–4] for heat exchange and temperature rise simulation on a realistic human head model.

In this paper we consider the problem of diffraction of electromagnetic wave on the resonance wire structure. The resonance properties of this systems gives ability to create the periodical structure of these wires embedded in dielectric in order to get the complex material with desired properties. We consider the mathematical approach of this problem and also the computer simulation of the system of wire pairs radiated by the plane wave.

Several aspects of computer-aided modeling and simulation of 3D complex material PBG devices are discussed. Software package for simulation, analysis, design and optimization of wide variety such devices has been created. Periodic structures of doped elements responsible for complex properties of integral objects are the basis of devices. It is proposed, that complex dielectric properties (ɛ, μ) of the main part, together with specially fitted doped elements create the rest admittances (α and β) of the meta-materials. The need of 3D numerical simulations and design are discussed. The Method of Auxiliary Sources (MAS) [1] is applied to simulate EM field distribution in microwave and THz frequency ranges.

The need for a highly efficient numerical simulation platform for designing photonic band gap (PBG) structures is outlined in the context of various functional device topologies. In this paper we describe the use of the Method of Auxiliary Sources (MAS) as a semi-analytical, frequency-domain method for computational optics, which has already proven its accuracy and efficiency in various other fields of electrodynamics. The proposed software package provides an easy-to-handle approach to full-wave analysis of two-dimensional (2D) PBG circuits, PBG-based antennas as well as to dense-integrated optics components that contain optical waveguides, scatterers, resonators and other functional elements. Experimental verifications of the numerical results have been conducted in the microwave frequency range for several device topologies. Described methodology can be used to create devices (waveguides, circulators, splitters, etc.) for higher frequencies, where conventional approaches are not applicable due to decrease of geometric sizes.

A new algorithm for construction of artificial blood vessel networks and a new approach to simulate heat exchange in tissue are presented. The algorithm produces discrete three-dimensional geometric representations of both arterial and venous networks. The key feature of the algorithm is that growth begins from the root points and it can work with any enclosed geometry. Unlike traditional schemes where heat exchange is calculated between vessels and cells, we consider that heat exchange between blood and tissue as well as the metabolic process happens mainly in capillary. The motivation of this paper is development of realistic vascular structure and simulation of the blood perfusion in tissue. It is needed for precise thermal analysis using the modified bio-heat equation to provide better prediction of thermal response of tissues exposed to RF energy.

A new algorithm for construction of artificial blood vessel networks and a new approach to simulate heat exchange in tissue are presented. The algorithm produces discrete three-dimensional geometric representations of both arterial and venous networks. The key feature of the algorithm is that growth begins from the root points and it can work with any enclosed geometry. The main difference of proposed method is that blood perfusion occurs mainly in capillary. Two different methods of constructing blood velocity vector field in tissue accounting capillary blood flow are presented. It is needed for precise thermal analysis using the modified bio-heat equation to provide better prediction of thermal response of tissues exposed to RF energy.

The electromagnetic synthesis and optimization of microwave focusing systems requires the development of specific CAD tools with appropriate characteristics (accuracy, computation time, etc.). The purpose of this paper is to benchmark two 2D numerical methods, namely the method of auxiliary sources (MAS) and the finite-difference time-domain (FDTD) technique. Several relevant test structures (integrated lens antennas, EBG resonator antennas, constrained lenses) have been designed to assess the impact of the intrinsic features of both algorithms (e.g. stair-case approximation in FDTD, kind and location of the auxiliary sources in MAS) upon the numerical results.

The primary objectives of this paper are creation of the program package for determination of shape and position of metallic and/or dielectric bodies embedded within a dielectric media, determination of dielectric parameters of the body suppose. The main goal is construction of a high-speed device for measurement and recording amplitude and phase information of the electromagnetic wave over a two-dimensional surface, connected to the computer will realize the detection process using developed software.