Planar Layered Media Research Articles

ВИЗНАЧЕННЯ ПАРАМЕТРІВ ЕЛЕКТРОМАГНІТНОГО ВИПРОМІНЮВАННЯ ДЛЯ ЛІКУВАННЯ ДИСПЕПСІЇ ТВАРИН

У статті наведено рівняння для дослідження залежності напруженості електричного поля в біологічно активних точках від параметрів радіоімпульсного випромінювання. Отримані результати дозволили провести аналіз якісних властивостей процесу взаємодії радіоімпульсного випромінювання з біологічно активними точками. Було запропоновано біологічно активні точки розглядати як діелектричний резонатор, поміщений в плоску діелектричне середовище. Тому, якщо частота заповнення радіоімпульсу близька до власної частоти такого резонатора, то можливо резонансне збільшення напруженості електричного поля в біологічно активних точках. При проведенні численних розрахунків було прийнято, що сумарний потенціал на мембрані біологічних клітин не повинен перевищувати величину в 100 мВ. У процесі теоретичного аналізу розробленої моделі було встановлено, що для підвищення життєздатності новонароджених телят хворих диспепсією їх біологічно активні точки слід опромінювати інформаційним радіоімпульсного випромінюванням в діапазоні змін параметрів: тривалість імпульсів 0,5 · 10-7 ... 1,5 · 10-7 с; період проходження імпульсів 0,5 · 10 .... 1,5 · 10-5 с; величина щільності потоку потужності 15 мкВт / см2; частота заповнення імпульсів 50ГГц; час експозиції 15 ... 20 с; напруженість електричного поля E0 = 8,8 В / м, Еср = 5,7 В / м.

Electrical capacitance of resistive film in plane-layered medium

The parasitic capaciences of film resistors can dramatically affect the output parameters of a microelectronic unit. A technique for computation of these capacitances is necessary for construction of mathematical models for CAD which are to be employed at the stage of circuit simulation, this stipulating the actuality of developing the technique for computations of the capacitances. The article presents analytic expressions for the capacitance of a current-carrying rectangular high-resistance film conductor (resistor), i. e., resistor stripe. The expressions describe the dependence of the capacitance on a non-uniformity of the charge distribution along the vector of the current density. The bounds within which the resistor’s capacitance changes with the ultimate change of the load resistance from 0 to ¥ are found. The estimation of the error caused by a computation of a resistor’s capacitance using formulae intended for a computation of a conductor capacitance is presented. A substantial nonlinearity of the input impedance of the film resistor is revealed. The nonlinearity is caused by a charge redistribution which takes place if the film resistor’s load resistance changes during the functioning of the integrated circuit.

Rapid Three-Dimensional Photoacoustic Imaging Reconstruction for Irregularly Layered Heterogeneous Media.

Photoacoustic imaging (PAI) is susceptible to speed of sound (SOS) differences in heterogeneous media which greatly reduce the resolutions and qualities of the imaging results. Several reconstruction methods have been reported to adapt for heterogenous media, but they are limited by specific deficiencies such as efficiency, accuracy, and model limitation problems. Among them, the plane wave model based on wavefield reconstruction is the most efficient and promising one for high-efficiency three-dimensional PAI. However, the classic plane wave model only suits for planar layered media, severely limiting its applications in practice. To this end, we modify the plane wave model to apply for irregularly layered heterogeneous media and propose a corresponding wavefield extrapolation to reconstruct photoacoustic image. This method employs split-step Fourier to compensate the SOS differences, extrapolates wavefields and reconstructs the image depth by depth. Furthermore, a floating discretization strategy is introduced to control and balance the efficiency and accuracy with a hyperparameter. The simulation and experiment results demonstrate that the proposed method can reconstruct the image with an equivalent resolution to time reversal's and even have higher efficiency and robustness. To reconstruct a three-dimensional image with 50×50×600 pixels, the proposed method takes only 5.5 seconds using a laptop loaded with Intel(R) Core (TM) i7-8550U CPU @1.8GHz.

Negative refraction of plane electromagnetic waves in non-uniform double-negative media.

We propose a new model of a plane-layered medium with a fixed positive refractive index, but variable non-vanishing dielectric permittivity and magnetic permeability. An analytical solution of the problem of plane electromagnetic wave propagation through the medium has been found. It is shown that the negative-refraction effect occurs in this type of medium; in particular, an explicit expression for the field has been first obtained in the region of its formation. This result suggests that the necessary condition for the occurrence of this effect in quite complex media is not the negativity of their refractive indices, but only the requirement of simultaneous negativity of the real parts of dielectric permittivity and magnetic permeability. We also demonstrate that the medium is passive (absorbing) if a plane E-polarized wave propagates in it, and active (amplifying) in the case of H-polarized wave propagation.

Algorithms for searching defects in engineering structures using GPR (Review article, Part I)

Relevance of the problem of the development of technical means (GPR) and algorithms for processing ultra-wideband signals follows from the wide range of possibilities that these means of non-destructive testing and remote sensing provides, together with the potential of modern computing tools and software. Of particular interest in this regard are the results obtained by using various effects associated with a change in the polarization state of both primary (probing) pulses and signals reflected from complex multilayer media to detect defects in them. This is due to the possibility of not only quickly detecting heterogeneities, but also with the relatively low cost of such work. The purpose of the work is a review of various technical means (pulsed georadars) and signal processing methods for detecting various internal inhomogeneities in plane-layered media. These heterogeneities include, in addition to various internal communications elements (cables) and technical elements (drainage pipes), also dangerous externally invisible defects - subsurface cracks and delamination (interruption of contact between the layers). Materials and methods. The paper provides an overview of methods developed by the author, among others, which are designed to solve primarily the practical problems of detecting subsurface inhomogeneities and defects in plane-layered media. The physical basis for the creation of these methods was the result of many years of research by the author related to the analysis of the polarization state of complex (including pulsed) signals scattered by various objects. Results. The basis of the considered results is made up of both scientific articles and patents of Ukraine for inventions and utility models obtained by the author. Conclusions. The review of the results and various methods presented in the article is another confirmation of the wide possibilities offered by new means of remote sensing and non-destructive testing. These tools include not only the devices themselves (elements for obtaining primary data), but also information processing algorithms and software, combined into a single methodology for collecting, processing and subsequent storage of data on the current state of the examined technical and natural objects.

Численно-аналитические методы в задаче морской электроразведки в плоскослоистой среде

Численно-аналитические методы в задаче морской электроразведки в плоскослоистой среде

Surface-Volume-Surface EFIE for Electromagnetic Analysis of 3-D Composite Dielectric Objects in Multilayered Media

The surface-volume-surface electric field integral equation (SVS-EFIE) is generalized for the case of scattering problems on the composite nonmagnetic dielectric objects situated in planar nonmagnetic layered medium. The piece-wise homogeneous regions of the scatterer can be arbitrarily positioned with respect to the layers of stratification. The SVS-EFIE being a class of single-source integral equations is formed by restricting the surface single-source electric field representation in each distinct region of the scatterer through the volume-EFIE (V-EFIE) enforced on the boundary of that region for only the tangential component of the total field. As a result, the SVS-EFIE utilizes only the electric field dyadic Green's functions. This allows for its cast into the mixed-potential form using classical Michalski-Zheng's formulation and method of moments (MoM) discretization featuring easily computable integrals with singularities no stronger than 1/R, R being the distance from the source to the observation point in such integrals. The matrices of MoM discretization are represented inhierarchical form (as H-matrices) enabling solution of the scattering problems in multilayered media with O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup> log N) CPUtimeand memory complexities, where α is a geometry-dependent constant ranging from 1 to 1.5 depending on the shape of the scatterer. While the MoM surface and volume meshes discretizing the regions of the scatterer are constructed to ensure that no mesh element crosses interfaces between the layers, the clusters of both the surface and volume elements in their respective recursive partitionings in the process of H-matrix construction are allowed to span multiple layers of the medium. Upon computation of the layered medium Green's function kernels with the discrete complex image method allowing clusters of elements to cross dielectric interfaces between the layers is shown to preserve compressibility of the corresponding H-matrix blocks.

One Solution of the Forward Problem of DC Resistivity Well Logging by the Method of Volume Integral Equations with Allowance for Induced Polarization

For theoretically studying the intensity of the influence exerted by the polarization of the rocks on the results of direct current (DC) well logging, a solution is suggested for the direct inner problem of the DC electric logging in the polarizable model of plane-layered medium containing a heterogeneity by the example of the three-layer model of the hosting medium. Initially, the solution is presented in the form of a traditional vector volume-integral equation of the second kind (IE2) for the electric current density vector. The vector IE2 is solved by the modified iteration–dissipation method. By the transformations, the initial IE2 is reduced to the equation with the contraction integral operator for an axisymmetric model of electrical well-logging of the three-layer polarizable medium intersected by an infinitely long circular cylinder. The latter simulates the borehole with a zone of penetration where the sought vector consists of the radial Jr and Jz axial (relative to the cylinder’s axis) components. The decomposition of the obtained vector IE2 into scalar components and the discretization in the coordinates r and z lead to a heterogeneous system of linear algebraic equations with a block matrix of the coefficients representing 2x2 matrices whose elements are the triple integrals of the mixed derivatives of the second-order Green’s function with respect to the parameters r, z, r', and z'. With the use of the analytical transformations and standard integrals, the integrals over the areas of the partition cells and azimuthal coordinate are reduced to single integrals (with respect to the variable t = cos ϕ on the interval [−1, 1]) calculated by the Gauss method for numerical integration. For estimating the effective coefficient of polarization of the complex medium, it is suggested to use the Siegel–Komarov formula.

Nonlinear spectral correction of the pulse GPR signals

Background: The problems of non-destructive testing of industrial structures and transport structures are relevant from the point of view of increasing the efficiency of their control systems and saving financial resources and materials. The relevance of scientific research in the field of remote sensing and methods for solving inverse problems is also associated with the prospects for the formulation and solution of biomedicine problems associated with computer technology. Objectives of the work is to study the possibilities of virtual adjustment of the properties of probing and reflected signals to increase the reliability of processing results and increase the accuracy of restoration of the properties of objects when solving thickness measurement problems. Materials and methods: The basis of the proposed approach is the correction of the amplitudes of pulse signals in order to increase the accuracy of the values ​​obtained as a result of processing by introducing a normalizing factor into the processing algorithm, the value of which would be a function obtained as a result of GPR calibration procedures. Another way to increase the reliability of the data processing procedure may be by computer correction of the waveform to approximate its shape to the shape of an idealized model pulse. Results: As a result of theoretical analysis, methods and algorithms for implementing the procedure for improving the processing of sets of primary sensing data obtained using pulsed georadars were proposed. Conclusion: The analysis of the methods for processing and adjusting the characteristics of pulsed ground-penetrating radar signals made it possible on the one hand to better understand the physical basis for the interaction of electromagnetic pulses with plane-layered media. On the other hand, practical methods of improving the quality control of various engineering and transport structures, as well as building structures, are proposed.

Calculation of field in plane-layered microelectronic materials

A modification of the method for calculation of horizontal and vertical components of monochromatic field that is generated in plane-layered medium by horizontal current flow and described using wave equation is proposed for problems of microelectronics. The proposed solution is based on the verified method of equivalent propagation constant that makes it possible to substantially reduce the amount of calculations in comparison with alternative methods based on rigorous dynamic approach. The analysis illustrates the application of the method at relatively small distances.

Near-Field Full-Waveform Inversion of Ground-Penetrating Radar Data to Monitor the Water Front in Limestone

Limestone has been a widely used building material for many years. Its degradation process has been strongly linked to its water content, to which the radar waves are sensitive. In this paper, the closed-form, near-field full-wave radar model of Lambot et al. is utilized for monitoring water ingress in limestone. This model is based on planar layered media Green's functions combined with an intrinsic representation of the antenna through global reflection and transmission functions. The Jonscher model is used to describe the frequency dependence of the limestone electromagnetic properties. Then, an inversion method based on a genetic algorithm is developed and optimized. The method is numerically validated by simulating electromagnetic wave propagation in medias, using a three-dimensional finite element software, namely high-frequency electromagnetic field simulation. Finally, the method is experimentally validated, with a stepped-frequency radar system and an ultrawide band antenna, during an imbibition process of a limestone slab. Results are compared to gammadensimetry measurements, a nuclear and semidestructive approach, performed as the reference. Analyses of the results show that the average relative difference between the estimated and the reference water front is 2.5%, thereby demonstrating the performance of the proposed nondestructive method.

On the computation of plane-wave impressed fields and far-zone fields of arbitrary current sources in planar multilayer dielectric and plasmonic media

A unified and succinct transmission line formulation is presented for the computation of the plane-wave impressed fields and far-zone radiation fields due to arbitrary electric and magnetic current source distributions embedded in planar layered media. The equivalence principle and the spectral-domain transmission-line network analogue of the multilayer medium are used to express the fields in terms of the voltage and current transmission-line Green functions. The new formulation is applied to sample problems involving both dielectric and plasmonic multilayer media.

Inhomogeneous media characterization: a hybrid method of state space and frequency diversity

This paper presents an analytical method for the reconstruction of permittivity profile of an inhomogeneous slab. The proposed method which is based on state transition matrix combines state space formulation and frequency domain data. This methodology and formulation lead to an accurate inversion of complex inhomogeneous profiles. Comparing with other analytical methods, the proposed approach avoids solving the nonlinear integro-differential equation, which consequently yields mathematical implementation. In order to validate the algorithm, some inhomogeneous profiles with different levels of complexity are considered and analyzed. The results show that the proposed method can be considered as a robust technique for one-dimensional inverse scattering problems. The results are valuable for the study and electromagnetic characterization of inhomogeneous and planar layered media.

Применение потенциалов Дебая для расчета первичного поля в изотропной упругой среде, возбуждаемой вертикальным источником

An analytical solution of the problem of exciting an isotropic elastic medium by a vertical point source is proposed. This problem is a model one and is also a part of the solution of other model problems such as wave excitation in a plane-layered medium. The solution is based on the method of Debye potentials, which is widely used in solving various problems of electrodynamics. The range of these problems includes radiation from an antenna of a fairly arbitrary kind over a plane-layered dielectric medium, consideration of the effect an intricate fairing of an aircraft has on the operation of the radar station antenna system (the effect on the antenna pattern and the direction-finding characteristics of the system as a whole), designing slit radiators with a feeding resonator, and radiation from horn and waveguide antennas into a magnetodielectric semi-space. In many cases, it is possible to obtain an analytical solution of the problem; if an analytical solution is not available, numerical methods developed using the Debye potentials are effective from the computational point of view. The significance of an analytical solution lies in the simplicity and clarity of the interpretation and understanding of the wave propagation processes in contrast to a numerical solution. However, the fundamental difference between the problems of exciting elastic bodies from electrodynamic ones is in that two types of waves, namely, transverse and longitudinal ones, propagate in elastic media. This feature substantially complicates both the analytical solution and the elastic wave propagation process in comparison with electromagnetic waves. In view of this specific feature, a technique for calculating the excitation of an isotropic elastic medium using the apparatus of Debye potentials is proposed. It is shown that the displacement field of an isotropic elastic medium excited by a vertical source is represented as the sum of longitudinal and transverse wave fields, and symmetrically in the plane perpendicular to the source axis. Simple analytic expressions for calculating the displacement field at an arbitrary point in space are obtained. The results of calculations using analytical formulas are compared with the data of numerical modeling in the COMSOL Multiphysics 3.5a computer program. In view of the fact that the COMSOL Multiphysics 3.5a computer program is intended for calculating structures with finite dimensions, an original model of unlimited elastic medium in the form of a large-radius sphere (around 20 wavelengths) with radially-symmetrical absorption was developed.

Improving the Efficiency of Quasi-Optical Bragg Reflectors

In the analysis of propagation of wave beams in quasi-optical transmission lines, the loss rate and transformation of modes by various elements of the transmission line are of great importance. The effects occurring when a spatially bounded, obliquely incident wave beam is reflected from a Bragg resonator being a periodic, plane-layered medium with varied dielectric permittivity are considered. Such a reflector can be used as a frequency-selective element of the transmission line. Since the reflection coefficient of a plane wave from the Bragg reflector depends on its incidence angle, there occurs a transformation of the reflected beam. Analytical expressions for the beam displacement, the angle of deflection of the beam from the mirror reflection direction, and the wavefront curvature variation have been obtained. The influence of the mentioned effects on characteristics of the reflected wave beam in the main band of the Bragg reflector is numerically analyzed. The possibility of compensation for these distortions is considered.

RAYTRACING IN THE METHOD OF SEISMIC EMISSION TOMOGRAPHY

Many remote methods of multi-channel data processing require calculation of extremely great number of signal propagation rays. A description is given of highly efficient approximate routing methods for gradient and plane-layered high-speed medium models, as well as models with complex geometry of interfaces. The results of experimental research with the use of the aforesaid raytracing methods and emission tomography for seismic and magnetosonic waves are presented.

Worldline approach for numerical computation of electromagnetic Casimir energies: Scalar field coupled to magnetodielectric media

We present a worldline method for the calculation of Casimir energies for scalar fields coupled to magnetodielectric media. The scalar model we consider may be applied in arbitrary geometries, and it corresponds exactly to one polarization of the electromagnetic field in planar layered media. Starting from the field theory for electromagnetism, we work with the two decoupled polarizations in planar media and develop worldline path integrals, which represent the two polarizations separately, for computing both Casimir and Casimir-Polder potentials. We then show analytically that the path integrals for the transverse-electric (TE) polarization coupled to a dielectric medium converge to the proper solutions in certain special cases, including the Casimir-Polder potential of an atom near a planar interface, and the Casimir energy due to two planar interfaces. We also evaluate the path integrals numerically via Monte-Carlo path-averaging for these cases, studying the convergence and performance of the resulting computational techniques. While these scalar methods are only exact in particular geometries, they may serve as an approximation for Casimir energies for the vector electromagnetic field in other geometries.

A Graphical User Interface for Scattering Analysis of Electromagnetic Waves Incident on Planar Layered Media

This paper introduces a MATLAB-based Graphical User Interface (GUI) which could help electromagnetics engineers and researchers who are interested in designing layered media for various applications. The paper begins with presenting the analysis method the program employs, continues by encountering specific considerations and techniques of implementation, and ends with providing different numerical examples. These examples show good efficiency of the program for analysis of diverse problems.

Efficient evaluation of Sommerfeld integrals for the optical simulation of many scattering particles in planarly layered media.

A strategy for the efficient numerical evaluation of Sommerfeld integrals in the context of electromagnetic scattering at particles embedded in a plane parallel layer system is presented. The scheme relies on a lookup-table approach in combination with an asymptotic approximation of the Bessel function in order to enable the use of fast Fourier transformation. Accuracy of the algorithm is enhanced by means of singularity extraction and a novel technique to treat the integrand at small arguments. For short particle distances, this method is accomplished by a slower but more robust direct integration along a deflected contour. As an example, we investigate enhanced light extraction from an organic light-emitting diode by optical scattering particles. The calculations are discussed with respect to accuracy and computing time. By means of the present strategy, an accurate evaluation of the scattered field for several thousand wavelength scale particles can be achieved within a few hours on a conventional workstation computer.

A fast algorithm to forward model the triaxial induction logging response in layered transversely isotropic dipping formations

We have developed a new analytic method to compute the response of triaxial induction logging tools in layered transverse isotropic (TI) dipping formations without borehole and invasion zones. A triaxial induction tool is composed of one or more sets of three orthogonal transmitter coils and three orthogonal receiver coils arranged along the tool axis. The tool axis may intercept a formation with dip, azimuthal, and rotation angles. Based on the electromagnetic (EM) field in planarly layered media, formulations of the EM fields generated by these three transmitting coils are derived. A fast-forward-modeling algorithm to compute the responses of an induction tool was developed. Compared with the algorithm using the coefficient propagator method previously developed, the proposed algorithm calculates the generalized reflection and transmission coefficients only once for each layer regardless of the position of the transmitters, and therefore, it greatly speeds up the computation. The simulation code solves for all nine components of the magnetic field in a TI layered medium. Results of this new method were developed for several formation models, which agreed very well with the published data. For a dipping or nondipping case in a 28-layer formation, the proposed method was about 37 times faster, which was more appropriate to be used in an inversion algorithm.