Planar Layered Media Research Articles

Near-Field Power Efficiency Maximization of a Bessel-Shaped Beam Through Planar Layered Media

Near-Field Power Efficiency Maximization of a Bessel-Shaped Beam Through Planar Layered Media

Fast Direct Solution of Electromagnetic Scattering From Metallic Objects in a Planarly Layered Medium

Fast Direct Solution of Electromagnetic Scattering From Metallic Objects in a Planarly Layered Medium

On the Surface Plasmonic Waves Excited by a Dipole Above Anisotropic and Spatially Dispersive Two-Dimensional Surfaces of Infinite Extent in Planarly Layered Media

The surface plasmonic waves excited by a vertical or horizontal oriented Hertzian dipole above anisotropic and spatially dispersive two-dimensional surfaces of infinite extent embedded in planarly layered uniaxial media are investigated using the dyadic Green function approach. The spectral-domain transmission line analogy Green function formulation and iso-frequency-contour equations are derived. The methods to accurately and efficiently evaluate the two-dimensional Fourier integral arising from the spatial-domain Green function computation are also developed. To resolve the numerical inefficiency due to the highly oscillatory integrand and singularities of surface plasmonic waves that possess large wavenumber, the methods of extrapolating the real-axis integration combined with singularity subtraction are proposed and found to be applicable to a wide range of observation distances. As an application example of the proposed formulation, we compute the scattered fields of a vertical dipole above the graphene biased by drift current which exhibits significant spatial dispersion. It is shown that the light-matter interaction of graphene plasmons can be significantly reinforced when placed above uniaxially anisotropic epsilon-near-zero substrates. The proposed formulation may provide the methodology for the computational analysis of two-dimensional materials and surface plasmonic waves.

Constituents of electromagnetic 2-D layered media Green's functions for all material types and radiation conditions

Layered media Green's functions (LMGFs) are obtained for line sources with complex longitudinal wavenumbers in planarly layered media by numerically evaluating Sommerfeld integrals. The results obtained in this article can be applied to the numerical analysis of structures in layered media composed of any combination of right-handed materials (RHMs) and left-handed materials (LHMs). In the derivation, due to the complex-valued longitudinal wavenumber values, two different boundary conditions are used to include plane waves with: (i) decaying and (ii) outgoing Poynting vectors in the LMGFs. As a result, two completely different LMGFs are obtained by using two different radiation conditions and corresponding Sommerfeld integration paths (SIP) that are rigorously tailored on the complex integrand plane. In this work, all the necessary numerical tools for calculating the 2-D LMGFs are provided to be implemented in a computer program from scratch.

Features of radiothermal study of ice in the microwave range

The subject of the study is ice formations, which are formed as a result of the release of groundwater to the surface of ice sheets or soil. These formations cause significant damage in human economic activity. The work investigated natural ice located on fresh ice cover, as well as artificial ice formations on the ground. The glaciers located in the Transbaikal region near the city of Chita were investigated. The power of thermal radiation of these objects in the microwave range was determined at wavelengths of 2.3 cm and 0.88 cm. The power of thermal radiation in the microwave range was determined using radiometric receivers at wavelengths of 0.88 cm and 2.3 cm mounted on a car or on a fixed support. Cores of ice removed from the ice were studied to determine the layer-by-layer distribution of ice mineralization. A model of a plane-layered non-isothermal medium was used to calculate the thermal radiation of ice. The possibility of registering ice formations by radiothermal radiation of these objects in the microwave range is shown. If there is a layer of water on the ice, the radio brightness temperature will be significantly lower than the object on the surface of which there is no water mass. By the value of the radio brightness temperature in the microwave range for several ranges, as a result of which it is possible to indirectly estimate the thickness of ice formations. At the same time, it is necessary to take into account the variations in the radiofrequency temperature of the medium depending on its thickness due to the interference of radiothermal radiation of a plane-layered medium.

Heat Conduction Problem for a Nonstationary Point Heat Source in a Plane-Layered Medium

Heat Conduction Problem for a Nonstationary Point Heat Source in a Plane-Layered Medium

Development and generalization of the method of reflections in problems of electrostatics and thermal conductivity of plane-layered media

The method of mirror reflections of electrostatics for a point charge located next to a plane-layered medium consisting of a single film on a dielectric half-space is formulated. The method is generalized to the case of an arbitrary system of charges. The proposed approach is applied to mathematically similar problems of electrostatics and stationary heat conduction of plane-layered media. In particular, the problems of finding distributions of the electrostatic potential around a conducting sphere, an ellipsoid of revolution and a drop-shaped body located near the dielectric film on the dielectric half-space. It is shown how to apply the results obtained for electrostatic problems to similar problems of finding the temperature distribution of uniformly heated bodies of the same geometry located near a heat-conducting film in a heat-conducting half-space. Keywords: plane-layered medium, mirror reflection method, electrostatics, thermal conductivity.

Развитие и обобщение метода отражений в задачах электростатики и теплопроводности плоскослоистых сред

The method of mirror reflections of electrostatics for a point charge located next to a plane-layered medium consisting of a single film on a dielectric half-space is formulated. The method is generalized to the case of an arbitrary system of charges. The proposed approach is applied to mathematically similar problems of electrostatics and stationary heat conduction of plane-layered media. In particular, the problems of finding distributions of the electrostatic potential around a conducting sphere, an ellipsoid of revolution and a drop-shaped body located near the dielectric film on the dielectric half-space. It is shown how to apply the results obtained for electrostatic problems to similar problems of finding the temperature distribution of uniformly heated bodies of the same geometry located near a heat-conducting film in a heat-conducting half-space.

An Adaptive Rational Fitting Technique of Sommerfeld Integrals for the Efficient MoM Analysis of Planar Structures

The integral equation method is one of the most successful computational models for microwave devices or integrated circuits in planar layered media. However, the efficient and accurate evaluation of the associated Green’s function consisting of Sommerfeld integrals (SIs) is still a remaining challenge. To mitigate this difficulty, this work proposes a spatial domain rational function fitting technique (RFFT) for SIs so that the approximation accuracy is controllable. In conjunction with an adaptive sampling strategy, the proposed RFFT minimizes the orders of rational functions, and the resultant SI evaluation efficiency is optimized. In addition, we investigate the semi-analytical singularity treatment for the rational expression of SIs in method of moment (MoM) implementation. Extensive simulation of representative planar devices validates the correctness of the proposed method and demonstrates its superior performance over conventional SI approximation methods.

Quadruple-Dyadic Spectral Green's Functions of Current Sources in Planar Layered Media: Application to Plasmonic Layer-Structures

Quadruple-Dyadic Spectral Green's Functions of Current Sources in Planar Layered Media: Application to Plasmonic Layer-Structures

Scattering evaluation of an infinite PEC plane coated with an anisotropic medium under arbitrary source excitation

A spectral-domain asymptotic method based on the dyadic Green’s function is proposed to study the electromagnetic (EM) scattering of an infinite perfectly conducting (PEC) plane coated with a uniaxial electric anisotropic medium (UEAM) under arbitrary source excitation. We specifically analyze the ray propagation path of the incidence wave from the individual point source, which acts at the planar-layered medium structure to obtain the dyadic Green’s functions (DGFs) of different types of EM waves. These DGFs from the reflected, transmitted, and entire secondary scattered fields are employed to establish the relationship between the arbitrary excitation source and different types of scattered fields. According to the corresponding “source-field” connection between the excitation source and the scattered field components in the spectral domain, we can first derive the expression of the spectral-domain DGF matrix components and then use the saddle point method to obtain the spatial-domain dyadic Green’s function. Finally, we use the integral equation solution to construct the scattered field for an infinite PEC plane coated with the UEAM layer under arbitrary source excitation. The comparison of simulation results from the proposed method and the method of moments (MoM) method confirms the algorithm validation. So it is expected to be a valid algorithm for dealing with electrically large and complex targets coated with the UEAM layer under any source excitation in the future.

Mode analysis of plasmonic waveguides in planarly layered media

Spectral properties of the modes supported by plasmonic waveguides in planarly layered media are studied by the method of Multiple MultiPoles (MMP). It is shown that the most important entities in the mode analysis are the wavenumbers of the upper and lowermost layers and the wavenumbers of the guided waves supported by the layered medium. These wavenumbers introduce branch points and associated branch cuts on the complex plane where the out-of-plane wavenumbers of the modes are searched. These branch points and associated cuts make the mode analysis in layered media more demanding than the mode analysis in homogeneous media, where there is only one branch point and associated branch cut related to the wavenumber of the homogeneous medium. Several numerical examples are given to address the differences introduced by the layered media in the mode analysis and guidelines that can be used in any well-known computational electromagnetics method are provided.

Efficient Electromagnetic Modeling of Multidomain Planar Layered Medium by Surface Integral Equation

A novel electromagnetic modeling method for multidomain planar layered medium (MD-PLM) by surface integral equation (SIE) is proposed. The MD-PLM refers to the whole space that is separated into multiple PLM volumes, e.g., the infinite-sized PLM background with inserted finite PLM objects or multilayered parallel-plate structures. In the conventional SIE method for this scenario, only the exterior domain is considered as PLM that is modeled by layered medium Green's functions (LMGFs), while the interior domain is treated by the multidomain homogeneous SIE. However, in this work, the surface equivalence formulation for this special scenario is reestablished by the LMGFs. Then, both the exterior and interior domains are considered as PLM that is modeled by the corresponding LMGFs and SIE in each subdomain. As a result, only the boundary of each sub-PLM domain is required to be discretized rather than the interfaces of each interior medium, which is different from the way in conventional SIE. Consequently, compared with the conventional SIEs, the proposed method can reduce a large quantity of unknowns and significantly increase the efficiency by reducing the memory consumption. By some numerical examples, the performance of this method is evaluated and compared with the conventional methods. The validity and efficiency of the newly proposed method are also well demonstrated in the examples.

Use of Abcd-Matrix Method For The Simulation of Laser-Ultrasonic Probing Pulse Propagation In A Layered Medium of The Optical-Acoustic Transducer

As a first step methods for modeling the propagation of acoustic waves in layered media was analyzed and the need to develop a new, faster method is substantiated. As a consequence, presented a method for modeling the propagation of elastic waves based on signal transformation using ABCD matrices, for the implementation of which a computer program in the Python language has been developed. For the verification of the method was analyzed the correlation between the simulated signal and the signal obtained experimentally from a medium with predetermined parameters. Further on the basis of the data obtained, the applicability of this method for modeling the propagation of acoustic signals in a plane-layered medium has been proved. As a next step modern methods of ultrasound generation and their influence on the characteristics of the probing signal was reviewed. Confirmed that laser-ultrasound techniques allow the best control over the characteristics of the probe signal. Therefore, the influence of the duration of the laser pulse, the properties of light absorption and the acoustic characteristics of the generator medium on the probing signal amplitude and bandwidth of the spectrum was estimated. To reduce the influence of the considered characteristics on the diagnostic process using the ABCD-matrix method the optimal characteristics of the optical-acoustic transducer for diagnostics at low frequencies have been determined. Finally, the main advantage of the proposed modeling method is the high speed of calculating the shape and spectrum of the signal at any point in the medium at a given time.

Radar methods for determining the thickness of dielectric layers

This paper describes two methods, the amplitude method and the method based on geometric optics. The methods were applied to practical data obtained by georadar tests. As a result, the refractive index and thickness of the investigated planar layered medium were calculated. When using the amplitude method, the refractive index of the investigated medium is 1.3, the thickness is 0.11 m. When using the method based on geometric optics, the refractive index of the investigated medium is 1.43, the thickness is 0.102 m. After comparing the results of these methods, it was found that the error of the amplitude method is higher than that of the geometrical optics method.

Interaction of an electromagnetic wave with a plane-layered medium

For protection from high-temperature aerodynamic heating, the on-board antennas of reentry spacecraft are covered with heatresistant radio-transparent thermal protection. Aerodynamic heating, in addition to the actual heating of the antenna thermal protection up to melting, causes the formation of a plasma formation covering the antenna. Thus, the antenna emits media through a multilayer medium: solid heat shield, melt heat shield, plasma. The effect of the multi-layer environment covering the antenna often leads to the loss of radio communications on the descent trajectory. The assessment of the presence of radio communication is possible only on the basis of the results of the study of the interaction of an electromagnetic wave with a multilayer dielectric medium. The work investigates the radiation of a plane wave through a multilayer dielectric medium. Expressions are obtained for the complex transmission and reflection coefficients of a three-layer medium, one of the layers of which is a plasma formation. The developed analytical relationships characterizing the interaction of an electromagnetic wave with a multilayer dielectric medium make it possible to determine the characteristics of the board-to-ground communication channel and the presence or absence of radio communication on the descent trajectory.

Numerical simulation of seismic waves in porous media components

This work presents a mathematical algorithm for modeling the propagation of poroelastic waves. We have shown how the classical Biot equations can be put into Ursin’s form in a plane-layered 3D porous medium. Using this form, we have derived explicit for- mulas that can be used as the basis of an efficient computational algorithm. To validate the algorithm, numerical simulations were performed using both the poroelastic and equivalent elastic models. The results obtained confirmed the proposed algorithm’s reliability, identify- ing the main wave events in both low-frequency and high-frequency regimes in the reservoir and laboratory scales, respectively. We have also illustrated the influence of some physical parameters on the attenuation and dispersion of the slow wave.

Solution of the Problem of Diffraction by a Plane Screen in a Plane Layered Medium with the Help of the Method of Continued Boundary Conditions

The 3D problem of diffraction of the field of a point source by a plane screen located on the interface of a plane layered medium is considered. The algorithm of the numerical solution of this problem is developed on the basis of the method of continued boundary conditions. In particular, the case, when the screen is located on the interface between two media and on the upper boundary of a dielectric layer surrounded by identical dielectric half-spaces, is considered. The correctness of the obtained results is controlled by verifying the accuracy of the fulfillment of the optical theorem. The angular dependences of the scattering pattern are constructed for the screens having circular, rectangular, and elliptic shapes.

A Surface Integral Equation Formulation for Efficient Simulation of Finite-Sized Multilayered Parallel-Plate Structure

The multilayered parallel-plate structure (MPPS) is a typical structure in microwave engineering. In numerical simulation, MPPS is usually modeled by an infinitely large planarly layered medium (PLM) to simplify the computation. For a realistic microwave circuit, however, the substrate is always finite in spatial extent, i.e., it is a finite-sized MPPS (FS-MPPS). To address this issue, a novel surface integral equation (SIE) formulation is proposed for the efficient simulation of FS-MPPS. In this article, the surface equivalence principle is first revisited. For the exterior and interior problems, different Green’s functions are utilized. In particular, the common homogeneous-medium Green’s function is used for the exterior homogeneous region, whereas the layered-medium Green’s function (LMGF) is applied for the interior multilayered structure. In this manner, FS-MPPS is no longer directly approximated by the infinite PLM model, but instead, it is modeled accurately by SIE whose integration kernel is derived from PLM. Finally, a PMCHWT SIE is established for the electromagnetic analysis of FS-MPPS. Due to the finite nature of the inner problem, the setting of PLM and LMGF is not unique. This nonuniqueness is studied in theory and verified by numerical simulation. It is revealed that such a nonuniqueness of the setting of the inner problem does not change the uniqueness of the final solution. To validate the proposed approach, a multidomain FS-MPPS and an FS-MPPS with embedded dielectric structures are investigated. Compared with the conventional brute-force SIE methods for FS-MPPS, where all the interfaces of the layered structure should be discretized and assigned with degrees of freedom (DOFs), the proposed method is more succinct and efficient.

Numerical Simulation and Analysis of Multicomponent Induction Logging Response in Anisotropic Formation

In this article, the response characteristics of multicomponent induction logging (MCIL) tool in anisotropic formation are analyzed. To solve the 1-D MCIL problems, we use a planar layered anisotropic medium (PLAM) Green's function (PLAMGF) method which is derived from the layered-medium Green's function (LMGF) and combined with MCIL excitation source and anisotropic formation environment, and then use it to investigate the equivalence of the MCIL tool responses in two models, i.e. the microscopic thin interbed formation and macroscopic anisotropic formation, and also analyze the effects of shoulder bed and formation dip on MCIL tools. In addition, in order to solve the complex 3-D problems, such as the effects of borehole, tool eccentricity and invasion on the tool response, we use the finite element method (FEM) based on a proposed new meshing scheme to simulate and analyze. This new meshing scheme includes two aspects: the use of cylindrical hexahedron element and the flexible meshing strategy combined with domain decomposition. Finally, some key detection performances of coaxial coils and coplanar coils of MCIL tool are studied. Numerical experiments are conducted to prove the effectiveness of our proposed method and provide the detailed results of the aforementioned aspects.