Homogeneous Anisotropic Medium Research Articles

Time-reversed electromagnetic fields in anisotropic media.

Electromagnetic time reversal is commonly used for field imaging and focusing. This Letter builds upon the concept of the time-reversal cavity, which constitutes the main theoretical framework of time reversal theory. We study the behavior of the fields using modern methods of mathematical physics involving Colombeau generalized functions. This approach allows for a direct expression of time-reversed electric and magnetic fields in anisotropic time-reversal-invariant and nonreciprocal media. Moreover, the results hold for any arbitrary localized source and can readily be applied beyond the dipole approximation. Finally, a general result allows the prediction of the quality of focusing of the time-reversed fields as a function of the electrical permittivity and the magnetic permeability tensors in homogeneous anisotropic media, which contributes to the understanding of time reversal in complex media such as super-resolution enabling metamaterials.

Characterization of heterogeneities in the sandy facies of the Opalinus Clay (Mont Terri underground rock laboratory, Switzerland)

SUMMARY This contribution is presenting a multidisciplinary investigation of heterogeneities in a clay rock formation, based on seismic tomography, logging and core analysis, as a reconnaissance study for a diffusion experiment. Diffusion experiments in clay rock formations provide crucial experimental data on diffusive transport of radionuclides (RN) in extremely low hydraulic conductivity media. Previous diffusion experiments, conducted, for example, in the Mont Terri underground rock laboratory within the relatively homogeneous shaly facies of Opalinus Clay, and modelling studies of these experiments have demonstrated that the clay rock could sufficiently well be described as a homogeneous anisotropic medium. For other lithofacies, characterized by larger heterogeneity, such simplification may be unsuitable, and the description of heterogeneity over a range of scales will be important. The sandy facies of the Opalinus Clay exhibits a significantly more pronounced heterogeneity compared to the shaly facies, and a combined characterization and RN diffusion study has been initiated to investigate various approaches of heterogeneity characterization and subsequent diffusion in a heterogeneous environment. As an initial step, two inclined exploratory boreholes have been drilled to access the margins of the experiment location. These boreholes have been used to acquire a cross-hole tomographic seismic data set. Optical, natural gamma and backscattering logging were applied and rock cores were analysed. The integrated results of these investigations allowed the identification of an anomalous brighter layer within the investigated area of the sandy facies of approximately 1 m thickness and with its upper bound at roughly 10 m depth within the inclined exploratory wells. Mineralogical analyses revealed only slight variations throughout the rock cores and indicated that the anomalous layer exhibited a slightly higher quartz content, and locally significantly higher calcite contents, accompanied by a lower content of clay minerals. The anomalous layer was characterized by reduced natural gamma emissions, due to the lower clay content, and increased neutron backscattering likely indicating an increased porosity. Seismic P-wave velocities, derived from anisotropic tomography, exhibited a maximal gradient near the top of this layer. The transition from the overlaying darker rock matrix into this layer has been identified as an appropriate location for the setup of a tracer diffusion experiment in a heterogeneous environment.

Fraunhofer Diffraction by a Slit into a Homogeneous Anisotropic Medium

Fraunhofer Diffraction by a Slit into a Homogeneous Anisotropic Medium

Semi-Analytic Sensitivity of the MCIL Responses in Homogeneous Biaxial Anisotropic Media

We presented a semi-analytic solution for the sensitivity of the response tensor of the multi-component induction logging (MCIL) tool in a homogeneous biaxial anisotropic (BA) medium. By using the perturbation principle and the spectral representation of electromagnetic (EM) fields, the sensitivity was formulated as a seven-fold integral whose integrand involves two sets of spectral electric fields. Fortunately, such a complicated integral can be reduced to a three-fold integral, which consists of two parts: one is a definite integral over the spatial variable <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</i> that can be analytically integrated; the remaining is a two-fold integral over the spectral variable k that is computed by numerical quadrature. We verified our formulation by comparing it with the exact solution and the finite-difference (FD) approximation.

Theory of perturbation of electric potential by a 3D object made of an anisotropic dielectric material

The extended boundary condition method (EBCM) was formulated for the perturbation of a source electric potential by a 3D object composed of a homogeneous anisotropic dielectric medium whose relative permittivity dyadic is positive definite. The formulation required the application of Green’s second identity to the exterior region to deduce the electrostatic counterpart of the Ewald–Oseen extinction theorem. The electric potential inside the object was represented using a basis obtained by implementing an affine bijective transformation of space to the Gauss equation for the electric field. The EBCM yields a transition matrix that depends on the geometry and the composition of the 3D object, but not on the source potential.

On a surprising instability result of Perfectly Matched Layers for Maxwell’s equations in 3D media with diagonal anisotropy

The analysis of Cartesian Perfectly Matched Layers (PMLs) in the context of time-domain electromagnetic wave propagation in a 3D unbounded anisotropic homogeneous medium modelled by a diagonal dielectric tensor is presented. Contrary to the 3D scalar wave equation or 2D Maxwell's equations some diagonal anisotropies lead to the existence of backward waves giving rise to instabilities of the PMLs. Numerical experiments confirm the presented result.

Planar hyper-lens with uniform pre-designed magnification factor by homogeneous medium

A hyper-lens with planar object/image surfaces and uniform magnification factor is designed based on directional projecting property of optic-null medium (ONM). The proposed planar hyper-lens only requires one homogeneous anisotropic medium, i.e. ONM. We use metallic plates inside ϵ-near-zero medium to realize the proposed hyper-lens. 0.191λ 0 resolution is observed (0.238λ 0 can be clearly resolved) in experimental measurement, which consists very well with 3D numerical simulations and verifies the performance of the proposed planar hyper-lens. The planar hyper-lens with uniform pre-designed magnification factor may have some applications in super-resolution imaging technology.

Local fields and effective conductivity of composites with anisotropic components

A homogeneous anisotropic conductive medium with a set of anisotropic heterogeneities of arbitrary shapes is considered. Calculation of local fields in the medium subjected to arbitrary external fields is reduced to systems of volume integral equations. For numerical solution, these equations are discretized using Gaussian approximating functions concentrated at the nodes of a regular grid. The elements of the matrices of the discretized problems have form of 1D-integrals that can be tabulated. For regular node grids, these matrices have Teoplitz’ structures, and fast Fourier transform algorithms can be used for iterative solution of the discretized problems. The method is applied to calculation of fields around isolated anisotropic spherical and cylindrical inclusions in an anisotropic homogeneous host medium. The results are used for calculation of the tensor of effective conductivity of the medium containing random sets of cylindrical inclusions. The self-consistent effective field method is used for solution of the homogenization problem. Dependencies of the components of the tensor of the effective conductivity on the volume fraction and orientations of the inclusions are presented.

Optimization approach for axisymmetric electric field cloaking and shielding

In this paper we study inverse problems of electric conductivity that arise in the design of spherical shielding or cloaking shells and other functional devices used to control static electric fields. The shells are considered consisting of a finite number of layers filled with homogeneous isotropic or anisotropic medium. The inverse problems under study are reduced to control problems with the layers electric conductivities taken as controls. A different choice of minimized functionals allows us to solve a wide range of design problems using one approach. A numerical algorithm to solve these problems is based on particle swarm optimization. Various results of numerical experiments are discussed in order to find the most effective designs. The findings obtained in this study describe a broad set of specific easy-to-manufacture structures that have the highest cloaking or shielding performance in the class of layered shells.

Christoffel equation in the polarization variables

To study the topology of polarization fields in homogeneous anisotropic media, we formulate the classic Christoffel equation in the polarization variables and solve it for the slowness vectors of plane waves corresponding to a given polarization. This task might emerge in passive seismology when neither ray nor wavefront-normal direction of a body wave recorded by a single three-component seismometer is available, so that velocities or slownesses of plausible wave arrivals have to be inferred from the recorded direction of particle motion. Our analysis shows that, unless the Christoffel equation degenerates and yields an infinite number of different slowness vectors, the finite nonzero number of its real-valued solutions varies from one to four. Unexpectedly, we find a subset of triclinic solids in which the polarization field contains holes — there exist finite-size solid angles of polarization directions unattainable to any plane wave.

Single-shot measurement of the space-varying polarization state of light through interferometric quantification of the geometric phase

Light beam carrying spatially varying state of polarization generates space varying Pancharatnam-Berry geometric phase while propagating through homogeneous anisotropic medium. We show that determination of such space varying geometric phase provides a unique way to quantify the space varying polarization state of light using a single-shot interferometric measurement. We demonstrate this concept in a Mach-Zehnder interferometric arrangement using a linearly polarized reference light beam, where full information on the spatially varying polarization state is successfully recovered by quantifying the space varying geometric phase and the contrast of interference. The proposed method enables single-shot measurement of any space varying polarization state of light from the measured interference pattern with a polarized reference beam. This approach shows considerable potential for instantaneous mapping of complex space varying polarization of light in diverse applications, such as astronomy, biomedical imaging, nanophotonics, etc., where high precision and near real-time measurement of spatial polarization patterns are desirable.

Geometrical Optics of an Anisotropic Media with Space Modulated Gyrotropy

The problem of the polarized light propagation in an optically homogeneous anisotropic medium with spatially modulated gyrotropy is considered. The analysis was carried out using a numerical solution of a system of coupled equations obtained in the approximation of geometric optics. For illustrative purposes, the results of numerical analysis are also presented on the Poincare sphere. The resonance character of the dependence of the amplitude of polarization beats as a function of the spatial frequency of gyrotropy modulation is shown.

Surface transformation multi-physics for controlling electromagnetic and acoustic waves simultaneously.

A multi-physics null medium that performs as a perfect endoscope for both electromagnetic and acoustic waves is designed by transformation optics, which opens a new way to control electromagnetic and acoustic waves simultaneously. Surface transformation multi-physics, which is a novel graphical method to design multi-physics devices, is proposed based on the directional projecting feature of a multi-physics null medium. Many multi-physics devices, including beam shifters, scattering reduction, imaging devices and beam steering devices, for both electromagnetic and acoustic waves can be simply designed in a surface-corresponding manner. All devices designed by surface transformation multi-physics only need one homogeneous anisotropic medium (null medium) to realize, which can be approximately implemented by a brass plate array without any artificial sub-wavelength structures. Numerical simulations are given to verify the performances of the designed multi-physics devices made of brass plate array.

NUMERICAL-FIELD ANALYSIS OF THE CHARACTERISTICS OF A THREE-PHASE MAGNETIC FIELD INDUCTOR FOR THE TREATMENT OF VARIOUS SUBSTANCES WITH CURRENT STABILIZATION

Introduction. A three-phase magnetic field inductor (MFI) similar to the asynchronous motor stator, which provides processing of various substances, is considered. This is done by means of oblong ferromagnetic elements moving with a rotating magnetic field and located in its cylindrical working chamber. Problem. The aim of the work is to develop the theory and conduct practical calculations of the parameters and characteristics of the MFI that connect the electromagnetic quantities and their phase relationships in the mode of its load. Methodology. The studies are carried out on the basis of numerical calculations of the magnetic field in the MFI taking into account the ferromagnetic elements in its working chamber. The calculation model of the chamber is represented by a homogeneous anisotropic magnetic medium for which the method of determining different magnetic permeabilities by its longitudinal and transverse axes is given. In order to obtain the characteristics of the presented MFI, the method of determining the electromagnetic parameters and phase relationships of the quantities accompanying its operation has been developed. Results. The theory and results of numerical-field analysis of electromagnetic quantities, their phase relationships and corresponding characteristics of three-phase MFI are presented. Calculations of characteristics are made for the inductor load mode depending on the phase shift of the magnetomotive force of the stator winding relative to the longitudinal axis of the chamber and while ensuring the constant value of the current of this winding. The characteristics include magnetic flux coupling, EMF and stator winding voltage, phase shifts between them and current, electromagnetic moment, input and output power, electrical and magnetic loss power, power factor and efficiency. Practical value. The technique of numerical-field calculations of electromagnetic quantities and their phase relationships is developed, and also the set of characteristics which should promote designing and perfection of inductors of the considered type is received. The presented technique is universal as it allows to display their cores practically of any shape.

An inverse problem for the system of viscoelasticity equations in homogeneous anisotropic media

An inverse problem for the system of viscoelasticity equations in homogeneous anisotropic media

An Inverse Problem for the System of Viscoelasticity Equations in Homogeneous Anisotropic Media

Under study is the problem of reconstructing the memory function of a. viscoelastic medium from the system of viscoelastic equations for a. homogeneous anisotropic medium. As additional information, the Fourier image of the displacement vector with respect to the spatial variables for the values V0# 0 of the transformation parameter is given. It is demonstrated that, provided the data of the problem satisfy some conditions of agreement and smoothness, the solution of the problem is uniquely determined in the class of continuous functions and depends continuously on the given functions.

Time-Resolved Integrative Optical Imaging of Diffusion during Spreading Depression

An improved version of the integrative optical imaging method has been developed that substantially increases the time resolution of diffusion measurements. We present a theory for time-resolved integrative optical imaging that incorporates a time-dependent effective diffusion coefficient in homogeneous anisotropic media and a time-dependent nonspecific linear clearance. The method was applied to measure the very fast changes in extracellular diffusion that occur during spreading depression in rat hippocampal slices. We were able to achieve a time resolution of approximately 1 s, an improvement of at least 10 times compared to the standard methods for extracellular diffusion measurement. We have found that diffusion of a small fluorescent extracellular marker (MW 3000) completely stopped during the maximum direct current shift associated with the spreading depression wave, then gradually resumed over several minutes afterward. The effect of spreading depression on extracellular space is much larger than previously estimated by other methods with lower time resolution.

Plane Wave Solutions to the Equations of Electrodynamics in an Anisotropic Medium

Under examination is the system of equations of electrodynamics for a nonconducting nonmagnetic medium with the simplest anisotropy of permittivity. We assume that permittivity is characterized by the diagonal matrix ϵ = diag(e1, e1, e2), with the functions e1 and e2 equal to positive constants beyond a bounded convex domain Ω ⊂ ℝ3. Two modes of traveling plane waves exist in a homogeneous anisotropic medium. The structure is studied of the solutions related to the traveling plane waves incident from infinity on an inhomogeneity located in Ω.

Multi-scale shape optimisation of lattice structures: an evolutionary-based approach

This study deals with the problem of the least-weight design of a lattice structure subject to constraints of different nature. To face this problem, a general multi-scale optimisation procedure is proposed. This approach aims at optimising both global and local geometric parameters defining the shape of the representative volume element of the lattice at the mesoscopic scale. The optimisation procedure involves design requirements defined at different scales: geometric and manufacturing constraints are involved at the mesoscopic scale, whilst thermodynamic constraints on the positive definiteness of the stiffness tensor of the lattice (modelled as an equivalent homogeneous anisotropic medium) intervene at the macroscopic scale. Finally, since lattice structures usually undergo compressive loads, a requirement on the first local buckling load is considered too. The proposed approach is based on (a) the non-uniform rational basis splines curves theory to describe the shape of the struts composing the lattice, (b) the strain energy homogenisation technique of periodic media to perform the scale transition and (c) a special genetic algorithm to perform optimisation calculations. The optimised solutions provided by the presented method are characterised by a weight saving of about $$39\%$$ with slightly enhanced mechanical properties when compared to conventional octahedral lattice structures.

Stimulated Brillouin scattering in layered media: nanoscale enhancement of silicon.

We report a theoretical study of stimulated Brillouin scattering (SBS) in general anisotropic media, incorporating the effects of both acoustic strain and local rotation. We apply our general theoretical framework to compute the SBS gain for layered media with periodic length scales smaller than all optical and acoustic wavelengths, where such composites behave like homogeneous anisotropic media. We predict that a layered medium composing nanometer-thin layers of silicon and As2S3 glass has a bulk SBS gain of 1.28×10-9 W-1 m. This is more than 500 times larger than that of silicon and almost double the gain of As2S3. The enhancement is due to a combination of roto-optic, photoelastic, and artificial photoelastic contributions in the composite structure.