Dielectric Permeability Tensor Research Articles

A point-to-point convolutional neural network for reconstructing electromagnetic parameters of multiple cavities scattering with inhomogeneous anisotropic media

We propose a point-to-point convolutional neural network (CNN) model to reconstruct the electromagnetic parameters of multiple cavities filled with inhomogeneous anisotropic media. The input of the model is a grid matrix of electromagnetic field magnitude solved by Petrov–Galerkin finite element interface method, and the output is a distribution matrix of the electromagnetic parameters of the cavities. The uniform non-body-fitted mesh is set in the computational domain, which does not need to be updated repeatedly at the complex interfaces of different media. Compared with the standard finite element, this mesh reduction method effectively saves the cost of mesh generation. Level set functions are applied to capture these arbitrarily shaped interfaces. The matrix coefficients caused by the dielectric constant and permeability tensors of anisotropic media can also be handled with this method. The point-to-point CNN model effectively reconstructs the value and the distribution of electromagnetic parameters in the cavities, also predicting the shape and the position of the interfaces. Three optimized schemes are then proposed to improve reconstruction accuracy. Numerical results show that the size of the convolution kernel and the number of fully connected layers are the crucial parameters in determining interfaces and reducing the number of artefacts.

Surface electromagnetic waves in anisotropic superlattices

This paper studies the existence of electromagnetic surface waves localized on a boundary of half-infinite periodic superlattices formed by an arbitrary periodic sequence of layers of homogeneous or functionally graded materials with generally anisotropic dielectric permittivity and magnetic permeability tensors. The geometry in question implies either two superlattices attached together to form a photonic bicrystal or else a superlattice in contact with vacuum or any other homogeneous dielectric or metal. Using the formalism of transfer and impedance matrices, a series of statements is proved on the maximum number of surface waves which may exist within a forbidden band at a fixed tangential wave number. This number embraces possible occurrences of surface waves in a given bicrystal and in its counterpart obtained by swapping the upper and lower superlattices. A maximum total number of surface waves in both these structures with an arbitrary arrangement of their unit cells is 2 in the lowest forbidden band (extending from zero frequency) and 4 in any upper forbidden band. The same statements apply to the case where one of the half spaces is occupied by a homogeneous material. A factor 2 smaller number of surface waves occur in a bicrystal composed of superlattices with a symmetric arrangement of unit cells. The existence considerations are further specialized for the surface waves with TE and TM polarizations.

Optical analogues to the equatorial Kerr\u2013Newman black hole

Optical analogues to black holes allow the investigation of general relativity in a laboratory setting. Previous works have considered analogues to Schwarzschild black holes in an isotropic coordinate system; the major drawback is that required material properties diverge at the horizon. We present the dielectric permittivity and permeability tensors that exactly reproduce the equatorial Kerr–Newman metric, as well as the gradient-index material that reproduces equatorial Kerr–Newman null geodesics. Importantly, the radial profile of the scalar refractive index is finite along all trajectories except at the point of rotation reversal for counter-rotating geodesics. Construction of these analogues is feasible with available ordinary materials. A finite-difference frequency-domain solver of Maxwell’s equations is used to simulate light trajectories around a variety of Kerr–Newman black holes. For reasonably sized experimental systems, ray tracing confirms that null geodesics can be well-approximated in the lab, even when allowing for imperfect construction and experimental error.

Homogenization method for one-dimensional photonic crystals with magnetic and chiral inclusions

We have theoretically investigated the electromagnetic properties for one-dimensional (1D) photonic crystals with magnetic and artificial chiral inclusions in the quasi-static limit, that is when the size of the unit cell of the crystal is small with respect to the wavelength of the operating wave. We suggest a homogenization theory to determine the effective tensors of the optical response, to achieve this objective, we apply the Bloch’s plane waves method to describe the electromagnetic modes that can propagate in the periodic structure under consideration. Subsequently, the Maxwell’s “microscopic” equations are homogenized replacing the Bloch waves by plane waves that attenuate the fast oscillations of the electromagnetic fields within the unit cell (macroscopic level), i.e., the average-macroscopic electromagnetic fields are determined by the component corresponding to the null reciprocal lattice vector in the expansion in plane waves. The numerical implementation of our theory of homogenization allow us to study the effective bianisotropic electromagnetic response (effective dielectric permittivity, magnetic permeability and electric-magnetic coupling tensors, this last is described by an effective chiral parameter) for 1D photonic crystals whose constituents in its unit cell are a dielectric layer and another magnetic (both isotropic and anisotropic) or chiral inclusion layer. The results are illustrated and discussed by the effective parameters as a function of the filling fraction of the inclusion and show for each case of homogeneous effective medium different components of anisotropy in the electromagnetic response of permittivity, permeability and chirality with the increase of the filling fraction. Besides, the behaviors of the obtained graphs agree well with Rytov’s formulas of effective medium. The relevant results of this theory will be very useful for the study and better understanding of the nature and design of metamaterials with predetermined anisotropic optical properties.

Study and Research the Tensor of Dielectric Permittivity and Attenuation Transient in the Bended on Spiral Optical Fiber

This paper investigates the assumption of spiralshaped index leads to an optimal result for the optical fiber modes. It also shows how to decrease the effect of optical fibers parameters such as attenuation and dispersion on the quality of transmitted signals, and to improve it into an acceptable form. The dielectric permeability tensor εij related to the curvature and torsion parameters ( χ , υ ) in the coordinates system ( r, φ ) was analyzed. The dependence of εij tensor on the bent on spiral optical fiber parameters was mathematically calculated. Also to study the exchange of power between the waves HEo 11 and HEe 11 .The Transient attenuation dependence on spiral parameters of optical fiber with a length of (one kilometer) as a case study will be studied also.

Homogenization of the dielectric and magnetic permeability tensors for anisotropic and bianisotropic layered media

The paper deals with the problem of calculating the effective properties of a multilayer system consisting of layers of anisotropic or bianisotropic media. It is assumed that the electromagnetic field is described by the Maxwell equations, and the layers are coordinate surfaces in some orthogonal coordinate system. No assumptions are made in advance about the properties of the dielectric and magnetic permeability tensors. The thickness of the layers is considered to be small in comparison with the wavelengths of all waves that can propagate in the system (long-wave approximation) and in comparison with the curvature radii of the layers as well as with the characteristic size of inhomogeneity in the layers. To construct an approximate solution, it is proposed to use a generalization of the matrix homogenization method. For the applicability of the method, it is necessary to rewrite the system of initial equations for a layered medium in a special form. The main advantage of the proposed approach, to find the parameters of an effective medium, is the absence of the need to solve complex partial differential equations. It is enough only to operate with matrices. The matrix homogenization method also makes it possible to obtain effective characteristics of a periodic structure with each period consisting of a set of thin layers. The study is illustrated by examples of finding effective tensors of dielectric and magnetic permeabilities for a system of planar, cylindrical, and spherical layers. In addition, the dependence of the magnetoelectric coefficient on the layer thicknesses for the cases listed above are compared.

On the exact nature of the coupled-fields of magneto-electro-elastic ellipsoidal inclusions with non-uniform eigenfields and general anisotropy

Abstract The current work reveals the exact nature of the induced interior and exterior coupled-fields of magneto-electro-elastic ellipsoidal inclusions with non-uniform generalized eigenfields, consisting of eigenstrain, eigenelectric, and eigenmagnetic fields. The medium has general rectilinear anisotropic elastic moduli, piezoelectric, piezomagnetic, dielectric, magneto-electric, and magnetic permeability tensors. The non-uniform eigenfields are assumed to be representable as the product of any arbitrary functions whose arguments are the equation of the boundary of the ellipsoidal inclusion with homogeneous polynomials. As a special case, it has been proved that the homogeneous polynomial eigenstrain, eigenelectric, and eigenmagnetic fields simultaneously induce inhomogeneous polynomial strain, electric, magnetic, stress, electric displacement, and magnetic induction fields of the same degree at the interior points of the inclusion. Certain series forms of the eigenfields in cylindrical coordinates are also treated. A special class of impotent eigenstrain, eigenelectric, and eigenmagnetic fields which give rise to vanishing strain, electric, and magnetic fields within the ellipsoidal domain is introduced and proved. Furthermore, the energies pertinent to the magneto-electro-elastic inclusions with arbitrary geometries and eigenfields are formulated. Also, the exact analytical expressions of the magneto-electro-elastic jump conditions of the generalized stress and the gradient of the generalized displacement fields are obtained. A number of theorems, lemmas, and corollaries in connection with the exact nature of the solution are stated and proved for the first time. The presented formulations and theoretical developments are of great value in the determination of the exact induced interior and exterior coupled-fields of anisotropic quantum wire/quantum dot structures as well as anisotropic piezoelectric/piezomagnetic composites.

Dielectric permeability tensor and linear waves in spin-1/2 quantum kinetics with non-trivial equilibrium spin-distribution functions

A consideration of waves propagating parallel to the external magnetic field is presented. The dielectric permeability tensor is derived from the quantum kinetic equations with non-trivial equilibrium spin-distribution functions in the linear approximation on the amplitude of wave perturbations. It is possible to consider the equilibrium spin-distribution functions with nonzero z-projection proportional to the difference of the Fermi steps of electrons with the chosen spin direction, while x- and y-projections are equal to zero. It is called the trivial equilibrium spin-distribution functions. In the general case, x- and y-projections of the spin-distribution functions are nonzero which is called the non-trivial regime. A corresponding equilibrium solution is found in Andreev [Phys. Plasmas 23, 062103 (2016)]. The contribution of the nontrivial part of the spin-distribution function appears in the dielectric permeability tensor in the additive form. It is explicitly found here. A corresponding modification in the dispersion equation for the transverse waves is derived. The contribution of the nontrivial part of the spin-distribution function in the spectrum of transverse waves is calculated numerically. It is found that the term caused by the nontrivial part of the spin-distribution function can be comparable with the classic terms for the relatively small wave vectors and frequencies above the cyclotron frequency. In a majority of regimes, the extra spin caused term dominates over the spin term found earlier, except the small frequency regime, where their contributions in the whistler spectrum are comparable. A decrease of the left-hand circularly polarized wave frequency, an increase of the high-frequency right-hand circularly polarized wave frequency, and a decrease of frequency changing by an increase of frequency at the growth of the wave vector for the whistler are found. A considerable decrease of the spin wave frequency is found either. It results in an increase of module of the negative group velocity of the spin wave. The found dispersion equations are used for obtaining of an effective quantum hydrodynamics reproducing these results. This generalization requires the introduction of the corresponding equation of state for the thermal part of the spin current in the spin evolution equation.

Kinetic analysis of spin current contribution to spectrum of electromagnetic waves in spin-1/2 plasma. I. Dielectric permeability tensor for magnetized plasmas

The dielectric permeability tensor for spin polarized plasmas is derived in terms of the spin-1/2 quantum kinetic model in six-dimensional phase space. Expressions for the distribution function and spin distribution function are derived in linear approximations on the path of dielectric permeability tensor derivation. The dielectric permeability tensor is derived the spin-polarized degenerate electron gas. It is also discussed at the finite temperature regime, where the equilibrium distribution function is presented by the spin-polarized Fermi-Dirac distribution. Consideration of the spin-polarized equilibrium states opens possibilities for the kinetic modeling of the thermal spin current contribution in the plasma dynamics.

Kinetic analysis of spin current contribution to spectrum of electromagnetic waves in spin-1/2 plasma. II. Dispersion dependencies

The dielectric permeability tensor for spin polarized plasmas derived in terms of the spin-1/2 quantum kinetic model in six-dimensional phase space in Part I of this work is applied for study of spectra of high-frequency transverse and transverse-longitudinal waves propagating perpendicular to the external magnetic field. Cyclotron waves are studied at consideration of waves with electric field directed parallel to the external magnetic field. It is found that the separate spin evolution modifies the spectrum of cyclotron waves. These modifications increase with the increase of the spin polarization and the number of the cyclotron resonance. Spin dynamics with no account of the anomalous magnetic moment gives a considerable modification of spectra either. The account of anomalous magnetic moment leads to a fine structure of each cyclotron resonance. So, each cyclotron resonance splits on three waves. Details of this spectrum and its changes with the change of spin polarization are studied for the first and second cyclotron waves. A cyclotron resonance existing at $\omega\approx0.001\mid\Omega_{e}\mid$ due to the anomalous magnetic moment is also described, where $\mid\Omega_{e}\mid$ is the cyclotron frequency. The ordinary waves does not have any considerable modification. The electrostatic and electromagnetic Berstein modes are studied during the analysis of waves propagating perpendicular to the external magnetic field with the electric field perturbation directed perpendicular to the external field. A modification of the oscillatory structure caused by the equilibrium spin polarization is found in both regimes. Similar modification is found for the extraordinary wave spectrum.

Indefinite by Nature: From Ultraviolet to Terahertz

A class of strongly anisotropic materials having their principal elements of dielectric permittivity or magnetic permeability tensors of opposite signs, so-called indefinite or hyperbolic materials, has recently attracted significant attention. These materials enabled such novel properties and potential applications as all-angle negative refraction, high density of states, and imaging beyond the diffraction limit using a so-called hyperlens. While several studies identified a few examples of negative refractions in birefringent crystals existing in nature, the majority of optical materials with hyperbolic dispersion relations known to date are engineered composite materials, “metamaterials”, such as metal-dielectric subwavelength multilayered structures or metal nanowires in a dielectric matrix. In this paper, we investigate naturally existing hyperbolic materials with indefinite permittivity for a range of frequencies from terahertz to ultraviolet. These include graphite, MgB2, cuprate, and ruthenate. Sp...

П’ЄЗООПТИЧНИЙ ЕФЕКТ ПОГЛИНАЛЬНОГО СЕРЕДОВИЩА

Розглянуто застосування п’єзооптичного ефекту поглинального середовища для визначення параметрів напружено-деформованого стану. Проведено аналіз дійсної та уявної частини тензора діелектричної проникності. Показано, що зміни дійсної частини тензора діелектричної проникності, а саме показника заломлення n, фіксуються інтерференційними методами механіки, а зміни уявної частини (натурального показника поглинання α) можна вимірювати шляхом аналізу поглинання світла і, таким чином, визначати напружено-деформований стан

Synchrotron radiation-based far-infrared spectroscopic ellipsometer with full Mueller-matrix capability

We developed far-IR spectroscopic ellipsometer at the U4IR beamline of the National Synchrotron Light Source in Brookhaven National Laboratory. This ellipsometer is able to measure both, rotating analyzer and full-Mueller matrix spectra using rotating retarders, and wire-grid linear polarizers. We utilize exceptional brightness of synchrotron radiation in the broad spectral range between about 20 and 4000 cm(-1). Fourier-transform infrared (FT-IR) spectrometer is used for multi-wavelength data acquisition. The sample stage has temperature variation between 4.2 and 450 K, wide range of θ-2θ angular rotation, χ tilt angle adjustment, and X-Y-Z translation. A LabVIEW-based software controls the motors, sample temperature, and FT-IR spectrometer and also allows to run fully automated experiments with pre-programmed measurement schedules. Data analysis is based on Berreman's 4 × 4 propagation matrix formalism to calculate the Mueller matrix parameters of anisotropic samples with magnetic permeability μ ≠ 1. A nonlinear regression of the rotating analyzer ellipsometry and∕or Mueller matrix (MM) spectra, which are usually acquired at variable angles of incidence and sample crystallographic orientations, allows extraction of dielectric constant and magnetic permeability tensors for bulk and thin-film samples. Applications of this ellipsometer setup for multiferroic and ferrimagnetic materials with μ ≠ 1 are illustrated with experimental results and simulations for TbMnO3 and Dy3Fe5O12 single crystals. We demonstrate how magnetic and electric dipoles, such as magnons and phonons, can be distinguished from a single MM measurement without adducing any modeling arguments. The parameters of magnetoelectric components of electromagnon excitations are determined using MM spectra of TbMnO3.

Lattice models of nontrivial “optical spaces” based on metamaterial waveguides

Metamaterials are being used to model various exotic "optical spaces" for such applications as novel lenses and cloaking. While most efforts are directed toward the engineering of continuously changing dielectric permittivity and magnetic permeability tensors, an alternative approach may be based on lattices of metamaterial waveguides. Here we demonstrate the power of the latter technique by presenting metamaterial lattice models of various four-dimensional spaces.

Dielectric Permeability of Nanocylinder

In the nanocylinder, a cut-off from the molecular crystal, dielectric permeability tensor is investigated. Excitons in the nanocylinder arise due to the exciting of the electron subsystem of the molecule. In evaluation of dielectric permeability Dzhyaloshinskii–Pitaevskii approach is used, connected with retarded and advanced exciton Green’s functions and correct use of Paulion Green’s function. It turned out that refraction and absorption indices depend on configuration coordinates, having maximal values at boundary cross-sections and minimal value at central cross-section of the nanocylinder broken symmetry structure. Although it was expected that boundary conditions make higher refractive and absorptive characteristics of the nanocylinder, this appeared not to be possible because Paulion Green’s function is not proportional to the exciton concentration.

The long-wave theory of N pairwise alternate homogeneous and heterogeneous layers difraction

Basic physics of theory is comparison of electrodynamic properties of heterogeneous media of nonuniform layer with chaotic or regular distribution of scatterers with small wave size and uniform anisotropic media with efficient values of components of dielectric permittivity and magnetic permeability tensors. Scattering coefficients of perpendicular and parallel polarization waves of bounded sequence are obtained by using circuit theory and matrix functions methods. We consider thick periodic grates of magnetodielectric bars with equal and orthogonal symmetry lines orientation and different geometrical and material parameters as two periodic nonuniform layers. We proved direct analytic formulas, which describe width and position of quasitransparency (quasicutoff) zones of band-pass and resonant wave passage and its dynamics on parametric relations of reflection factors. It is discovered effects that prove an opportunity of investigated structure usage in multifunctional electromagnetic field directors.

On the Crystal Optics of TlInS 2 Crystals in Incommensurate Phase

We studied the linear and nonlinear optical properties of soliton regime of incommensurate phase of crystals TlInS 2 . The space dependence of the dielectric permeability and nonlinear susceptibility tensors is determined. The characteristic matrices for soliton regime of incommensurate phase are found by solving the linear and nonlinear Maxwell equations. The transmission coefficient in modulated incommensurate phase is shown to be an oscillation function of temperature. The temperature dependence of the intensity of the second harmonic is established. It is shown that the intensity of the second harmonic in an incommensurate phase increases with temperature decreasing. We compare the obtained results with experiment.

A Domain Decomposition Method for the Solution of Large Electromagnetic Scattering Problems

A domain decomposition method (DDM) is presented for the solution of electromagnetic scattering problems by inhomogeneous 3-D bodies. The computational domain is partitioned into concentric subdomains on the interfaces of which Robin-type transmission conditions are prescribed. On the outer boundary terminating the computational domain, the radiation condition is taken into account by prescribing either an integral equation (IE) or an absorbing boundary condition. In the former case, the DDM decouples the inner problems, that correspond to the solution of Maxwell's equations inside each subdomain, from the outer problem solved by employing the IE. The convergence of the DDM algorithm to the solutions of the original problems is demonstrated when the dielectric permittivity and magnetic permeability tensors characterizing the inhomogeneous medium are those of passive materials.

Statistical Methods for Property Calculation of Textured Materials

Statistical methods for calculating the effective static and dynamic characteristics of textured microheterogeneous materials such as polycrystals, composites and rocks are considered. Effective static characteristics based on the example of the elastic modules tensor are analyzed. Effective dynamic characteristics based on the example of the dielectric permeability tensor in calculating the scattering factor, phase and group velocities of the propagation of plane electromagnetic waves are presented.

Extending the Euler-Heisenberg Lagrangian to some nonperturbative and inhomogeneous field configurations.

In this paper we discuss the Euler-Heisenberg effective Lagrangian in nonperturbative and inhomogeneous field configurations characterized by a strong magnetic field of the form ${\mathit{B}}_{\mathit{x}}$=${\mathit{B}}_{\mathit{y}}$=0,rotectinebreak ${\mathit{B}}_{\mathit{z}}$=B(x,y). Our treatment exploits some interesting properties of the second-order Dirac Hamiltonian describing the electronic motion in the transverse plane (x,y). In particular, we take advantage of the existence of an energy gap separating the excited states from the lowest-lying modes. The latter are exactly calculable and give the leading nontrivial contribution to the effective Lagrangian. Our results show that the presence of gradients can be accounted for by introducing an effective magnetic field strength defined as the sum of the square moduli of the ground state wave functions. This surprisingly simple conclusion is mainly due to a quantum-mechanical supersymmetry of the problem, that of the second-order Dirac Hamiltonian in the transverse plane (x,y). We recall that the same supersymmetry plays an important role for the spontaneous mass generation in the Nambu\char21{}Jona-Lasinio model interacting with an external magnetic field. As a simple application of our effective Lagrangian, we discuss the asymptotic behavior of the dielectric permeability tensor of the vacuum as a function of the external field configuration. No anomalous enhancement of the effective electromagnetic coupling is observed. Implications of this result for the GSI peaks are briefly considered.