Dielectric Permittivity Tensor Research Articles

Efficient determination of Born-effective charges, LO-TO splitting, and Raman tensors of solids with a real-space atom-centered deep learning approach

We introduce a deep neural network (DNN) framework called the Real-space Atomic Decomposition NETwork (radnet), which is capable of making accurate predictions of polarization and of electronic dielectric permittivity tensors in solids and aims to address limitations of previously available machine learning models for Raman predictions in periodic systems. This framework builds on previous, atom-centered approaches while utilizing deep convolutional neural networks. We report excellent accuracies on direct predictions for two prototypical examples: GaAs and BN. We then use automatic differentiation to efficiently calculate the Born-effective charges, longitudinal optical-transverse optical (LO-TO) splitting frequencies, and Raman tensors of these materials. We compute the Raman spectra, and find agreement with ab initio results. Lastly, we explore ways to generalize the predictions of polarization while taking into account periodic boundary conditions and symmetries.

Hyperbolic Polaritons in Topological Nodal Ring Semimetals.

In mirror-symmetric systems, there is a possibility of the realization of extended gapless electronic states characterized as nodal lines or rings. Strain induced modifications to these states lead to the emergence of different classes of nodal rings with qualitatively different physical properties. Here we study optical response and the electromagnetic wave propagation in type I nodal ring semimetals, in which the low-energy quasiparticle dispersion is parabolic in momentum k_{x} and k_{y} and is linear in k_{z}. This leads to a highly anisotropic dielectric permittivity tensor in which the optical response is plasmonic in one spatial direction and dielectric in the other two directions. The resulting normal modes (polaritons) in the bulk material become hyperbolic over a broad frequency range, which is furthermore tunable by the doping level. The propagation, reflection, and polarization properties of the hyperbolic polaritons not only provide valuable information about the electronic structure of these fascinating materials in the most interesting region near the nodal rings but also pave the way to tunable hyperbolic materials with applications ranging from anomalous refraction and waveguiding to perfect absorption in ultrathin subwavelength films.

Dirac points, new photonic band gaps, and effect of magnetically induced transparency in dichroic cholesteric liquid crystals with wavelength-dependent magneto-optical activity parameter.

We investigated the properties of cholesteric liquid crystals (CLCs) being in an external static magnetic field directed along the helix axis. We considered a dichroic CLC, that is, CLC with parameters ReΔ=Reɛ_{1}-Reɛ_{2}/2=0 and ImΔ=Imɛ_{1}-Imɛ_{2}/2≠0, where ɛ_{1,2} are the principal values of the local dielectric permittivity tensor. We have shown that in the case of the wavelength dependence of the magneto-optic activity parameter, new features appear in the optics of dichroic CLCs, in particular, in this case new Dirac points appear. Dirac points are points where there is an intersection of any two wave vector curves (they degenerate) and a linear law of the wave vector dependence on the frequency near these points. And moreover, at some Dirac points photonic band gaps (PBGs) appear; at others, lines of magnetically induced transparency (MIT), that is, a full transmission band appears, in an absorbing medium. In this case a polarization-sensitive transmission band appears too. At certain values of the helix pitch of the CLC and of the magnitude of the external magnetic field, three PBGs of different nature appear: a transmittance band, two narrow lines of MIT, and at others a broadband MIT, etc. This system is nonreciprocal, and the nonreciprocity changes over a wide range. It is observed both for reflection and transmittance and for absorption. The soft-matter nature of CLCs and their response to external influences lead to easily tunable multifunctional devices that can find a variety of applications. They can be applied as tunable narrow-band or broadband filters and mirrors, a highly tunable broad/narrow-band coherent perfect absorber, transmitter, ideal optical diode, and in other devices.

An optical absorption of the composite with the nanoparticles, which are covered by the surfactant layer

The optical properties of the nanocomposite with two-layer spherical inclusions “metallic core – surfactant layer” have been studied in the work. The question connected with an influence of the processes at the interface “metal – adsorbate” on the excitation of the surface plasmonic resonances in the nanoparticle has been studied. The fact of splitting of the surface plasmonic resonance due to the influence of the absorption bond near the surface of the metallic nanoparticles and due to the emergence of the additional energy states has been established. The relations for the effective parameters which describe the losses of coherence under the scattering at the chemical interface have been obtained. The calculations for the frequency dependencies of the diagonal components of the dielectric permittivity tensor of the two-layer nanoparticle and for the absorption coefficient of the nanocomposite have been performed. It has been shown that the frequency dependencies for the real and imaginary parts of the longitudinal component of the dielectric tensor are close to the similar dependencies for the real and imaginary parts of the dielectric function for the spherical metallic nanoparticle. At the same time the real and imaginary parts of the transverse component weakly depend on the frequency in the visible spectrum and oscillate in the infrared range. It has been established that the absorption coefficient of the composite can have one or two maximums depending on the sizes and the material of the particles-inclusions.

Mathematical modeling of electromagnetic radiations incident on a symmetric slit with Leontovich conditions in an-isotropic medium

This article presents the rigorous analysis of the an-isotropic medium affecting the diffraction process of EM-signals of high frequency by a symmetric slit of finite width. Leontovich boundary conditions for the present model are taken into consideration to show the existence of impedance. The ionosphere having non-thermal plasma contains the geomagnetic field which turns the medium into an an-isotropic medium. The well-known Helmholtz equation for electromagnetic (EM) waves is formulated through Maxwell’s equations with consideration of dielectric permittivity tensor for an an-isotropic medium due to non-thermal plasma. The Fourier transform is employed for the equations formulated for this model and then a pair of Wiener–Hopf equations (coupled form) is devised. These Wiener–Hopf equations are then tackled and an asymptotic method is used to achieve the target. Results for the isotropic medium can be obtained by assigning the values to permittivity elements controlling the medium. Graphical results are sketched for better visualization of the separated field for the an-isotropic medium and isotropic medium as well.

Dipole-dipole correlations in the nematic phases of symmetric cyanobiphenyl dimers and their binary mixtures with 5CB.

We report on the temperature dependence of birefringence and of the static dielectric permittivity tensor in a series of binary mixtures between the symmetric, bent-shaped, 1'',9''-bis(4-cyanobiphenyl-4'-yl)nonane (CB9CB) dimer and the monomeric nematogen 5CB. In the studied composition range the mixtures exhibit two nematic phases with distinct birefringence and dielectric features. Birefringence measurements are used to estimate the temperature dependence of the tilt between the axis defining the nanoscale helical modulation of the low temperature nematic phase with the (local) direction of the maximal alignment of the cyanobiphenyl units. Planar as well as magnetically and/or electrically aligned samples are used to measure the perpendicular and parallel components of the dielectric permittivity in both nematic phases. A self-consistent molecular field theory that takes into account flexibility and symmetry of the constituent mesogens is introduced for the calculation of order parameters and intra-molecular orientational dipolar correlations of the flexible dimers as a function of temperature/concentration. Utilising the tilt angle, as calculated from the birefringence measurements, and the predictions of the molecular theory, dielectric permittivity is modelled in the framework of the anisotropic version of the Kirkwood-Fröhlich theory. Using the inter-molecular Kirkwood correlation factors as adjustable parameters, excellent agreement between theory and permittivity measurements across the whole temperature range and composition of the mixtures is obtained. The importance of the orientational, intra- and inter-molecular, dipolar correlations, their relative impact on the static dielectric properties, as well as their connection with the local structure of the nematic phases of bent-shaped bimesogens, is discussed.

Interaction of two-frequency electromagnetic waves with anisotropic media over hydrocarbon accumulation

The article analyzes the interaction of two-frequency electromagnetic waves with anisotropic media over hydrocarbon accumulation. The behavior of the real component έ3 of the dielectric permittivity tensor is investigated. The choice of signal characteristics is based on the use of different electromagnetic wave emission sources with amplitude and frequency ratio coefficients in the modes of powerful low-frequency and high-frequency signals. The dielectric permittivity tensor component έ3 as a function of dielectric permittivity and frequency of sounding signals was analyzed. Sounding modes of anisotropic media over hydrocarbons are recommended to identify the medium over the deposits and increase the accuracy of determining the boundaries of hydrocarbon accumulation. The obtained results of the research can be used in prospecting geophysics.

ELECTROMAGNETIC METHODS OF SEARCHING AND DEFINITION
 OF HYDROCARBON DEPOSITS

The article studies the characteristics of an anisotropic medium over hydrocarbons with the complex use
 of electromagnetic geo-exploration methods. The simulation of the components of dielectric permittivity tensors
 in the mode of amplitude-modulated, frequency-modulated, amplitude-frequency-modulated and radio pulse signals
 is carried out. The frequencies of the electron plasma and electron cyclotron resonances for the specified
 regimes are established. A study was made of the influence of modes of probing signals on the characteristics
 of an anisotropic medium above deposits and the components of the dielectric tensor. The effect of particle concentration
 variation on the real components of the components of the dielectric permittivity of an anisotropic
 medium above the UVZ is analyzed. Recommendations are given for improving the methods of electrical exploration
 and their application for prospecting geophysics.

ELECTROMAGNETIC METHODS OF SEARCHING AND DEFINITION OF HYDROCARBON DEPOSITS

The article studies the characteristics of an anisotropic medium over hydrocarbons with the complex use of electromagnetic geo-exploration methods. The simulation of the components of dielectric permittivity tensors in the mode of amplitude-modulated, frequency-modulated, amplitude-frequency-modulated and radio pulse signals is carried out. The frequencies of the electron plasma and electron cyclotron resonances for the specified regimes are established. A study was made of the influence of modes of probing signals on the characteristics of an anisotropic medium above deposits and the components of the dielectric tensor. The effect of particle concentration variation on the real components of the components of the dielectric permittivity of an anisotropic medium above the UVZ is analyzed. Recommendations are given for improving the methods of electrical exploration and their application for prospecting geophysics.

Frequency-controlled dielectrophoresis-driven wetting of nematic liquid crystals

We show that surface-localized dielectrophoresis-driven wetting of anisotropic nematic liquid crystal sessile droplets obeys the same relationship, , which has previously been found for isotropic liquid droplets, even though the nematic liquid crystal phase possesses a uniaxial dielectric permittivity tensor. We also demonstrate that the dielectrowetting coefficient , which determines the magnitude of the reduction in the contact angle, from to , through the action of a potential difference , can be controlled by the frequency of the applied voltage between interdigitated electrodes beneath a droplet of highly dispersive nematic liquid crystal. Our Q-tensor modelling of the electric field-induced 2-dimensional n-director distortions within a nematic droplet elucidates how this linear relationship holds for voltages when exceeds 3°–4°.

A Mathematical Study of a Hyperbolic Metamaterial in Free Space

Wave propagation in hyperbolic metamaterials is described by the Maxwell equations with a frequency dependent tensor of dielectric permittivity, whose eigenvalues are of different signs. In this case the problem becomes hyperbolic (Klein-Gordon equation) for a certain range of frequencies. The principal theoretical and numerical difficulty comes from the fact that this hyperbolic equation is posed in a free space, without initial conditions provided. The subject of the work is the theoretical justification of this problem. In particular, this includes the construction of a radiation condition, a well-posedness result, a limiting absorption principle and regularity estimates on the solution.

On the Limitations of Using Polarimetric Radar Sounding to Infer the Crystal Orientation Fabric of Ice Masses

AbstractWe introduce a transfer matrix model for radio‐wave propagation through layered anisotropic ice that permits an arbitrary dielectric permittivity tensor in each layer. The model is used to investigate how crystal orientation fabrics without a vertical principal direction affect polarimetric radar returns over glaciers and ice sheets. By expanding the c‐axis orientation distribution in terms of a spherical harmonic series, we find that radar returns from synthetic fabric profiles are relatively insensitive to the harmonic mode responsible for a nonvertical principal direction; however, only for normally incident waves. Consequently, the strength of this mode might be relatively difficult to infer in glaciers and ice sheets, which in turn has implications for the ability to determine the full second‐order structure tensor, needed to infer the local flow regime, flow history, or to represent the directional viscosity structure of glacier ice for ice‐flow modeling.

Magnetic and antiferromagnetic nonreciprocity of light propagation in magnetoelectric CuB2O4

The nonreciprocal propagation, reflection, and absorption of light are most strongly pronounced in the magneto-optical Faraday and Kerr effects that are observed in any paramagnetic and diamagnetic material in the presence of a magnetic field, as well as spontaneous nonreciprocal effects in ferromagnets and ferrimagnets. But nonreciprocity in antiferromagnets is not at all an obvious effect. In this paper, we analyze reciprocal and nonreciprocal propagation of light in a magnetoelectric antiferromagnet ${\mathrm{CuB}}_{2}{\mathrm{O}}_{4}$ that demonstrates a large variety of intriguing optical effects. We present a description of the magnetic and antiferromagnetic nonreciprocal propagation and absorption of light on the basis of space and time symmetry considerations in the paramagnetic and commensurate antiferromagnetic state below the N\'eel temperature. We employ the expansion of the dielectric permittivity tensor as a function of the wave vector of propagating light, an applied magnetic field, and the antiferromagnetic and ferromagnetic order parameters. All these contributions to the dielectric permittivity serve as a basis for solving the relevant Maxwell's equations. Such an approach allowed us to establish the basic mechanisms affecting the propagation of light and sources of nonreciprocity, and it can be applied to other antiferromagnetic crystals. Results of calculations are compared with available experimental data for ${\mathrm{CuB}}_{2}{\mathrm{O}}_{4}$.

Magnetically tuned hybrid resonance emission of terahertz waves from the interaction of intense laser beams with warm collisional inhomogeneous plasma

Enhancing the terahertz emission at hybrid resonant frequencies is observed from a warm collisional inhomogeneous plasma irradiated by intense laser beams in the presence of an external transverse magnetic field. To reach this result, we utilize the dielectric permittivity tensor of the plasma affected by the strength and the direction of the magnetic field and analyze the nonlinear current density induced by the ponderomotive force due to the beating of two Gaussian laser beams. The calculations reveal resonance emission at several frequencies, which depend on the thermal speed of the electrons, the wavenumber, the electron plasma frequency, the collision frequency, and the cyclotron frequency. However, the amplitude of THz waves at these frequencies mainly depends on the electron temperature as well as the external magnetic field strength.

Analytical calculation of dielectric permittivity tensor from magneto-optical ellipsometry measurements

Magneto-optical ellipsometry combines ellipsometry and magneto-optical Kerr effect measurements which are two powerful techniques. The main difficulty is usually in data processing as a number of parameters should be extracted from measured ellipsometric (ψ, Δ) and magneto-ellipsometric (δψ, δΔ) parameters. Standard procedure of solving magneto-ellipsometry equations involves numerical calculations. In this paper we show that it is possible to find out all elements of dielectric permittivity tensor without numerical calculation methods. It means that the inverse problem of magneto-optical ellipsometry can be solved analytically in the case of expansion of magneto-ellipsometric parameters δψ and δΔ with respect to two small parameters. We present a full set of mathematical expressions that enable us to calculate complex refraction index and complex magneto-optical parameter of a sample from magneto-optical ellipsometry measurements, thereby obtaining diagonal and off-diagonal complex elements of dielectric permittivity tensor. This analytical approach can be used in case of the contribution from magnetism into reflection coefficients being small.

Longitudinal and Transverse Electrocaloric Effects in Glycinium Phosphite Ferroelectric

A modified proton ordering model of glycinium phosphite ferroelectric, which involves the piezoelectric coupling of the proton and lattice subsystems, is used for the investigation of the electrocaloric effect. The model also accounts for the dependence of the effective dipole moment on a hydrogen bond on an order parameter, as well as a splitting of parameters of the interaction between pseudospins in the presence of shear stresses. In the two-particle cluster approximation, the influence of longitudinal and transverse electric fields on components of the polarization vector and the dielectric permittivity tensor, as well as on thermal characteristics of the crystal, is calculated. Longitudinal and transverse electrocaloric effects are studied. The calculated electrocaloric temperature change is quite small, about 1K; however, it can change its sign under the influence of a transverse field.

Reversed Cherenkov-transition radiation in a waveguide partly filled with an anisotropic dispersive medium

We analyze the electromagnetic field of a bunch that moves uniformly in a circular metal waveguide and crosses a boundary between a vacuum area and an area filled with an anisotropic dispersive nonmagnetic medium. The medium is characterized by the diagonal dielectric permittivity tensor with components possessing frequency dispersion of plasma types. The investigation of the waveguide mode components is performed with the methods of the complex variable function theory. It is shown that in compliance with the parameters of the medium, Cherenkov radiation (CR) generated in the filled area of the waveguide can have reversed direction in relation to the bunch motion. CR can penetrate into the vacuum area of the waveguide, that is, the intensive reversed Cherenkov-transition radiation (RCTR) can be generated. The main properties of this radiation are described, and essential differences from the RCTR in the case of isotropic left-handed medium are revealed.

Rotating ion beam effects on temperature gradient instability in completely ionized plasmas.

The aim of this paper is to investigate the effects of a rotating ion beam on the temperature gradient instability (TGI) in completely ionized plasmas. The interplay of the temperature and density gradients provides the basis for experiencing an unstable inhomogeneous plasma medium due to TGI taken under consideration. The density and temperature gradients are considered perpendicular to the magnetic field where a nonrelativistic rotating ion beam such as O^{+} is present. By implementing the kinetic theory together with a zeroth-order approximation of geometrical optics, the dielectric permittivity tensor of the inhomogeneous plasma is obtained where by a suitable linear eikonal equation, the growth rate of the TGI in the collisional regime is calculated in the presence of a rotating ion beam. In such a configuration an unstable condition is experienced in regions with opposite electron density and temperature gradients, where it is destabilized by the temperature and plasma density gradients and the frequent electron collisions. As a consequence, the results reveal that the TGI can be damped or modified through interaction with the rotating ion beam depending on the characteristics of the ion beam, namely, velocity and density.

Comparative analysis of temperature dependencies of the elastic compliance and dielectric permittivity tensor components in BaTiO3 single crystal

The regression analysis of the temperature dependences of the components of the elastic compliance tensor in the tetragonal phase and the inverse permittivity coefficients in the cubic and tetragonal phases is performed in single crystal BaTiO3. Two modified logarithmic functions having a critical temperature are proposed that approximate well the experimental results of in two phases and in a tetragonal phase. It is found that the dielectric constant has a maximum in the region of Tc, and the maximum of is shifted to the region of higher temperatures. There is a large correlation (0.99) between the changes the elastic compliance coefficient and the dielectric constant It is concluded that the anomalies in the elastic and dielectric properties are due to softening of the lattice when approaching a first-order phase transition.

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.