Components Of Permittivity Tensor Research Articles

Determination of optimal directions of the wave vector of the phase holographic grating in cubic photorefractive crystal

The dependence of the change in the components of the inverse permittivity tensor of a cubic photorefractive Bi12SiO20 crystal on the direction of the wave vector of holographic grating in the crystal coordinate system has been studied. It is shown that, when recording a phase hologram, the largest change in the refractive index of Bi12SiO20 crystal is attained when the holographic grating wave vector is oriented along symmetrically equivalent 111 directions. The maximum possible modulation amplitude of the refractive index of a holographic grating with the wave vector oriented along the 110 directions is found to exceed that in the case of orientation along the 100 directions. The components of the inverse permittivity tensor of Bi12SiO20 crystal were calculated taking into account that a phase hologram is recorded under linear electro-optic, photoelastic, and inverse piezoelectric effects.

Mixing Rules for Left-Handed Disordered Metamaterials: Effective-Medium and Dispersion Properties.

Left-handed materials are known to exhibit exotic properties in controlling electromagnetic fields, with direct applications in negative reflection and refraction, conformal optical mapping, and electromagnetic cloaking. While typical left-handed materials are constructed periodic metal-dielectric structures, the same effect can be obtained in composite guest-host systems with no periodicity or structural order. Such systems are typically described by the effective-medium approach, in which the components of the electric permittivity tensor are determined as a function of individual material properties and doping concentration. In this paper, we extend the discussion on the mixing rules to include left-handed composite systems and highlight the exotic properties arising from the effective-medium approach in this framework in terms of effective values and dispersion properties.

Polarization Sensitivity in Scattering-Type Scanning Near-Field Optical Microscopy—Towards Nanoellipsometry

Electric field enhancement mediated through sharp tips in scattering-type scanning near-field optical microscopy (s-SNOM) enables optical material analysis down to the 10-nm length scale and even below. Nevertheless, the out-of-plane electric field component is primarily considered here due to the lightning rod effect of the elongated s-SNOM tip being orders of magnitude stronger than any in-plane field component. Nonetheless, the fundamental understanding of resonantly excited near-field coupled systems clearly allows us to take profit from all vectorial components, especially from the in-plane ones. In this paper, we theoretically and experimentally explore how the linear polarization control of both near-field illumination and detection can constructively be implemented to (non-)resonantly couple to selected sample permittivity tensor components, e.g., explicitly to the in-plane directions as well. When applying the point-dipole model, we show that resonantly excited samples respond with a strong near-field signal to all linear polarization angles. We then experimentally investigate the polarization-dependent responses for both non-resonant (Au) and phonon-resonant (3C-SiC) sample excitations at a 10.6 µm and 10.7 µm incident wavelength using a tabletop CO2 laser. Varying the illumination polarization angle thus allows one to quantitatively compare the scattered near-field signatures for the two wavelengths. Finally, we compare our experimental data to simulation results and thus gain a fundamental understanding of the polarization’s influence on the near-field interaction. As a result, the near-field components parallel and perpendicular to the sample surface can be easily disentangled and quantified through their polarization signatures, connecting them directly to the sample’s local permittivity.

A semi-analytic method for the computation of the effective properties of composites of two isotropic constituent materials

We develop a computational framework for the semi-analytic representation of the effective transport properties of two-component composite materials, in the spirit of Bergman’s spectral representation. The components of the effective permittivity (or conductivity) tensor are expanded as power series in a contrast parameter between the two phases. The coefficients (the moments of a spectral measure) of these expansions are determined recursively through the numerical evaluations of integrals defined solely on the boundary between the constituent phases, and discretized by high-order (possibly exponentially converging) quadrature schemes. The high precision reached by these coefficients allows the series representation to be recast into Padé approximants (or continued fractions) to provide analytical expressions valid over large (possibly infinite) regions of the parameter complex plane. Examples, thus far limited to two-dimensional rhombic unit cells, demonstrate that the method is reliable for microgeometries and material parameters for which other methods are far less dependable. The analytical representations are particularly useful to study the optical or electrostatic resonant behaviour of some composite materials.

Bulk ReSe2: Record High Refractive Index and Biaxially Anisotropic Material for All-Dielectric Nanophotonics

We show that bulk rhenium diselenide, ReSe2, is characterized by a record high value of the refractive index exceeding 5 in the near-infrared frequency range. We use back focal plane reflection spectroscopy to extract the components of the ReSe2 permittivity tensor and reveal its extreme biaxial anisotropy. We also demonstrate the good agreement between the experimental data and the predictions of the density functional theory. The combination of the large refractive index and giant optical anisotropy makes ReSe2 a promising material for all-dielectric nanophotonics in the near-infrared frequency range.

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.

Особенности характеристик КНЧ-волн в многокомпонентной ионосферной плазме

We have examined the properties of low-frequency electromagnetic waves in multicomponent ionospheric plasma in the 1–30 Hz band, using the magnetoionic theory. Complex permittivity tensor components and refractive indices of normal waves (ordinary and extraordinary) were calculated at altitudes from 80 to 750 km. The calculations show that the refractive indices are highly dependent on frequency and height. Polarization of ordinary and extraordinary waves is elliptical over the entire range of the frequencies investigated. The refractive index and the polarization of normal waves are demonstrated to tend to magnetohydrodynamic (MHD) values only at frequencies lower than 1 Hz. The group velocity vector of an extraordinary wave is not directed along the magnetic field, as follows from the MHD approximation, but it lies inside a cone within ±(5–10) degrees, depending on frequency. The group velocity vector of an ordinary wave is practically independent of the angle with the geomagnetic field as in the MHD approximation. The proposed method for calculating the characteristics of normal waves in the ionosphere can be used to study ULF wave propagation from both natural and artificial ionospheric sources, which arise under the action of powerful HF radio waves in the lower and upper ionosphere.

Peculiarities of ULF wave characteristics in a multicomponent ionospheric plasma

We have examined the properties of low-frequency electromagnetic waves in multicomponent ionospheric plasma in the 1–30 Hz band, using the magnetoionic theory. Complex permittivity tensor components and refractive indices of normal waves (ordinary and extraordinary) were calculated at altitudes from 80 to 750 km. The calculations show that the refractive indices are highly dependent on frequency and height. Polarization of ordinary and extraordinary waves is elliptical over the entire range of the frequencies investigated. The refractive index and the polarization of normal waves are demonstrated to tend to magnetohydrodynamic (MHD) values only at frequencies lower than 1 Hz. The group velocity vector of an extraordinary wave is not directed along the magnetic field, as follows from the MHD approximation, but it lies inside a cone within ±(5–10) degrees, depending on frequency. The group velocity vector of an ordinary wave is practically independent of the angle with the geomagnetic field as in the MHD approximation. The proposed method for calculating the characteristics of normal waves in the ionosphere can be used to study ULF wave propagation from both natural and artificial ionospheric sources, which arise under the action of powerful HF radio waves in the lower and upper ionosphere.

Quadraxial metamaterial.

We study the dispersion of electromagnetic waves in a spatially dispersive metamaterial with Lorentz-like dependence of principal permittivity tensor components on the respective components of the wave vector performing the analysis of isofrequency contours. The considered permittivity tensor describes a triple non-connected wire medium. It is demonstrated that the metamaterial has four optic axes in the frequency range below the artificial plasma frequency. The directions of the optical axes do not depend on frequency and coincide with the diagonals of quadrants. The conical refraction effect is observed for all four optic axes.

Electromagnetic energy density in hyperbolic metamaterials

We present the theory of electromagnetic energy propagation through a dispersive and absorbing hyperbolic metamaterial (HMM). In this way, the permittivity tensor components of HMM (especially, nanowire HMM) may appear to be hopeless, but as a non-trivial step, we find that they can be cast into more transparent forms. We find under the influence of an electromagnetic wave, the responses of nanowire HMM (multilayer HMM) in the directions perpendicular to and parallel to the optical axis are similar to those of Lorentz (Drude) and Drude (Lorentz) media, respectively. We obtain simple expressions for the electromagnetic energy density formula of both typical structures of HMMs, i.e., nanowire and multilayer HMMs. Numerical examples reveal the general characteristics of the direction-dependent energy storage capacity of both nanowire and multilayer HMMs. The results of this study may shed more physical insight into the optical characteristics of HMMs.

A high–order spectral algorithm for the numerical simulation of layered media with uniaxial hyperbolic materials

Electromagnetic metamaterials are artificial media assembled from components which have dimensions much smaller than the wavelength of the illuminating radiation. It has been demonstrated that these media can have properties beyond those found in conventional materials with important applications to many areas of science and engineering. Among the collection of such materials currently garnering significant attention are the Hyperbolic Metamaterials. These are highly anisotropic structures which have a hyperbolic dispersion relation due to the fact that one principal component of the relative permittivity or permeability tensor has the opposite sign of the other two. For such materials scattered wave information at all scales is transmitted far away which suggests a number of important applications, the most immediate of which is imaging objects below the diffraction limit (superlensing). Clearly it is of great current interest to have numerical simulation capabilities for these fascinating materials. As the hyperbolic response is quite strong and its nature is very sensitive, numerical simulations of these configurations should be robust and highly accurate. For this reason we focus on High–Order Spectral algorithms which efficiently produce high fidelity solutions. More specifically, we describe a High–Order Perturbation of Surfaces approach which enjoys the greatly reduced operation counts and memory savings of interfacial methods while avoiding the complexities and indefinite linear systems faced by Integral Equation algorithms. We give a full discussion of our formulation in terms of Impedance–Impedance Operators (which avoids spurious singularities of other formulations) and implementation details, followed by numerical validation and simulation of results which appear in the engineering literature.

Energy loss reduction of a charge moving through an anisotropic plasma-like medium

We analyze radiation of a charge moving in a vacuum channel in an anisotropic non-gyrotropic medium with plasma-like components of the permittivity tensor. The expressions for field components are obtained and analyzed. It is shown that the field contains both the radiation field and the plasma oscillations. Most attention is focused on the energy loss of the charge per the unit path length. The dependencies of the loss on the charge velocity and the plasma frequencies are studied. The relative roles of radiation loss and polarization one are considered. The most interesting result is that the energy loss is negligible when one of the permittivity tensor components is equal to 1, and the charge velocity tends to the speed of light in vacuum. This effect can be promising for applying in collimators of ultrarelativistic bunches.

Analysis of high frequency EM-waves diffracted by a finite strip with impedance in anisotropic medium

This article presents the rigorous analysis of the EM-plane wave diffraction by a conductible strip of finite length in an anisotropic medium. Leontovich boundary conditions are imposed along the strip to consider the effects of impedance. The presence of geomagnetic field in ionosphere containing cold plasma makes anisotropic medium. Mathematical formulation of this model using Maxwell's equations along with dielectric permittivity of cold plasma gives Helmholtz equation which gets transformed by the application of Fourier transform. Two coupled Wiener–Hopf equations are formulated which are then solved by the standard Wiener–Hopf procedure. The modified stationary phase method is used to find the asymptotic result of separated field in an anisotropic medium. The problem turns out to be for isotropic medium on assigning the particular values to the components of permittivity tensor as under the consideration of large operating frequency as compared to cyclotron frequency while it is of same order with plasma frequency. Graphical analysis is performed to investigate the effects of physical parameter on separated (diffracted by finite plate) field for both isotropic and anisotropic medium.

Experimental investigation of optically controlled topological transition in bismuth-mica structure

The hyperbolic materials are strongly anisotropic media with a permittivity/permeability tensor having diagonal components of different sign. They combine the properties of dielectric and metal-like media and are described with hyperbolic isofrequency surfaces in wave-vector space. Such media may support unusual effects like negative refraction, near-field radiation enhancement and nanoscale light confinement. They were demonstrated mainly for microwave and infrared frequency ranges on the basis of metamaterials and natural anisotropic materials correspondingly. For the terahertz region, the tunable hyperbolic media were demonstrated only theoretically. This paper is dedicated to the first experimental demonstration of an optically tunable terahertz hyperbolic medium in 0.2–1.0 THz frequency range. The negative phase shift of a THz wave transmitted through the structure consisting of 40 nm (in relation to THz wave transmitted through substrate) to 120 nm bismuth film (in relation to both THz waves transmitted through substrate and air) on 21 µm mica substrate is shown. The optical switching of topological transition between elliptic and hyperbolic isofrequency contours is demonstrated for the effective structure consisting of 40 nm Bi on mica. For the case of 120 nm Bi on mica, the effective permittivity is only hyperbolic in the studied range. It is shown that the in-plane component of the effective permittivity tensor may be positive or negative depending on the frequency of THz radiation and continuous-wave optical pumping power (with a wavelength of 980 nm), while the orthogonal one is always positive. The proposed optically tunable structure may be useful for application in various fields of the modern terahertz photonics.

Контроль диэлектрической проницаемости и толщины анизотропных диэлектрических покрытий методом поверхностных электромагнитных волн

The widespread use of anisotropic composite dielectric coatings operating in the microwave range in various science-intensive areas has led to the search and selection of effective methods of radio wave nondestructive testing of their electrophysical parameters. The existing approaches based on the estimation of the reflection and transmission coefficients of electromagnetic waves have low accuracy and reliability of estimating the components of the complex permittivity tensor and the thickness of such coatings, do not take into account their frequency dispersion and placement on a metal base. We present the new method of local measurements of components of the complex permittivity tensor with allowance for their frequency dispersion and a thickness anisotropic dielectric coatings with radial surface microwaves. The method is based on the solution of inverse problem in the determination of components of the complex permittivity tensor and a thickness coatings from the frequency and angular dependence of the attenuation coefficient of the field of a radial surface electromagnetic wave excited in a test sample. A numerical and experimental study show that for a measurement bandwidth of 9–13,5 GHz the errors in estimating the anisotropy coefficients do not exceed 10% with a confidence coefficient of 0.95. We introduce and substantiate a statistical limit of the resolution of the anisotropy of permittivity; this makes it possible to evaluate the possibility of discriminating between two close values any pair of components of the permittivity tensor. Numerical and field experiments have shown that the method can provide their assessment with a difference of 0.2–0.3% or less in the frequency band of 9–13.5 GHz.

Numerical analysis of Dyakonov surface-wave propagation at the interface of anisotropic and gyrotropic media

The propagation of Dyakonov surface waves was numerically investigated for the interfaces of two biaxial anisotropic media. Variation of the propagation direction changes the field energy localization from one of the partnering media to another. It is possible to find a specific propagation direction, which is characterized by the strongest energy localization in the boundary plane. This direction corresponds to the central angle of the angular existence domain. On the other hand, variation of the components of the media permittivity tensor, including the introduction of gyrotropy, changes the possible propagation directions, which is a potential way to control surface eigenmodes.

Structural, ferroelectric, and optical properties of Bi3+ doped YFeO3: A first‐principles study

AbstractThe orthoferrites with the general formula RFeO3 (R = Ho, Er, Lu, Sc, and Y) have recently attracted a great deal of attention because they are promising candidates for a second generation of multiferroic materials. In this computational work, the structural, ferroelectric and optical properties of the YFeO3 perovskite oxide (YFO) and a Bi‐doped YFeO3 were analyzed. Bi‐substitution in YFO leads to an increase of its lattice parameters by virtue of the larger ionic radius of Bi3+. Both compounds exhibit a G‐type antiferromagnetic ground state. The calculations disclose a significant spontaneous polarization along the [101] direction of YFO‐Bi, which originates in the asymmetric distribution of the charges around the Bi3+ ions, as a result of the Bi‐6s electrons. The electric polarizability of YFO is increased upon Bi3+‐doping and the more significant components of the real permittivity tensor of YFO‐Bi are those associated with the direction along which the maximum value of spontaneous polarization is observed. The spontaneous polarization of YFO‐Bi found in this work reveals that this compound holds the potential for the next generation of multi ferroic materials.

Plasmon-polariton gap and associated phenomenon of optical bistability in photonic hypercrystals

Photonic hypercrystals are a novel type of metamaterial combining the properties of photonic crystals and hyperbolic metamaterials. The transmission of transverse magnetic polarized light through photonic hypercrystal is studied. Along with the conventional gaps, the angular incidence of such radiation at the plasmon frequency of the perpendicular component of permittivity tensor of hyperbolic metamaterials gives rise to the appearance of the unconventional plasmon-polariton gap. Some properties of this gap and the associated phenomenon of optical bistability at the edge of this gap are explored.

Methods of effective media as optimal methods for modeling the physical properties of nanostructures

This paper considers various methods of effective media as a tool for studying both optical and magneto-optical properties of various nanostructures, primarily magnetic nanostructures. Formulas for finding diagonal and non-diagonal components of the permittivity tensor for all basic approximations of the effective medium were obtained explicitly. These formulas are valid for both nanocomposites and granular alloys. The possibility of predicting various optical and magneto-optical properties of such structures is discussed using the example of the transverse Kerr effect as a promising non-contact method for studying nanostructures for a ferromagnetic nanocomposite (CoFeZr) x (MgF 2 ) 100-x . A possible application of the obtained formulas is discussed. Various methods of effective media make it possible to study nanostructures in a wide range of values of the concentration of the metal (magnetic) component Х . The paper notes and discusses the contribution of various mechanisms that affect the physical properties of such structures, especially in the IR region of the spectrum, where the quasi-classical dimensional effect is most pronounced. The form factor of nanocomposite particles and the average particle size are such contributions that can be taken into account. The contribution of the quasi-classical dimensional effect to the diagonal and non-diagonal components of the structure's permittivity tensor is analyzed within the framework of the Drude-Lorentz model. The problem being solved in this work is relevant, since interesting and important effects are observed in magnetic nanostructures, such as the Kerr effect, anomalous absorption, giant magnetoresistance, tunnel magnetoresistance, and many others. These effects play an important role in modern electronic devices, which makes this work particularly relevant.

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.