Dielectric Tensor Elements Research Articles

Damping characteristics of helicon and Trivelpiece–Gould waves in high density and low magnetic field helicon plasma

By employing a warm plasma model and considering a cyclotron harmonic effect in dielectric tensor elements, the power deposition properties of the azimuthally symmetric mode of the helicon and Trivelpiece–Gould (TG) waves due to collisional and kinetic damping in high density (∼1 × 1013 cm−3), low magnetic fields (∼30–50 G), and low to moderate neutral gas pressure (∼0.5–10 mTorr) helicon plasma are investigated. Theoretical calculations indicate that the magnetic field imposed a significant influence on the mode coupling surface properties between the helicon and TG waves; in a typical helicon plasma electron temperature range, Te ∈ (3, 5) eV, there exists the critical neutral gas pressure, below or above which different waves due to different damping mechanisms play the dominant role in the power deposition; meanwhile, in low neutral gas pressure (∼0.5 mTorr) circumstances, TG waves due to Landau damping dominate the power deposition and this dominance gradually becomes intensified as the magnetic field increases.

Magneto-optic Kerr effect in Gd20Co80 alloy

The magneto-optical Kerr effect in Gd20Co80 alloy and cobalt thin films has been studied in a broad spectral range applying spectral ellipsometry experimental technique. The results of the experiments showed the complex nature of the complex Kerr angle dispersion curves. A quantum mechanical formalism for degenerate and non-degenerate Landau levels for quasi-free electrons in ferromagnetic material has been developed in order to analyze the experimental data. The equivalence of relations for off-diagonal dielectric tensor elements for non-degenerate Landau levels to the classical case of the motion of quasi-free electrons along circular trajectories in a magnetic field has been theoretically shown. The degenerate Landau levels in this approach are the result of motion of electrons in small confined volumes near rare-earth alloy atoms. Rotation of light polarization occurs in this case due to transitions between subbands having different magnetic quantum numbers. This theoretical approach allowed us to interpret in detail shapes and sign of the complex Kerr angle dispersion curves, which actually include the contributions of optical transitions between degenerate and non-degenerate energy levels. The complex Kerr angle sign is determined by the magnetization magnetic field direction for non-degenerate Landau levels and the Hund rule for degenerate Landau levels.

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.

Isotropic or anisotropic screening in black phosphorous: Can doping tip the balance?

Black phosphorus (BP), a layered van der Waals (vdW) crystal, has unique in-plane band anisotropy and many resulting anisotropy properties such as the effective mass, electron mobility, optical absorption, thermal conductivity and plasmonic dispersion. However, whether anisotropic or isotropic charge screening exist in BP remains a controversial issue. Based on first-principles calculations, we study the screening properties in both of single-layer and bulk BP, especially concerning the role of doping. Without charge doping, the single-layer and bulk-phase BP show slight anisotropic screening. Electron and hole doping can increase the charge screening of BP and significantly change the relative static dielectric tensor elements along two different in-plane directions. We further study the charge density change induced by potassium (K) adatom near the BP surface, under different levels of charge doping. The calculated two-dimensional (2D) charge redistribution patterns also confirm that doping can greatly affect the screening feature and tip the balance between isotropic and anisotropic screening. We corroborate that screening in BP exhibits slight intrinsic anisotropy and doping has significant influence on its screening property.

Infrared active phonons in monoclinic lutetium oxyorthosilicate

A combined generalized spectroscopic ellipsometry measurement and density functional theory calculation analysis is performed to obtain the complete set of infrared active phonon modes in Lu2SiO5 with a monoclinic crystal structure. Two different crystals, each cut perpendicular to a different crystal axis, are investigated. Ellipsometry measurements from 40to1200cm−1 are used to determine the frequency dependent dielectric function tensor elements. The eigendielectric displacement vector summation approach and the eigendielectric displacement loss vector summation approach, both augmented with anharmonic lattice broadening parameters proposed recently for low-symmetry crystal structures [Mock et al., Phys. Rev. B 95, 165202 (2017)], are applied for our ellipsometry data analysis. All measured and model calculated dielectric function tensor and inverse dielectric function tensor elements match excellently. 23 Au symmetry and 22 Bu symmetry infrared active transverse and longitudinal optical modes are found. We also determine the directional limiting modes and the order of the phonon modes within the monoclinic plane. Results from density functional theory and ellipsometry measurements are compared and nearly perfect agreement is observed. We further compare our results to those obtained recently for the monoclinic crystal Y2SiO5, which is isostructural to Lu2SiO5 [Mock et al., Phys. Rev. B 97, 165203 (2018)]. We find that the lattice mode behavior of monoclinic Lu2SiO5 is qualitatively identical with Y2SiO5 and differs only quantitatively. We anticipate that members of the isostructural group of monoclinic symmetry oxyorthosilicates such as Dy2SiO5 or Yb2SiO5 will likely behave very similar in their phonon mode properties as reported here for Lu2SiO5.

Dispersion characteristics of nonreciprocal gyroelectric silicon-on-insulator rectangular waveguide

A C-band rectangular waveguide with gyroelectric semiconductor is designed to study the non-reciprocal propagation characteristics of surface magnetoplasmons (SMPs), which are generated by an external magnetic field. The effective refractive index method is used to obtain the effective refractive index and transverse electric field distribution of the waveguide, and a two-dimensional rectangular waveguide is approximately regarded as a combination of two one-dimensional planar waveguides. The dispersion equation of planar waveguide with <inline-formula><tex-math id="M2">\begin{document}$ {\rm{E}}_{mn}^x$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20190109_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20190109_M2.png"/></alternatives></inline-formula> mode in rectangular waveguide is derived. The influences of the structural parameters of rectangular waveguide and the refractive index of material on the non-reciprocal dispersion relation and time-delay characteristics are analyzed by numerical method. Due to the effect of external magnetic field, the off-diagonal elements of dielectric tensor in magnetic photonic crystal are changed. The generation of electrical anisotropy leads the time reversal symmetry to be broken. As a result, the dispersion curves of the rectangular waveguide are asymmetric with respect to propagation constant, and the complete one-way transmission of SMPs can be realized in the asymmetric frequency region. The dispersion curve tends to be a dispersion curve of planar waveguide as the width of rectangular waveguide increases, but the non-reciprocal frequency range is approximately unchanged. The width of the core region and the refractive index of the side material have a significant influence on the non-reciprocal dispersion characteristics: the group velocity of SMPs decreases with <i>ω</i> and propagation constant decreasing. The group velocity is related to the waveguide width, propagation constant and the operating wavelength. The relationship between the normalized group velocity and the width of the waveguide separately operating at 1530, 1550 and 1565 nm are studied. The group velocity is relatively slow when the width of waveguide’s core region is between 140 nm and 233.5 nm, and the minimum group velocity reaches 5.43 × 10<sup>－2</sup><i>c</i>. As for the slow light effect, the rectangular waveguide is better than planar waveguide. The rectangular waveguide has a large engineering tolerance in the width of core region, which is 93.5 nm. In addition, the dispersion curves of the rectangular waveguide with SiO<sub>2</sub>, Air, Au and Ag as the left and right cladding layers are calculated. As a result, the group velocity is proportional to the refractive index of the side material in the <i>y</i> direction of the rectangular waveguide. The slow light effect is the most obvious when the material is silver, and the minimum transmission speed can reach 2.8 × 10<sup>－3</sup><i>c</i>.

An alternative derivation of the dielectric tensor for perpendicular wave propagation in magnetised plasmas modelled with kappa velocity distributions

A new derivation of the dielectric tensor elements for the special case of wave propagation perpendicular to a constant, uniform magnetic field in a collisionless, non-relativistic, multi-species magnetised plasma modelled with isotropic kappa distributions is presented. The new approach is consistent with the one commonly used for parallel propagation, unifying the starting point for each special case. The results obtained agree with those of previous calculations, verifying their correctness, but, in addition, alternative forms of the dielectric tensor elements are given as by-products of the new calculation. The generality of the method used and its aptness for use with the kappa distribution should make it suitable for similar calculations using kappa distribution variants, such as a bi-kappa distribution.

Anisotropy and phonon modes from analysis of the dielectric function tensor and the inverse dielectric function tensor of monoclinic yttrium orthosilicate

We determine the frequency dependence of the four independent Cartesian tensor elements of the dielectric function for monoclinic symmetry Y$_2$SiO$_5$ using generalized spectroscopic ellipsometry from 40-1200 cm$^{-1}$. Three different crystal cuts, each perpendicular to a principle axis, are investigated. We apply our recently described augmentation of lattice anharmonicity onto the eigendielectric displacement vector summation approach [A. Mock et al., Phys. Rev. B 95, 165202 (2017)], and we present and demonstrate the application of an eigendielectric displacement loss vector summation approach with anharmonic broadening. We obtain excellent match between all measured and model calculated dielectric function tensor elements and all dielectric loss function tensor elements. We obtain 23 A$_{\mathrm{u}}$ and 22 B$_{\mathrm{u}}$ symmetry long wavelength active transverse and longitudinal optical mode parameters including their eigenvector orientation within the monoclinic lattice. We perform density functional theory calculations and obtain 23 A$_{\mathrm{u}}$ symmetry and 22 B$_{\mathrm{u}}$ transverse and longitudinal optical mode parameters and their orientation within the monoclincic lattice. We compare our results from ellipsometry and density functional theory and find excellent agreement. We also determine the static and above reststrahlen spectral range dielectric tensor values and find a recently derived generalization of the Lyddane-Sachs-Teller relation for polar phonons in monoclinic symmetry materials satisfied [M. Schubert, Phys. Rev. Lett. 117, 215502 (2016)].

Scattering and propagation of a Laguerre–Gaussian vortex beam by uniaxial anisotropic bispheres

Within the framework of the generalized multi-particle Mie (GMM) theory, analytical solution to electromagnetic scattering of two interacting homogeneous uniaxial anisotropic spheres by a Laguerre–Gaussian (LG) vortex beam is investigated. The particles with different size and dielectric parameter tensor elements are arbitrarily configured. Based on the continuous boundary conditions at each sphere surface, the interactive scattering coefficients are derived. The internal and near-surface field is investigated to describe the propagation of LG vortex beam through the NaCl crystal. In addition, the far fields of some typical anisotropic medium such as LiNbO3, TiO2 bispheres illuminated by an LG vortex beam are numerically presented in detail to analyze the influence of the anisotropic parameters, sphere positions, separation distance and topological charge etc. The results show that LG vortex beam has a better recovery after interacting with a spherical particle compared with Gaussian beam. The study in the paper are useful for the further research on the scattering and propagation characteristics of arbitrary vortex beam in anisotropic chains and periodic structure.

Elevated temperature dependence of the anisotropic visible-to-ultraviolet dielectric function of monoclinic β-Ga2O3

We report on the temperature dependence of the dielectric tensor elements of n-type conductive β-Ga2O3 from 22 °C to 550 °C in the spectral range of 1.5 eV–6.4 eV. We present the temperature dependence of the excitonic and band-to-band transition energy parameters using a previously described eigendielectric summation approach [A. Mock et al., Phys. Rev. B 96, 245205 (2017)]. We utilize a Bose-Einstein analysis of the temperature dependence of the observed transition energies and reveal electron coupling with average phonon temperature in excellent agreement with the average over all longitudinal phonon plasmon coupled modes reported previously [M. Schubert et al., Phys. Rev. B 93, 125209 (2016)]. We also report a linear temperature dependence of the wavelength independent Cauchy expansion coefficient for the anisotropic below-band-gap monoclinic dielectric tensor elements.

Optical cavity resonance with magnetized plasma

Indefinite media with mixed signs of dielectric tensor elements possess unbounded equifrequency surfaces that have been utilized for diverse applications such as superimaging, enhanced spontaneous emission, and thermal radiation. One particularly interesting application of indefinite media is an optical cavity supporting anomalous scaling laws. In this Letter, we show that by replacing an indefinite medium with magnetized plasma one can construct a tunable indefinite cavity. The magnetized plasma model is based on realistic semiconductor material properties at terahertz frequencies that show hyperbolic dispersion in a certain frequency regime. The hyperbolic dispersion features are utilized for the design of optical cavities. Dramatically different sizes of cavities can support the same resonance mode at the same frequency. For a cavity of fixed size, the anomalous scaling law between the resonance frequency and mode number is confirmed. The resonance frequency can be strongly modulated by changing the strength of the applied magnetic field. The proposed model provides active controllability of terahertz resonances on the deep subwavelength scale with realistic semiconductor materials.

Anisotropy, phonon modes, and lattice anharmonicity from dielectric function tensor analysis of monoclinic cadmium tungstate

We determine the frequency dependence of four independent CdWO$_4$ Cartesian dielectric function tensor elements by generalized spectroscopic ellipsometry within mid-infrared and far-infrared spectral regions. Single crystal surfaces cut under different angles from a bulk crystal, (010) and (001), are investigated. From the spectral dependencies of the dielectric function tensor and its inverse we determine all long wavelength active transverse and longitudinal optic phonon modes with $A_u$ and $B_u$ symmetry as well as their eigenvectors within the monoclinic lattice. We thereby demonstrate that such information can be obtained completely without physical model line shape analysis in materials with monoclinic symmetry. We then augment the effect of lattice anharmonicity onto our recently described dielectric function tensor model approach for materials with monoclinic and triclinic crystal symmetries [Phys. Rev. B, 125209 (2016)], and we obtain excellent match between all measured and modeled dielectric function tensor elements. All phonon mode frequency and broadening parameters are determined in our model approach. We also perform density functional theory phonon mode calculations, and we compare our results obtained from theory, from direct dielectric function tensor analysis, and from model lineshape analysis, and we find excellent agreement between all approaches. We also discuss and present static and above reststrahlen spectral range dielectric constants. Our data for CdWO$_4$ are in excellent agreement with a recently proposed generalization of the Lyddane-Sachs-Teller relation for materials with low crystal symmetry [Phys. Rev. Lett. 117, 215502 (2016)].

Electronic structure and optical properties of the single crystal and two-dimensional structure of CdWO4 from first principles

In this paper, we have investigated the electronic structure and optical properties of the single crystal and two-dimensional (2D) structure of cadmium tungstate (CdWO4). This investigation includes calculation of the density of states (DOS), dielectric tensor elements and reflectivity. All the calculations have been done by full potential augmented plane waves plus local orbitals (FP-APW+lo) with Wien2k code. The calculated band gaps for the single crystal and 2D structure along [010] direction are 4.2 and 5.02eV, respectively. The results show that in the 2D structure of CdWO4, the electron density of the surface oxygen atoms is much more than the electron density of the inside oxygen atoms. This difference in the density has the main role in the optical properties. The results of the dielectric tensor elements and reflectivity for the single crystal are in good agreement with the experimental values. The results of the dielectric tensor elements and reflectivity for the 2D structure in comparison with the single crystal have shown that the intensity and place of the calculated peaks reduced and shifted, respectively. These results can be related to the surface oxygen atoms and thickness of the 2D structure.

Anisotropy, phonon modes, and free charge carrier parameters in monoclinicβ-gallium oxide single crystals

We derive a dielectric function tensor model approach to render the optical response of monoclinic and triclinic symmetry materials with multiple uncoupled infrared and farinfrared active modes. We apply our model approach to monoclinic $\beta$-Ga$_2$O$_3$ single crystal samples. Surfaces cut under different angles from a bulk crystal, (010) and ($\bar{2}$01), are investigated by generalized spectroscopic ellipsometry within infrared and farinfrared spectral regions. We determine the frequency dependence of 4 independent $\beta$-Ga$_2$O$_3$ Cartesian dielectric function tensor elements by matching large sets of experimental data using a point by point data inversion approach. From matching our monoclinic model to the obtained 4 dielectric function tensor components, we determine all infared and farinfrared active transverse optic phonon modes with $A_u$ and $B_u$ symmetry, and their eigenvectors within the monoclinic lattice. We find excellent agreement between our model results and results of density functional theory calculations. We derive and discuss the frequencies of longitudinal optical phonons in $\beta$-Ga$_2$O$_3$. We derive and report density and anisotropic mobility parameters of the free charge carriers within the tin doped crystals. We discuss the occurrence of longitudinal phonon plasmon coupled modes in $\beta$-Ga$_2$O$_3$ and provide their frequencies and eigenvectors. We also discuss and present monoclinic dielectric constants for static electric fields and frequencies above the reststrahlen range, and we provide a generalization of the Lyddane-Sachs-Teller relation for monoclinic lattices with infrared and farinfrared active modes. We find that the generalized Lyddane-Sachs-Teller relation is fulfilled excellently for $\beta$-Ga$_2$O$_3$.

Mode conversion in magneto-optic rib waveguide made by silica matrix doped with magnetic nanoparticles

The TE-TM mode conversion is an important requirement for magneto-optical waveguide devices. It has been analyzed by means of a full-vectorial beam propagation method. The present work is based on the study of the influence of diagonal and off-diagonal elements of the complex dielectric tensor on the conversion efficiency in magneto-optical rib waveguide. We have found that in the presence of the absorption (taking into account the imaginary part of diagonal tensor) the conversion efficiency is affected by the absorption and these latter increases as the volume fraction of nanoparticles increases.

Electronic transitions and dielectric function tensor of a YMnO3 single crystal in the NIR-VUV spectral range

The dielectric function tensor elements of an YMnO3 single crystal yield M0 critical point like band-band absorption with discrete spectrally localized Lorentzian transitions within the band gaps.

Electromagnetic Wave Scattering From a Thin Annular Magnetized Relativistic Rotating Electron Beam With Dielectric Rod

By using relativistic corrections in dielectric tensor elements of thin annular magnetized relativistic rotating electron beam (TAMRREB), the scattering of a plane wave from the mentioned object, including the dielectric rod, is investigated. The resonance frequencies and their variations versus the geometrical dimensions of the beam, its density, and its rotating frequency are presented. The graphs of the backward scattering cross section and the graphs of polarized charge density on the boundaries of the problem for two different rotating frequencies, for two different plasma frequencies, for two different dielectric constants of rod, and for two different geometrical dimensions are simulated.

Extended magneto optic method to explore the longitude magneto optic Kerr effect of the magnetic ultrathin film grown on optically anisotropic substrate

The traditional magneto optic Kerr effect (MOKE) method is extended and the new method can be applied to investigate the magnetic properties of magnetic ultrathin film even multilayer containing anisotropic optical medium as long as we choose a proper coordinate system. Based on this method, any interface structure—magnetic ultrathin film grown on optically anisotropic substrate—can be explored by MOKE. The computer simulation shows relation between longitude Kerr rotation and incident angle. A further analysis indicates that the three elements of dielectric tensor of the anisotropic substrate play different roles in determining the relation between Kerr rotation and incident angle. Besides, the influence of the three dielectric constants of the substrate on the Kerr rotation is also found and parameters of special crystals have been taken into simulation to find the error ratio that the traditional method results for multilayer containing anisotropic optical substrate. These results show that the extended method can enhance the accuracy of measurement and help us to choose proper substrate for the ultrathin magnetic films when using MOKE to explore them.

Dielectric tensor elements for the description of waves in rotating inhomogeneous magnetized plasma spheroids

The dielectric permittivity tensor elements of a rotating cold collisionless plasma spheroid in an external magnetic field with toroidal and axial components are obtained. The effects of inhomogeneity in the densities of charged particles and the initial toroidal velocity on the dielectric permittivity tensor and field equations are investigated. The field components in terms of their toroidal components are calculated and it is shown that the toroidal components of the electric and magnetic fields are coupled by two differential equations. The influence of thermal and collisional effects on the dielectric tensor and field equations in the rotating plasma spheroid are also investigated. In the limiting spherical case, the dielectric tensor of a stationary magnetized collisionless cold plasma sphere is presented.

Magnetic Ordering and Structural Phase Transitions in a Strained UltrathinSrRuO3/SrTiO3Superlattice

Ruthenium-based perovskite systems are attractive because their structural, electronic, and magnetic properties can be systematically engineered. The SrRuO3/SrTiO3 superlattice, with its period consisting of one unit cell each, is very sensitive to strain change. Our first-principles simulations reveal that, in the high tensile strain region, it transits from a ferromagnetic metal to an antiferromagnetic insulator with clear tilted octahedra, while in the low strain region, it is a ferromagnetic metal without octahedra tilting. Detailed analyses of three spin-down Ru-t(2g) orbitals just below the Fermi level reveal that the splitting of these orbitals underlies these dramatic phase transitions, with the rotational force constant of RuO(6) octahedron high up to 16 meV/Deg(2), 4 times larger than that of TiO(6). Differently from nearly all the previous studies, these transitions can be probed optically through the diagonal and off-diagonal dielectric tensor elements. For a 1% change in strain, our experimental spin moment change is -0.14±0.06 μ(B), quantitatively consistent with our theoretical value of -0.1 μ(B).