On the validity of modeling rayleigh scatterers by spheroids

For single homogeneous lossy dielectric Rayleigh particles, the manner in which the particle shape affects the absorption and scattering is examined by computing the polarizability tensor elements using a general purpose program valid for any rotationally symmetric body. The results for a number of generic shapes are compared with those for the corresponding spheroids. When the dielectric constant is real and negative, the resonances attributable to bulk and to shape-dependent or surface polariton modes are tracked as functions of the length-to-width ratio of the particle and the bulk dielectric constant. The adequacy of using spheroid approximations for individual particles in a dispersion is also discussed.     

The dielectric tensor components of anthracene derived from energy loss experiments

Energy loss spectra of anthracene single crystals corresponding to the dielectric tensor elements ? _xx , ? _yy and ? _zz were measured with 60 keV electrons, after having fixed the main axes of the dielectric tensor corresponding to ? _xx and ? _zz . The real and imaginary parts of the dielectric tensor elements are derived from the loss functions by a Kramers-Kronig-analysis. The results are compared with those obtained by other autors and with measurements on graphite.     

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.     

Local field corrections in trigonal Se

The inverse dielectric tensor ?^-1₀₀(q) in the static limit isevaluated in crystalline Se along two symmetry directions, by using a proper model Hamiltonian describing the covalent bond and modified sp³ orbitals as basis states. By comparing the results in diagonal approximation with these obtained including the off diagonal elements (ODE) of the dielectric matrix (DM) it is found that the local field corrections are very large and essential to reproduce the experimental dielectric tensor.     

Simulation of Characteristic Radiation of Highly Ionized Laser Plasma

In the tensor form, using the generalized Rayleigh–Gans–Debye approximation, the problem of the sum-frequency generation from a thin nonlinear layer deposited on a dielectric spherical particle placed in a dielectric medium is solved. The second-order nonlinear dielectric susceptibility tensor is chosen in a general form containing chiral components. In the vector and tensor forms, expressions are obtained that describe the spatial distribution of the sum-frequency radiation field generated by two plane electromagnetic elliptically polarized waves. Limiting expressions that describe the spatial distribution of the sum-frequency harmonic at small and large radii of the spherical layer are obtained. It is revealed that, at small radii of the spherical layer, the radiation due to the chiral anisotropy coefficients makes a dominant contribution to the generation.     

Measuring the Dielectric Permittivity of Sapphire at Temperatures 93–343 K

We consider a method for measuring the elements of the dielectric-permittivity tensor of a slightly lossy uniaxial anisotropic dielectric using the spectrum of resonance frequencies of a metal-dielectric resonator in the form of an axially anisotropic cylindrical specimen with endface metal mirrors. Measurements of both elements of the dielectric-permittivity tensor of sapphire at temperatures 93–343 K are performed using the spectrum of symmetric E modes. To avoid the influence of the residual gaps between the specimen and the mirrors, the endface surfaces of the specimen are metallized. We performed independent measurements of the axial and transverse elements of the permittivity tensor at room temperature from the spectra of azimuthal E modes and symmetric H modes. The values of the axial and transverse elements of the dielectric-permittivity tensor of sapphire in the range 93–343 K are presented with a spacing of 10 K.     

Analysis of Trapping Force and Torque for Fiber-optical Trap by the Finite-differential Time-domain (FDTD) Method

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Analysis of Trapping Force and Torque for Fiber-optical Trap by the Finite-differential Time-domain (FDTD) Method

In this paper,the FDTD method is used to calculate the light field distribution in an uncoated fiber probe with a small dielectric particle.By integrating Maxwell′s stress tensor in the FDTD calculation,the time-averaged force exerted on the dielectric particles with different sizes and at different positions is obtained.The calculation results are also verified experimentally.The force near the axis in the vicinity of the tip is about 10-14 N for the incident 10 mW laser of 980 nm.Furthermore,the torque exerting on an ellipsoidal dielectric particle by focusing light field with two fiber probes is calculated and the dependence of this torque on both the declination angle of the ellipsoidal particle and the incident laser power ratio of the two probes is obtained.The detailed intensity map within the particle is also given.     

Dielectric Characteristics for Radio Frequency Waves in a Laboratory Dipole Plasma

Transverse and parallel dielectric permittivity elements have been derived for radio frequency waves in a laboratory dipole magnetic field plasma. Vlasov equation is resolved for both the trapped and untrapped particles as a boundary value problem to define their separate contributions to the dielectric tensor components. To estimate the wave power absorbed in the plasma volume the perturbed electric field and current density components are decomposed in a Fourier series over the poloidal angle. In this case, the dielectric characteristics can be analyzed independently of the solution of the Maxwell's equations. As usual, imaginary part of the parallel permittivity elements is necessary to estimate the electron Landau damping of radio frequency waves, whereas imaginary part of the transverse permittivity elements is important to estimate the wave dissipation by the cyclotron resonances. Computations of the imaginary part of the parallel permittivity elements are carried out in a wide range of the wave frequencies. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sum-Frequency Generation from a Thin Cylindrical Layer

In the Rayleigh–Gans–Debye approximation, we have solved the problem of the sum-frequency generation by two plane elliptically polarized electromagnetic waves from the surface of a dielectric particle of a cylindrical shape that is coated by a thin layer possessing nonlinear optical properties. The formulas that describe the sum-frequency field have been presented in the tensor and vector forms for the second-order nonlinear dielectric susceptibility tensor, which was chosen in the general form, containing chiral components. Expressions describing the sum-frequency field from the cylindrical particle ends have been obtained for the case of a nonlinear layer possessing chiral properties. Three-dimensional directivity patterns of the sum-frequency radiation have been analyzed for different combinations of parameters (angles of incidence, degrees of ellipticity, orientations of polarization ellipses, cylindrical particle dimensions). The mathematical properties of the spatial distribution functions of the sum-frequency field, which characterize the symmetry of directivity patterns, have been revealed.     

Theoretical calculation of the dielectric tensor and field equations in columns with elliptical cross-sections including inhomogeneous magnetized cold collisionless drift and rotating plasmas

In this paper the effects of the inhomogeneity of the density of charged particles and the initial axial, rotating and radial motion on the dielectric permittivity tensor and the field equations in a long column of multi-layer magnetized plasmas with confocal elliptical cross-sections are investigated. The elements of the dielectric permittivity tensor and the generalized field equations of each region are obtained. The field equations for hybrid modes in each region of the inhomogeneous plasma with coaxial elliptical cylindrical boundaries are presented.     

Effective-dielectric-constant method for the problem of wave diffraction by a close-spaced dielectric grating

A simple method for determination of effective dielectric constants is proposed that allows a close-spaced two-dimensionally periodic dielectric layer with rectangular elements to be replaced by a homogeneous and anisotropic layer of the same thickness. The method makes it unnecessary to solve the complicated problem of determination of the fields within the elements for calculation of the plane-wave reflection and transmission coefficients in a long-wave approximation, which considerably simplifies the calculations. Comparison with known solutions obtained by rigorous methods for one-dimensionally periodic gratings shows exact agreement of the results. The method is easily extended to magnetodielectric media as well as to multicomponent media, including those whose dielectric constants are functions of the coordinate perpendicular to the layer.Academician A. L. Mints Radio-Engineering Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 3-4, pp. 286–294, March–April, 1993.     

Magneto-optics in the ultrafast regime: thermalization of spin populations in ferromagnetic films

We have characterized by pump-probe polarimetry the time-dependent dielectric tensor in a CoPt3 ferromagnetic film excited by 20 fs laser pulses. It is shown that, after the thermalization time of the electrons (approximately 50 fs), the dynamics of the real and the imaginary parts of the Voigt vector are identical. In addition, their relative variation is 10 times larger than that of the diagonal elements of the tensor, which allows one to infer that the spins dominate the magneto-optical response. During the thermalization process, the temporal behavior of the tensor elements opens new questions concerning the dynamics of the spins associated to a nonthermal electronic population in a ferromagnet.     

Simulation of a periodic dielectric corrugation with an equivalent anisotropic layer

A periodic, corrugated, dielectric layer is simulated by an anisotropic dielectric layer of equal thickness. The tensor elements of the equivalent dielectric layer are given in terms of the permittivity of the dielectric material, the period of the surface corrugation, and the width of the corrugations. The validity of this technique is verified by comparing the reflection coefficient of the equivalent layer with that of the corresponding corrugated layer using the moment method. Employing a multiple layer approach, the technique is extended to handle periodic surfaces with arbitrary cross sections which can be used to design millimeter wave dielectric plate polarizers and absorbers.     

THE THEORETICAL INVESTIGATION OF THz ELECTROMAGNETIC WAVES IN A ROD DEGENERATE PLASMA-WAVEGUIDE

By using the Fourier components of dielectric tensor elements of cold collisionless degenerate plasmas, the dispersion relation of electromagnetic waves in a cylindrical metallic waveguide with a degenerate plasma column protected by an annular dielectric layer are obtained. The permissible frequency regions for slow and fast waves in E-mode (TM) are presented. Furthermore, the graph of cutoff frequency versus the radius of plasma column for the fast waves is investigated. In addition, the time growth rate for excitation of symmetric slow E-modes (TM) by a thin annular relativistic electron beam (TAREB) is studied. The graph of time growth rate respect to radius of dielectric layer and accelerating voltage are presented. PACS No. 52.25.     

PtMn/Co多层膜的磁光特性研究

采用磁控溅射法制备了一系列的Mn掺杂的PtMn/Co多层膜.通过测量得到的磁光常数和光学常 数,计算介电张量的对角元和非对角元,得到在掺杂较大时,克尔角的变化是由于介电张量 的非对角元引起的;在掺杂量较小时,克尔角的变化是由介电张量的对角元和非对角元以及 光学常数的变化引起的.     

Validation of the effective-medium approximation for the dielectric permittivity of oriented nanoparticle-filled materials: effective permittivity for dielectric nanoparticles in multilayer photonic composites

A formula for the effective permittivity for two-dimensional particles embedded in a host matrix is derived and a method for its numerical evaluation is described. The method is applied to specific cases of circular, square, rectangular and triangular particles. Shapes are assumed for the inclusion particles. Data for obtaining the effective permittivity is provided for a wide range of filling fractions, geometries and dielectric contrasts between the particles and the matrix under the assumption of the quasi-static approximation, that is, the wavelength of the electric field is assumed to be much larger than the particle size. Metallic particles with complex and frequency-dependent dielectric constants are treated, as well as no-loss dielectric inclusions. Calculations are validated by comparing the results of the reflectivity obtained for a composite layer using the transfer-matrix method, assuming the layer to be an effective medium, to those using the finite-element method and accounting for the heterogeneous material. PACS 78.20.-e; 78.20.Bh; 78.20.Ci; 78.66.Sq; 78.66.Vs     

Mechanical stress tensor for a fluid in a magnetostatic field

Summary Two constraints on the form of the mechanical stress tensor for an uncharged and linear dielectric fluid at rest in a magnetostatic field are determined. Moreover, it is shown that the stress tensor proposed by Helmholtz, that proposed by Einstein-Laub and that proposed by Liu-Müller are unacceptable as mechanical stress tensors for a dielectric fluid in the conditions stated above.     

Electromagnetic oscillations in a rectangular waveguide with a transversely magnetized ferrite plate

The complex propagation constant in a rectangular waveguide with a transversely magnetized ferrite plate has been found by a numerical calculation. The magnetic properties of the ferrite medium are described by the standard permeability tensor for a polycrystalline ferrite, having real and imaginary parts. The solutions are given as curves on the complex propagation-constant plane. The parameter is the relative magnetizing field, which varies over a wide range including a ferromagnetic resonance. From the family of curves obtained for various relative magnetizations and damping parameters, one can quantitatively evaluate the relation between the types of oscillations. This relation depends on the position of the ferrite plate in the waveguide and on the dielectric constant of the ferrite as well as on the magnetization and damping constant.Translated from Izvestiya VUZ. Fizika, No. 4, pp. 74–81, April, 1970.     

Degenerate and non-degenerate four-wave mixing in semiconductor quantum dots

Il Nuovo Cimento D - We present wave-mixing techniques which are used to determine the tensor elements of the non-linear dielectric susceptibility, the dynamics of non-linear optical effects and...