Quantitative modelling of the surface plasmon resonances of metal nanoclusters sandwiched between dielectric layers: the influence of nanocluster size, shape and organization

The effects of size, shape and organization on the surface plasmon resonances of Ag nanoclusters sandwiched between Si(3)N(4) layers are studied by transmission electron microscopy and anisotropic spectroscopic ellipsometry. We present an easy-to-handle model that quantitatively links the nanostructure and optical response of the films, which are considered as dielectric/metal:dielectric/dielectric trilayers, with the central nanocomposite layer being an effective medium whose optical properties are described by an anisotropic dielectric tensor. The components of this tensor are calculated using a generalization of the Yamaguchi theory taking into account the real organization, size and shape distributions of ellipsoidal nanoclusters, whose electronic properties are assumed to reflect shape-dependent finite size effects. Using this model, it is shown that the optical response of the films in the visible range is dominated by the excitation of the surface plasmon resonance of the clusters along their in-plane long axis, while no surface plasmon resonance resulting from an excitation along their in-plane short axis can be observed due to damping effects. Moreover, the spectral position of this resonance appears to be mainly affected by the average shape of the clusters, and weakly by their size, their shape distribution and the electromagnetic interaction between them.     

Analysis of electromagnetic scattering by uniaxial anisotropic bispheres

Based on the generalized multiparticle Mie theory and the Fourier transformation approach, electromagnetic (EM) scattering of two interacting homogeneous uniaxial anisotropic spheres with parallel primary optical axes is investigated. By introducing the Fourier transformation, the EM fields in the uniaxial anisotropic spheres are expanded in terms of the spherical vector wave functions. The interactive scattering coefficients and the expansion coefficients of the internal fields are derived through the continuous boundary conditions on which the interaction of the bispheres is considered. Some selected calculations on the effects of the size parameter, the uniaxial anisotropic absorbing dielectric, and the sphere separation distance are described. The backward radar cross section of two uniaxial anisotropic spheres with a complex permittivity tensor changing with the sphere separation distance is numerically studied. The authors are hopeful that the work in this paper will help provide an effective calibration for further research on the scattering characteristic of an aggregate of anisotropic spheres or other shaped anisotropic particles.     

Brillouin Diagrams for Optical Wave Propagation in Twisted Dielectric Media

Light propagation in an inhomogeneous, anisotropic medium is discussed. The medium shows the most general anisotropy (optically biaxial) and a special kind of inhomogeneity: rotation of a principal axis of the dielectric tensor about the z-axis. Since the analytic treatment is very troublesome, we use group theory to deduce qualitative statements on frequency splitting in the Brillouin diagram. As in all periodic anisotropic media, where two different group velocities exist, an infinite number of stop bands is produced by a splitting into maximally three stop bands at each point of interaction. Two special cases for the dielectric tensor are treated also: optically biaxial media with one axis in the z -direction and optically uniaxial media with an oblique optical axis. The group theory required is similar to the theory of crystallographic double space groups.     

The Metal-Dielectric Resonator Method of Measuring the Parameters of Radio Materials

The use of symmetrical H- and E-modes and asymmetrical E-modes in a longitudinally anisotropic dielectric cylinder with metal mirrors at the ends to measure its permittivity and dielectric loss tangent is considered. It is shown that the method has wider possibilities compared with the IEC-61338 recommendations. The results of a measurement of the dielectric parameters of a number of materials in the 2–78 GHz frequency band, including the permittivity tensor of sapphire, are presented. __________ Translated from Izmeritel'naya Tekhnika, No. 9, pp. 65–70, September, 2005.     

Time-dependent heat transfer in a plate with anisotropy of general form under the action of pulsed heat sources

An analytical solution to the problem of the theory of heat conduction in an anisotropic band under the pulsed (point) action of heat sources has been obtained for the first time by constructing the boundary influence function from using the Fourier and Laplace integral transforms. An arbitrary orientation of the principal axes of the thermal conductivity tensor and arbitrary (including negative) values of the off-diagonal components of the thermal conductivity tensor are taken into account. The found solution is extended to piecewise continuous densities of heat fluxes at the free boundaries of an anisotropic plate. The influences of the principal components and the orientation of the principal axes of the thermal conductivity tensor on time-dependent temperature fields in the anisotropic plate are determined. It is established that there are saddle points and separatrices dividing the temperature field into regions of influence of the boundary heat fluxes. The results are used to solve problems involving the thermal state of thermal protection made of anisotropic materials.     

The anisotropy of ac conductivity and dielectric constant of anisotropic conductor–insulator composites

We study the complex ac admittance tensor (ac conductivity and dielectric constant) of anisotropic conductor–insulator composite materials, based on anisotropic two-dimensional RC-networks consisting of randomly placed conductors and capacitors with different conductor existence (bond occupation) probabilities in two directions. We calculate numerically each component of the complex ac admittance tensor by applying a transfer matrix method and reveal the effect of the anisotropy of the bond occupation probability on the frequency characteristics of the ac admittance tensor. It is found that the dual relation holds for each diagonal component of the complex admittance tensor of the anisotropic two-dimensional RC-network. For the effective conductance in the metallic region, the anisotropy depends not only on the anisotropy of the bond occupation probability, but also on the frequency ω. We derive the analytical relation between the anisotropy of the conductance and the anisotropy of the bond occupation probability, at both the dc limit and ω RC = 1. The calculated results on the ac admittance are compared with the effective medium theory and how the accuracy of the theory is related with the microscopic current path is clarified.     

ON A MIXED-HYBRID FINITE ELEMENT METHOD FOR ANISOTROPIC PLATE BENDING PROBLEMS

The paper deals with a new mixed-hybrid finite element method for anisotropic elastic plate bending problems, which gives a simultaneous approximation to bending and twisting moment tensor and deflection fields in the interior of each triangle and traces of the displacement field and its normal derivative on sides of each triangle. Efficient computer implementation procedures for this mixed-hybrid scheme have been developed. Results of numerical experiments on different anisotropic plates of practical and research interest are given.     

Coupled-wave analysis of vector holograms. 3. Effects of intrinsic distribution of optical axis in anisotropic media

We investigated theoretically the interference of two counterpropagating polarized light beams in optically anisotropic media whose optical axis is in the film plane and is gradually rotated around the thickness direction. Results indicated that pure polarization modulation without intensity variation is obtained in the inhomogeneous media when the total angle of the rotation is much smaller than the total retardation. Reflective anisotropic gratings recorded by the polarization modulation were formulated as the perturbation of the dielectric tensor, and diffraction properties were studied using coupled-wave analysis (CWA) and a numerical method. By assuming that the period of the intrinsic distribution is substantially larger than that of the induced one, we demonstrated that CWA estimates the diffraction efficiency and the polarization state of the diffracted light with high accuracy.     

Magnetic field enhancement in electromagnetic forming systems using anisotropic materials

Electromagnetic Forming (EMF) is a type of high rate forming which exploits pulsed power techniques to create high intensive pulsed magnetic fields to rapidly reshape metal parts. This technique is sometimes called magnetic pulse forming. In this technique, a metal work-piece is pushed to a die and formed by a pressure created using an intensive, transient magnetic field. This magnetic field is produced by passing a pulse of electric current through a forming coil in a pulsed power circuit. Application of field shapers has been proposed to enhance the magnetic fields and consequently to increase the applied magnetic pressure at some desired regions. In this paper, 3D Finite element simulations have been applied to study the magnetic field distribution during an electromagnetic forming process with anisotropic material. Anisotropic magnetic material is described using a permeability tensor. Elements of this tensor are obtained from different magnetization curves dependent on the direction of the magnetic field. It has been shown that application of anisotropic materials with appropriate lamination directions can result in an enhancement of the magnetic field at desired points as well as in better overall efficiencies.     

From kinetic theory to hydrodynamics—Uniform anisotropic superfluids

Starting from kinetic theory, and neglecting dissipation, we derive the hydrodynamic equations for anisotropic superfluids. Only the case of a uniform texture in the absence of finite external fields is considered. Other than possessing a normal fluid density which is a diagonal tensor, anisotropic superfluids are characterized by the same hydrodynamics as in the isotropic case. These results constitute a generalization of the kinetic theory of Khalatnikov, which applies to the case of an isotropic quasiparticle spectrum dependent only on density.Supported in part by the National Science Foundation through grant number DMR74-23494.     

Optical Mode Characterization of the Configuration of a Thin Ferroelectric Liquid Crystal Cell Under an Applied Electric Field

Abstract

It is possible to probe directly the optic dielectric tensor configuration within a thin (about 3·5 μm) smectic layer of a ferroelectric liquid crystal (FLC) by the propagation of prism-coupled leaky Fabry-Perot optic modes. Incident monochromatic polarized light couples into the resonant modes of the system which are then observed as sharp dips in the reflected signal at specific incident angles. This work has shown that the FLC has an optic tensor profile which is consistent with the chevron formation of the smectic layers observed in X-ray scattering measurements. Also it is shown that under the application of a low d.c. applied field the optic dielectric tensor configuration distorts in a manner consistent with the retention of the chevron structure up to fields of about 10⁶ Vm^?1.     

Hypoelastic soft tissues. Part I: Theory

Refinements are made to an existing hypoelastic theory developed by Freed [18, 19] for the purpose of modeling the passive response of soft, fibrous, biological tissues. Oldroyd’s [27] operators for convected differentiation and integration, which he derived from the tensor transformation law, are re-derived here from an integral equation defined in the polar configuration. Fields that obey these convected polar operators are said to be viable tensor fields, from which a new definition for strain and its rate are obtained and applied to a hypoelastic theory for tissue. Anisotropy is addressed through a material tensor, from which viable tensor fields describing fiber strain and strain rate are constructed. Material anisotropy and material constitution are handled separately for maximum flexibility. Isochoric hypoelastic models for isotropic, anisotropic, and fiber/matrix composite materials are derived. A material function is introduced to address special attributes that biological fibers impart on tissue behavior, four of which are proposed that represent various ways through which the fiber constituents might be described. Application to in-plane biaxial deformation is the focus of part II of this paper [23].     

Electrodynamic field equations for composite superconducting structures in the mixed state

Governing vector partial differential equations for the linear electrodynamic response of an isotropic type-II superconductor in the mixed state are derived. A continuum theory of vortex motion is used, and two-fluid effects are also accounted for. The governing equation is sufficiently general to reduce to either normal metal or dielectric material results in special limits. The complex-valued conductivity tensor of the mixed state is made explicit, and is also discussed for an anisotropic superconductor. The theory is illustrated with a planar superconducting waveguide problem, wherein the complex propagation constant, phase velocity, and surface impedance are obtained.     

Explicit solutions for the optical properties of arbitrary magneto-optic materials in generalized ellipsometry

Analytic expressions for the eigenvalues for the four-wave components at an oblique angle of light incidence inside a randomly oriented anisotropic magneto-optic dielectric medium are reported explicitly. In particular, these solutions are valid as long as the dielectric function tensor consists of a symmetric and an antisymmetric part. The normalized Jones reflection and transmission coefficients, i.e., the generalized ellipsometric parameters of homogeneously layered systems having nonsymmetric dielectric properties, are obtained immediately from a recently reviewed 4 x 4 matrix approach. Our explicit solutions allow a future analysis of the generalized ellipsometric data of multilayered magneto-optic media regardless of the orientation of the material magnetization and crystalline axes and the angle of light incidence. Possible experimental thin-film situations are discussed in terms of generalized ellipsometric parameters and illustrated for birefringent free-carrier effects in heavily doped semiconductor thin films and for oblique magnetization directions in magneto-optic multilayer systems.     

Polarization energy calculations in molecular crystals

The self-consistent polarization field (SCPF) and Fourier transform methods of calculating the polarization energy of excess charges are compared. The SCPF method is extended (i) to treat molecules as a set of submolecules rather than single points in the inner region around the charge, and (ii) to treat the outer region around the charge as an anisotropic dielectric continuum rather Ethan an isotropic one. The contribution to the polarization energy from the outer region depends on the average 〈? ^?1〉, where ? is the dielectric tensor. These extensions allow the SCPF method to be used for elongated molecules, with potential applications to various systems lacking translational symmetry.     

Generalized far-infrared magneto-optic ellipsometry for semiconductor layer structures: determination of free-carrier effective-mass,mobility, and concentration parameters in n-type GaAs

We report for the first time on the application of generalized ellipsometry at far-infrared wavelengths (wave numbers from 150 cm(-1) to 600 cm(-1)) for measurement of the anisotropic dielectric response of doped polar semiconductors in layered structures within an external magnetic field. Upon determination of normalized Mueller matrix elements and subsequent derivation of the normalized complex Jones reflection matrix r of an n-type doped GaAs substrate covered by a highly resistive GaAs layer, the spectral dependence of the room-temperature magneto-optic dielectric function tensor of n-type GaAs with free-electron concentration of 1.6 x 10(18) cm(-3) at the magnetic field strength of 2.3 T is obtained on a wavelength-by-wavelength basis. These data are in excellent agreement with values predicted by the Drude model. From the magneto-optic generalized ellipsometry measurements of the layered structure, the free-carrier concentration, their optical mobility, the effective-mass parameters, and the sign of the charge carriers can be determined independently, which will be demonstrated. We propose magneto-optic generalized ellipsometry as a novel approach for exploration of free-carrier parameters in complex organic or inorganic semiconducting material heterostructures, regardless of the anisotropic properties of the individual constituents.     

Perfectly matched anisotropic layer for the numerical analysis ofunbounded eddy-current problems

An extension of the perfectly matched layer (PML) technique in quasi-static fields is developed. The new low frequency PML is based on a fictitious medium with diagonal tensor anisotropy. On the basis of a theoretical investigation, the material properties of the anisotropic layer are specified, so that it will be reflectionless for an arbitrary eddy-current field that may exist in free space. Furthermore, the PML is designed in such a way that outgoing eddy-current fields are sufficiently absorbed. The effectiveness of the low-frequency PML is validated by the implementation of the finite-element solution of a simple two-dimensional eddy-current problem as well as a more complicated three-dimensional one     

Wide-angle beam propagation method for liquid-crystal device calculations

A wide-angle beam propagation method suitable for analyzing anisotropic devices involving liquid crystals is presented. The mathematical formulation is based on a system of coupled differential equations involving an electric and a magnetic field component. The contribution of all dielectric tensor elements is included. A numerical implementation based on finite differences is used. Numerical examples are focused on light-wave propagation within twisted nematic pixels found in microdisplays, with all effects arising at pixel edges that are incorporated. A comparison between the results obtained and the prediction of finite-difference time-domain simulations is conducted, showing satisfactory agreement. The required computational effort is found to be minimal.