D. Y. Smith

The Optical Properties of Metallic Aluminum

Publisher Summary It is noted that the optical properties of metallic aluminum are among the most widely measured and analyzed of any material. They are generally dominated by three practically nonoverlapping groups of electronic transitions corresponding to absorptions by conduction band, L-shell, and K-shell electrons. The two strong interband transitions of the conduction-electron spectrum in the crystalline material are a consequence of the parallel-band effect that occurs in almost free-electron polyvalent metals. In these materials the occupied and unoccupied conduction bands are effectively parallel over substantial regions of k space in the vicinity of high-symmetry planes parallel to the zone faces. The key factor in obtaining accurate values of the optical properties came from the discovery that aluminum could be sputtered or evaporated to form highly reflecting metal films.

Dispersion relations and sum rules for magnetoreflectivity

Dispersion relations and sum rules for the dichroic reflectivity and phase shifts of circularly polarized modes are developed for the magneto-optical case. The reduction in crossing-relation symmetry arising from the presence of a magnetic field and the consequent non-Kramers-Kronig form of the dichroism dispersion relations are discussed in terms of the analyticity of the amplitude reflectivity. Sum rules are derived from the low- and high-frequency limits of the dichroism dispersion relations. These rules include the general results that ∫0∞ω-1 ln[r+(ω)/r-(ω)]dω=0 and ∫0∞[θ+(ω)-θ-(ω)] dω=πωc, where r±(ω) and θ±(ω) are the amplitude and phase of the amplitude reflectivity for the circular modes and ωc is the cyclotron frequency. Approximate finite-energy dispersion relations and sum rules are developed and their range of validity examined.

Dispersion relations for complex reflectivities

A simplified derivation of the dispersion relations connecting the phase and amplitude of the normal optical reflectivity of a vacuum-matter interface is presented. The non-Kramers-Kronig form of the expression for reflectivity in terms of phase is shown to be a consequence of the fact that amplitudes are determined only up to a multiplicative constant by the phase. The phase, however, is uniquely determined by the amplitude.

Comments on the dispersion relations for the complex refractive index of circularly and elliptically polarized light

The generalization to circularly polarized modes of the Kramers-Kronig relations for the complex refractive index is discussed in terms of the analyticity of the index to clarify the physical basis of the generalized dispersion relations. A compact form for the circular-mode dispersion relations is obtained that is particularly useful in treating dichroic effects and for deriving optical sum rules. The procedure is generalized to elliptically polarized modes. It is shown that the generalized dispersion relations must be used for the optical constants of elliptic modes that retain their ellipticity to arbitrarily small frequencies, while dispersion relations of the Kramers-Kronig form apply to elliptic modes that are linearly polarized in the limit of small frequencies.

Superconvergence relations and sum rules for reflection spectroscopy

Superconvergence relations for the complex reflectivity r˜(ω), its amplitude r(ω), and its phase θ(ω) are considered. It is shown that infinite families of sum rules can be systematically generated for various moments of Re r˜m(ω) and Im r˜m(ω); these rules are analogous to similar sum rules for the refractive index. They provide self-consistency checks on ellipsometric and interferometric measurements in which both phase and amplitude information are obtained experimentally. For the more common situation in which only the reflectivity amplitude is measured, it is customary to decouple amplitude and phase by considering the complex function ln r˜(ω) = ln r(ω) + iθ(ω) Simple superconvergence rules do not hold for this quantity because of the divergence of ln r(ω) at high frequencies where r(ω) approaches zero. However, this difficulty can be partially overcome by treating the logarithmic derivative of ln r˜ or by limiting consideration to finite energy intervals. The resulting rules are applicable to nonmetals and include a superconvergence relation for dr/dω and finite-energy reflectance-conservation and phase f-sum rules. The derivative rule is applicable to reflectance and modulated-reflectance studies, whereas the finite-energy rules provide direct self-consistency checks on infrared spectra. Examples of the application of these rules to the reststrahl spectra of an ionic solid are discussed.

Excited states of the f center in alkali halides

Abstract Several F-center excited states have been computed in the semicontinuum model. For absorption the 2s state in RbCl is computed to lie 0.07 eV above the 2p, in agreement with recent experiments; for emission, the two states tend to cross. A number of other results based on the semicontinuum model are also given.

Cauchy's dispersion equation reconsidered: Dispersion in silicate glasses

We formulate a novel method of characterizing optically transparent substances using dispersion theory. The refractive index is given by a generalized Cauchy dispersion equation with coefficients that are moments of the uv and ir absorptions. Mean dispersion, Abbé number, and partial dispersion are combinations of these moments. The empirical relation between index and dispersion for families of glasses appears as a consequence of Beers law applied to the uv spectra.

Parallel simulation of high reynolds number vascular flows

Publisher Summary The chapter provides an overview of the governing equations, time advancement scheme, and spectral element method. The chapter describes boundary condition treatment for simulating transition in bifurcation geometries. The chapter also presents parallel considerations and performance results, and provides results for transitional flow in an arteriovenous graft model. The simulation of turbulent vascular flows presents significant numerical challenges. Because such flows are weakly turbulent, they lack an inertial subrange that is amenable to subgrid-scale (SGS) modeling required for large-eddy or Reynolds-averaged Navier–Stokes simulations. The only reliable approach at present is to directly resolve all scales of motion. While the Reynolds number is not high, the physical dissipation is small. Weakly turbulent blood flow—such as the one that occurs in post-stenotic regions or subsequent to graft implantation—exhibits a much broader range of scales than does its laminar counterpart, and thus requires an order of magnitude increase in spatial and temporal resolution, making fast iterative solvers and parallel computing necessities.

X-Ray Optical Properties: A Review Of The Constraints And The Data Base

Elements of the theory of x-ray scattering relevant to x-ray optics applications are reviewed. Dispersion-theory and sumrule constraints are considered in relation to determining the refractive index from measured attenuation spectra. Current tabulations of x-ray cross sections and scattering factors are summarized and discussed.

Impurity-ligand effects on the magneto-optically measured spin-orbit splitting of trapped electron centres

Abstract The spin-orbit interaction of FA-type centres (FA, Z2 + ) has been studied experimentally and theoretically. It is found to have a greater anisotropy than anticipated from early experiments on FA(Na) centres. Nearest-neighbour impurities with sufficiently large spin-orbit interaction may dominate the effect to yield both negative and positive spin-orbit energies depending on the relative orientation of the centres and the measuring light beam.