A new magneto-optical sum rule is derived for circular magnetic dichroism in the x-ray region (CMXD). The integral of the CMXD signal over a given edge allows one to determine the ground-state expectation value of the orbital angular momentum. Applications are discussed to transition-metal and rare-earth magnetic systems.

X-ray circular-dichroism as a probe of orbital magnetization

Infrared optical constants collected from the literature are tabulated. The data for the noble metals and Al, Pb, and W can be reasonably fit using the Drude model. It is shown that -epsilon1(omega) = epsilon2(omega) approximately omega(2)(p)/(2omega(2)(tau)) at the damping frequency omega = omega(tau). Also -epsilon1(omega(tau)) approximately - (1/2) epsilon1(0), where the plasma frequency is omega(p).

/pdf/optical-properties-of-the-metals-al-co-cu-au-fe-pb-ni-pd-pt-xouhrd4v2j.pdf

Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared

The computer code system PENELOPE (version 2008) performs Monte Carlo simulation of coupled
electron-photon transport in arbitrary materials for a wide energy range, from a few hundred eV to
about 1 GeV. Photon transport is simulated by means of the standard, detailed simulation scheme.
Electron and positron histories are generated on the basis of a mixed procedure, which combines
detailed simulation of hard events with condensed simulation of soft interactions. A geometry package
called PENGEOM permits the generation of random electron-photon showers in material systems
consisting of homogeneous bodies limited by quadric surfaces, i.e., planes, spheres, cylinders, etc. This
report is intended not only to serve as a manual of the PENELOPE code system, but also to provide the
user with the necessary information to understand the details of the Monte Carlo algorithm.

/pdf/penelope-2006-a-code-system-for-monte-carlo-simulation-of-43nx3zmw6c.pdf

PENELOPE-2006: A Code System for Monte Carlo Simulation of Electron and Photon Transport

This review discusses how low-energy, valence excitations created by swift electrons can render information on the optical response of structured materials with unmatched spatial resolution. Electron microscopes are capable of focusing electron beams on sub-nanometer spots and probing the target response either by analyzing electron energy losses or by detecting emitted radiation. Theoretical frameworks suited to calculate the probability of energy loss and light emission (cathodoluminescence) are revisited and compared with experimental results. More precisely, a quantum-mechanical description of the interaction between the electrons and the sample is discussed, followed by a powerful classical dielectric approach that can be in practice applied to more complex systems. We assess the conditions under which classical and quantum-mechanical formulations are equivalent. The excitation of collective modes such as plasmons is studied in bulk materials, planar surfaces, and nanoparticles. Light emission induced by the electrons is shown to constitute an excellent probe of plasmons, combining sub-nanometer resolution in the position of the electron beam with nanometer resolution in the emitted wavelength. Both electron energy-loss and cathodoluminescence spectroscopies performed in a scanning mode of operation yield snap shots of plasmon modes in nanostructures with fine spatial detail as compared to other existing imaging techniques, thus providing an ideal tool for nanophotonics studies.

/pdf/optical-excitations-in-electron-microscopy-3d2rfnfkst.pdf

Optical excitations in electron microscopy

Self-consistent optical parameters of intrinsic silicon at 300 K including temperature coefficients

An iterative, self-consistent procedure for the Kramers-Kronig analysis of data from reflectance, ellipsometric, transmission, and electron-energy-loss measurements is presented. This procedure has been developed for practical dispersion analysis since experimentally no single optical function can be readily measured over the entire range of frequencies as required by the Kramers-Kronig relations. The present technique is applied to metallic aluminum as an example. The results are then examined for internal consistency and for systematic errors by various optical sum rules. The present procedure affords a systematic means of preparing a self-consistent set of optical functions provided some optical or energy-loss data are available in all important spectral regions. The analysis of aluminum discloses that currently available data exhibit an excess oscillator strength, apparently in the vicinity of the L edge. A possible explanation is a systematic experimental error in the absorption-coefficient measurements resulting from surface layers: possibly oxides: present in thin-film transmission samples. A revised set of optical functions has been prepared by an ad hoc reduction of the reported absorption coefficient above the L edge by 14%. These revised data lead to a total oscillator strength consistent with the known electron density and are in agreement with dc-conductivity and stopping-power measurementsmore » as well as with absorption coefficients inferred from the cross sections of neighboring elements in the periodic table. The optical functions resulting from this study show evidence for both the redistribution of oscillator strength between energy levels and the effects on real transitions of the shielding of conduction electrons by virtual processes in the core states.« less

Self-consistency and sum-rule tests in the Kramers-Kronig analysis of optical data: Applications to aluminum

A systematic procedure is given for the derivation of sum rules for the optical constants of material media from dispersion relations, in analogy with superconvergence techniques of high-energy physics. In addition to the well-known $f$-sum rules, a number of new sum rules are obtained for the refractive index, the dielectric tensor, and its inverse. In particular, it is shown that the average value of the real refractive index over the whole frequency spectrum is equal to unity. The physical implications of the new results are discussed in connection with the dispersion of optical constants, with the effect of external perturbations, and with the theory of natural optical activity.

Superconvergence and Sum Rules for the Optical Constants

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.

The Optical Properties of Metallic Aluminum

A physical interpretation of recently obtained sum rules for dielectric functions and for the index of refraction is provided in terms of the inertial properties of the linear dielectric response of material media. The superconvergent sum rules are then compared with experimental optical data for AgCl, Al, and Mo and shown to produce good agreement as well as a critical test of extrapolations and of the Kramers-Kronig relations. A straightforward extension to higher powers of the optical constants and their moments is briefly discussed.

Superconvergence and sum rules for the optical constants: Physical meaning, comparison with experiment, and generalization

The number of electrons effective in optical processes up to an energy $\ensuremath{\omega}$, ${n}_{\mathrm{eff}}(\ensuremath{\omega})$, may be defined in three distinct ways, a situation which had led to considerable confusion. This is a consequence of the fact that oscillator-strength sums may be constructed from the imaginary part of the dielectric function ${\ensuremath{\epsilon}}_{2}(\ensuremath{\omega})$, the extinction coefficient $\ensuremath{\kappa}(\ensuremath{\omega})$, or the energy-loss function Im[${\ensuremath{\epsilon}}^{\ensuremath{-}1}(\ensuremath{\omega})$]. Here these quantities are investigated for an electronic system embedded in a polarizable medium of dielectric constant ${\ensuremath{\epsilon}}_{b}$. This model closely approximates valence electrons moving in the background of polarizable ion cores in a condensed phase. The oscillator-strength sums are found to differ significantly and are not simply related at energies for which the embedded system's oscillator strength is not exhausted. In the limit in which exhaustion occurs, the sums differ only because of the shielding effects of the polarizable medium. The $f$ sum for ${\ensuremath{\epsilon}}_{2}(\ensuremath{\omega})$ then yields the system's conventional oscillator strength while the $f$ sums for $\ensuremath{\kappa}(\ensuremath{\omega})$ and Im[${\ensuremath{\epsilon}}^{\ensuremath{-}1}(\ensuremath{\omega})$] yield effective "strengths" that are reduced from the conventional value by factors of ${\ensuremath{\epsilon}}_{b}^{\frac{\ensuremath{-}1}{2}}$ and ${\ensuremath{\epsilon}}_{b}^{\ensuremath{-}2}$, respectively. Similar results hold for the three definitions of ${n}_{\mathrm{eff}}(\ensuremath{\omega})$. The analysis of a system in terms of partial $f$ sums is shown to provide a check on the self-consistency of optical data as well as a means of determining core polarizabilities. These effects are illustrated for metallic aluminum.

David Y. Smith

Papers

Self-consistency and sum-rule tests in the Kramers-Kronig analysis of optical data: Applications to aluminum

Superconvergence and Sum Rules for the Optical Constants

The Optical Properties of Metallic Aluminum

Superconvergence and sum rules for the optical constants: Physical meaning, comparison with experiment, and generalization

Finite-energy f -sum rules for valence electrons