Polarization of tightly focused laser beams

The polarization properties of monochromatic light beams are studied. In contrast to the idealization of an electromagnetic plane wave, finite beams which are everywhere linearly polarized in the same direction do not exist. Neither do beams which are everywhere circularly polarized in a fixed plane. It is also shown that transversely finite beams cannot be purely transverse in both their electric and magnetic vectors, and that their electromagnetic energy travels at less than c. The electric and magnetic fields in an electromagnetic beam have different polarization properties in general, but there exists a class of steady beams in which the electric and magnetic polarizations are the same (and in which energy density and energy flux are independent of time). Examples are given of exactly and approximately linearly polarized beams, and of approximately circularly polarized beams.Comment: 9 pages, 6 figure

Systematic treatment of displacements, strains and electric fields in density-functional perturbation theory

The methods of density-functional perturbation theory may be used to calculate various physical response properties of insulating crystals including elastic, dielectric, Born charge, and piezoelectric tensors. These and other important tensors may be defined as second derivatives of the total energy with respect to atomic-displacement, electric-field, or strain perturbations, or as mixed derivatives with respect to two of these perturbations. The resulting tensor quantities tend to be coupled in complex ways in polar crystals, giving rise to a variety of variant definitions. For example, it is generally necessary to distinguish between elastic tensors defined under different electrostatic boundary conditions, and between dielectric tensors defined under different elastic boundary conditions. Here, we describe an approach for computing all of these various response tensors in a unified and systematic fashion. Applications are presented for two materials, wurtzite ZnO and rhombohedral BaTiO3, at zero temperature.Comment: 14 pages. Uses REVTEX macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/xfw_sys/index.htm

Helicity, polarization, and Riemann-Silberstein vortices

Riemann-Silberstein (RS) vortices have been defined as surfaces in spacetime where the complex form of a free electromagnetic field given by F=E+iB is null (F.F=0), and they can indeed be interpreted as the collective history swept out by moving vortex lines of the field. Formally, the nullity condition is similar to the definition of "C-lines" associated with a monochromatic electric or magnetic field, which are curves in space where the polarization ellipses degenerate to circles. However, it was noted that RS vortices of monochromatic fields generally oscillate at optical frequencies and are therefore unobservable while electric and magnetic C-lines are steady. Here I show that under the additional assumption of having definite helicity, RS vortices are not only steady but they coincide with both sets of C-lines, electric and magnetic. The two concepts therefore become one for waves of definite frequency and helicity. Since the definition of RS vortices is relativistically invariant while that of C-lines is not, it may be useful to regard the vortices as a wideband generalization of C-lines for waves of definite helicity.Comment: 5 pages, no figures. Submitted to J of Optics A, special issue on Singular Optics; minor changes from v.

Low dimensional ordering and fluctuations in methanol-β\beta-hydroquinone-clathrate studied by X-ray and neutron diffraction

Methanol-$\beta$-hydroquinone-clathrate has been established as a model system for dielectric ordering and fluctuations and is conceptually close to magnetic spin systems. In X-ray and neutron diffraction experiments, we investigated the ordered structure, the one-dimensional (1D) and the three-dimensional (3D) critical scattering in the paraelectric phase, and the temperature dependence of the lattice constants. Our results can be explained by microscopic models of the methanol pseudospin in the hydroquinone cage network, in consistency with previous dielectric investigations

Coherent Quantum Optical Control with Subwavelength Resolution

We suggest a new method for quantum optical control with nanoscale resolution. Our method allows for coherent far-field manipulation of individual quantum systems with spatial selectivity that is not limited by the wavelength of radiation and can, in principle, approach a few nanometers. The selectivity is enabled by the nonlinear atomic response, under the conditions of Electromagnetically Induced Transparency, to a control beam with intensity vanishing at a certain location. Practical performance of this technique and its potential applications to quantum information science with cold atoms, ions, and solid-state qubits are discussed.Comment: 4 pages, 2 figures. V2: changes in presentation (text, figures, tables) and new references - final version as published in Phys. Rev. Lett

Limiting behaviour of Fréchet means in the space of phylogenetic trees

As demonstrated in our previous work on T4, the space of phylogenetic trees with four leaves, the topological structure of the space plays an important role in the non-classical limiting behaviour of the sample Fréchet means in T4. Nevertheless, the techniques used in that paper cannot be adapted to analyse Fréchet means in the space Tm of phylogenetic trees with m(⩾5)m(⩾5) leaves. To investigate the latter, this paper first studies the log map of Tm. Then, in terms of a modified version of this map, we characterise Fréchet means in Tm that lie in top-dimensional or co-dimension one strata. We derive the limiting distributions for the corresponding sample Fréchet means, generalising our previous results. In particular, the results show that, although they are related to the Gaussian distribution, the forms taken by the limiting distributions depend on the co-dimensions of the strata in which the Fréchet means lie

Abrupt grain boundary melting in ice

The effect of impurities on the grain boundary melting of ice is investigated through an extension of Derjaguin-Landau-Verwey-Overbeek theory, in which we include retarded potential effects in a calculation of the full frequency dependent van der Waals and Coulombic interactions within a grain boundary. At high dopant concentrations the classical solutal effect dominates the melting behavior. However, depending on the amount of impurity and the surface charge density, as temperature decreases, the attractive tail of the dispersion force interaction begins to compete effectively with the repulsive screened Coulomb interaction. This leads to a film-thickness/temperature curve that changes depending on the relative strengths of these interactions and exhibits a decrease in the film thickness with increasing impurity level. More striking is the fact that at very large film thicknesses, the repulsive Coulomb interaction can be effectively screened leading to an abrupt reduction to zero film thickness.Comment: 8 pages, 1 figur

Precision Measurement of the 29Si, 33S, and 36Cl Binding Energies

The binding energies of 29Si, 33S, and 36Cl have been measured with a relative uncertainty $< 0.59 \times 10^{-6}$ using a flat-crystal spectrometer. The unique features of these measurements are 1) nearly perfect crystals whose lattice spacing is known in meters, 2) a highly precise angle scale that is derived from first principles, and 3) a gamma-ray measurement facility that is coupled to a high flux reactor with near-core source capability. The binding energy is obtained by measuring all gamma-rays in a cascade scheme connecting the capture and ground states. The measurements require the extension of precision flat-crystal diffraction techniques to the 5 to 6 MeV energy region, a significant precision measurement challenge. The binding energies determined from these gamma-ray measurements are consistent with recent highly accurate atomic mass measurements within a relative uncertainty of $4.3 \times 10^{-7}$. The gamma-ray measurement uncertainties are the dominant contributors to the uncertainty of this consistency test. The measured gamma-ray energies are in agreement with earlier precision gamma-ray measurements.Comment: 13 pages, 4 figure

Quasiharmonic elastic constants corrected for deviatoric thermal stresses

The quasiharmonic approximation (QHA), in its simplest form also called the statically constrained (SC) QHA, has been shown to be a straightforward method to compute thermoelastic properties of crystals. Recently we showed that for non-cubic solids SC-QHA calculations develop deviatoric thermal stresses at high temperatures. Relaxation of these stresses leads to a series of corrections to the free energy that may be taken to any desired order, up to self-consistency. Here we show how to correct the elastic constants obtained using the SC-QHA. We exemplify the procedure by correcting to first order the elastic constants of MgSiO$_3$-perovskite and MgSiO$_3$-post-perovskite, the major phases of the Earth's lower mantle. We show that this first order correction is quite satisfactory for obtaining the aggregated elastic averages of these minerals and their velocities in the lower mantle. This type of correction is also shown to be applicable to experimental measurements of elastic constants in situations where deviatoric stresses can develop, such as in diamond anvil cells.Comment: 4 figures, 1 table, submitted to Phys. Rev. B, July 200

Modeling the iron oxides and oxyhydroxides for the prediction of environmentally sensitive phase transformations

Iron oxides and oxyhydroxides are challenging to model computationally as competing phases may differ in formation energies by only several kJ/mol, they undergo magnetization transitions with temperature, their structures may contain partially occupied sites or long-range ordering of vacancies, and some loose structures require proper description of weak interactions such as hydrogen bonding and dispersive forces. If structures and transformations are to be reliably predicted under different chemical conditions, each of these challenges must be overcome simultaneously, while preserving a high level of numerical accuracy and physical sophistication. Here we present comparative studies of structure, magnetization, and elasticity properties of iron oxides and oxyhydroxides using density functional theory calculations with plane-wave and locally-confined-atomic-orbital basis sets, which are implemented in VASP and SIESTA packages, respectively. We have selected hematite, maghemite, goethite, lepidocrocite, and magnetite as model systems from a total of 13 known iron oxides and oxyhydroxides; and use same convergence criteria and almost equivalent settings in order to make consistent comparisons. Our results show both basis sets can reproduce the energetic stability and magnetic ordering, and are in agreement with experimental observations. There are advantages to choosing one basis set over the other, depending on the intended focus. In our case, we find the method using PW basis set most appropriate, and combine our results to construct the first phase diagram of iron oxides and oxyhydroxides in the space of competing chemical potentials, generated entirely from first principlesComment: 46 pages - Accepted for publication in PRB (19 journal pages), January 201