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

Ab-initio elastic tensor of cubic Ti0.5_{0.5}Al0.5_{0.5}N alloy: the dependence of the elastic constants on the size and shape of the supercell model

In this study we discuss the performance of approximate SQS supercell models in describing the cubic elastic properties of B1 (rocksalt) Ti$_{0.5}$Al$_{0.5}$N alloy by using a symmetry based projection technique. We show on the example of Ti$_{0.5}$Al$_{0.5}$N alloy, that this projection technique can be used to align the differently shaped and sized SQS structures for a comparison in modeling elasticity. Moreover, we focus to accurately determine the cubic elastic constants and Zener's type elastic anisotropy of Ti$_{0.5}$Al$_{0.5}$N. Our best supercell model, that captures accurately both the randomness and cubic elastic symmetry, results in $C_{11}=447$ GPa, $C_{12}=158$ GPa and $C_{44}=203$ GPa with 3% of error and $A=1.40$ for Zener's elastic anisotropy with 6% of error. In addition, we establish the general importance of selecting proper approximate SQS supercells with symmetry arguments to reliably model elasticity of alloys. In general, we suggest the calculation of nine elastic tensor elements - $C_{11}$, $C_{22}$, $C_{33}$, $C_{12}$, $C_{13}$, $C_{23}$, $C_{44}$, $C_{55}$ and $C_{66}$, to evaluate and analyze the performance of SQS supercells in predicting elasticity of cubic alloys via projecting out the closest cubic approximate of the elastic tensor. The here described methodology is general enough to be applied in discussing elasticity of substitutional alloys with any symmetry and at arbitrary composition.Comment: Submitted to Physical Review

A selected history of expectation bias in physics

The beliefs of physicists can bias their results towards their expectations in a number of ways. We survey a variety of historical cases of expectation bias in observations, experiments, and calculations.Comment: 6 pages, 2 figure

Electromagnetic wave scattering by a superconductor

The interaction between radiation and superconductors is explored in this paper. In particular, the calculation of a plane standing wave scattered by an infinite cylindrical superconductor is performed by solving the Helmholtz equation in cylindrical coordinates. Numerical results computed up to $\mathcal{O}(77)$ of Bessel functions are presented for different wavelengths showing the appearance of a diffraction pattern.Comment: 3 pages, 3 figure

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.

The modalities of Iranian soft power: from cultural diplomacy to soft war

Through exploring Iran's public diplomacy at the international level, this article demonstrates how the Islamic Republic's motives should not only be contextualised within the oft-sensationalised, material or ‘hard’ aspects of its foreign policy, but also within the desire to project its cultural reach through ‘softer’ means. Iran's utilisation of culturally defined foreign policy objectives and actions demonstrates its understanding of soft power's potentialities. This article explores the ways in which Iran's public diplomacy is used to promote its soft power and craft its, at times, shifting image on the world stage

Quantum effects in the evolution of vortices in the electromagnetic field

We analyze the influence of electron-positron pairs creation on the motion of vortex lines in electromagnetic field. In our approach the electric and magnetic fields satisfy nonlinear equations derived from the Euler-Heisenberg effective Lagrangian. We show that these nonlinearities may change the evolution of vortices.Comment: REVTEX4 and 5 EPS figure

Optimal configuration of microstructure in ferroelectric materials by stochastic optimization

An optimization procedure determining the ideal configuration at the microstructural level of ferroelectric (FE) materials is applied to maximize piezoelectricity. Piezoelectricity in ceramic FEs differ significantly from that of single crystals because of the presence of crystallites (grains) possessing crystallographic axes aligned imperfectly. The piezoelectric properties of a polycrystalline (ceramic) FE is inextricably related to the grain orientation distribution (texture). The set of combination of variables, known as solution space, which dictates the texture of a ceramic is unlimited and hence the choice of the optimal solution which maximizes the piezoelectricity is complicated. Thus a stochastic global optimization combined with homogenization is employed for the identification of the optimal granular configuration of the FE ceramic microstructure with optimum piezoelectric properties. The macroscopic equilibrium piezoelectric properties of polycrystalline FE is calculated using mathematical homogenization at each iteration step. The configuration of grains characterised by its orientations at each iteration is generated using a randomly selected set of orientation distribution parameters. Apparent enhancement of piezoelectric coefficient $d_{33}$ is observed in an optimally oriented BaTiO$_3$ single crystal. A configuration of crystallites, simultaneously constraining the orientation distribution of the c-axis (polar axis) while incorporating ab-plane randomness, which would multiply the overall piezoelectricity in ceramic BaTiO$_{3}$ is also identified. The orientation distribution of the c-axes is found to be a narrow Gaussian distribution centred around ${45^\circ}$. The piezoelectric coefficient in such a ceramic is found to be nearly three times as that of the single crystal.Comment: 11 pages, 7 figure

Full stress tensor measurement using colour centres in diamond

Stress and strain are important factors in determining the mechanical, electronic, and optical properties of materials, relating to each other by the material's elasticity or stiffness. Both are represented by second rank field tensors with, in general, six independent components. Measurements of these quantities are usually achieved by measuring a property that depends on the translational symmetry and periodicity of the crystal lattice, such as optical phonon energies using Raman spectroscopy, the electronic band gap using cathodoluminescence, photoelasticity via the optical birefringence, or Electron Back Scattering Diffraction (EBSD). A reciprocal relationship therefore exists between the maximum sensitivity of the measurements and the spatial resolution. Furthermore, of these techniques, only EBSD and off-axis Raman spectroscopy allow measurement of all six components of the stress tensor, but neither is able to provide full 3D maps. Here we demonstrate a method for measuring the full stress tensor in diamond, using the spectral and optical polarization properties of the photoluminescence from individual nitrogen vacancy (NV) colour centres. We demonstrate a sensitivity of order 10 MPa, limited by local fluctuations in the stress in the sample, and corresponding to a strain of about 10^-5, comparable with the best sensitivity provided by other techniques. By using the colour centres as built-in local sensors, the technique overcomes the reciprocal relationship between spatial resolution and sensitivity and offers the potential for measuring strains as small as 10^-9 at spatial resolution of order 10 nm. Furthermore it provides a straightforward route to volumetric stress mapping. Aside from its value in understanding strain distributions in diamond, this new approach to stress and strain measurement could be adapted for use in micro or nanoscale sensors.Comment: 12 pages, 5 figures - supplementary informations included in appendi