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

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

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

Towards a systematic design of isotropic bulk magnetic metamaterials using the cubic point groups of symmetry

In this paper a systematic approach to the design of bulk isotropic magnetic metamaterials is presented. The role of the symmetries of both the constitutive element and the lattice are analyzed. For this purpose it is assumed that the metamaterial is composed by cubic SRR resonators, arranged in a cubic lattice. The minimum symmetries needed to ensure an isotropic behavior are analyzed, and some particular configurations are proposed. Besides, an equivalent circuit model is proposed for the considered cubic SRR resonators. Experiments are carried out in order to validate the proposed theory. We hope that this analysis will pave the way to the design of bulk metamaterials with strong isotropic magnetic response, including negative permeability and left-handed metamaterials.Comment: Submitted to Physical Review B, 23 page

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

Elastic constants of beta-eucryptite: A density functional theory study

The five independent elastic constants of hexagonal $\beta$-eucryptite have been determined using density functional theory (DFT) total energy calculations. The calculated values agree well, to within 15%, with the experimental data. Using the calculated elastic constants, the linear compressibility of $\beta$-eucryptite parallel to the c-axis, $\chi_c$, and perpendicular to it, $\chi_a$, have been evaluated. These values are in close agreement to those obtained from experimentally known elastic constants, but are in contradiction to the direct measurements based on a three-terminal technique. The calculated compressibility parallel to the c-axis was found to positive as opposed to the negative value obtained by direct measurements. We have demonstrated that $\chi_c$ must be positive and discussed the implications of a positive $\chi_c$ in the context of explaining the negative bulk thermal expansion of $\beta$-eucryptite.Comment: 3 eps figures, submitted for publicatio