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

The relationship between the Wigner-Weyl kinetic formalism and the complex geometrical optics method

The relationship between two different asymptotic techniques developed in order to describe the propagation of waves beyond the standard geometrical optics approximation, namely, the Wigner-Weyl kinetic formalism and the complex geometrical optics method, is addressed. More specifically, a solution of the wave kinetic equation, relevant to the Wigner-Weyl formalism, is obtained which yields the same wavefield intensity as the complex geometrical optics method. Such a relationship is also discussed on the basis of the analytical solution of the wave kinetic equation specific to Gaussian beams of electromagnetic waves propagating in a ``lens-like'' medium for which the complex geometrical optics solution is already available.Comment: Extended version comprising two new section

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

Spatio-temporal vortex beams and angular momentum

We present a space-time generalization of the known spatial (monochromatic) wave vortex beams carrying intrinsic orbital angular momentum (OAM) along the propagation direction. Generic spatio-temporal vortex beams are polychromatic and can carry intrinsic OAM at an arbitrary angle to the mean momentum. Applying either (i) a transverse wave-vector shift or (ii) a Lorentz boost to a monochromatic Bessel beam, we construct a family of either (i) time-diffracting or (ii) non-diffracting spatio-temporal Bessel beams, which are exact solutions of the Klein-Gordon wave equations. The proposed spatio-temporal OAM states are able to describe either photon or electron vortex states (both relativistic and nonrelativistic), and can find applications in particle collisions, optics of moving media, quantum communications, and astrophysics.Comment: 9 pages, 6 figures, to appear in Phys. Rev.

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.

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

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