Linear polarization

About: Linear polarization is a research topic. Over the lifetime, 14705 publications have been published within this topic receiving 253387 citations. The topic is also known as: plane polarization.

Electromagnetic Diffraction in Optical Systems. II. Structure of the Image Field in an Aplanatic System

Abstract: An investigation is made of the structure of the electromagnetic field near the focus of an aplanatic system which images a point source. First the case of a linearly polarized incident field is examined and expressions are derived for the electric and magnetic vectors in the image space. Some general consequences of the formulae are then discussed. In particular the symmetry properties of the field with respect to the focal plane are noted and the state of polarization of the image region is investigated. The distribution of the time-averaged electric and magnetic energy densities and of the energy flow (Poynting vector) in the focal plane is studied in detail, and the results are illustrated by diagrams and in a tabulated form based on data obtained by extensive calculations on an electronic computor. The case of an unpolarized field is also investigated. The solution is riot restricted to systems of low aperture, and the computational results cover, in fact, selected values of the angular semi-aperture a on the image side, in the whole range 0 ≤ α ≤ 90°. The limiting case α → 0 is examined in detail and it is shown that the field is then completely characterized by a single, generally complex, scalar function, which turns out to be identical with that of the classical scalar theory of Airy, Lommel and Struve. The results have an immediate bearing on the resolving power of image forming systems; they also help our understanding of the significance of the scalar diffraction theory, which is customarily employed, without a proper justification, in the analysis of images in lowaperture systems.

Three Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Polarization Analysis

Abstract: The Wilkinson Microwave Anisotropy Probe (WMAP) has mapped the entire sky in five frequency bands between 23 and 94 GHz with polarization-sensitive radiometers. We present 3 year full-sky maps of the polarization and analyze them for foreground emission and cosmological implications. These observations open up a new window for understanding how the universe began and help set a foundation for future observations. WMAP observes significant levels of polarized foreground emission due to both Galactic synchrotron radiation and thermal dust emission. Synchrotron radiation is the dominant signal at l < 50 and ν 40 GHz, while thermal dust emission is evident at 94 GHz. The least contaminated channel is at 61 GHz. We present a model of polarized foreground emission that captures the large angular scale characteristics of the microwave sky. After applying a Galactic mask that cuts 25.7% of the sky, we show that the high Galactic latitude rms polarized foreground emission, averaged over l = 4-6, ranges from ≈5 μK at 22 GHz to 0.6 μK at 61 GHz. By comparison, the levels of intrinsic CMB polarization for a ΛCDM model with an optical depth of τ = 0.09 and assumed tensor-to-scalar ratio r = 0.3 are ≈0.3 μK for E-mode polarization and ≈0.1 μK for B-mode polarization. To analyze the maps for CMB polarization at l < 16, we subtract a model of the foreground emission that is based primarily on a scaling WMAP's 23 GHz map. In the foreground-corrected maps, we detect l(l + 1)C/2π = 0.086 ± 0.029 (μK)2. This is interpreted as the result of rescattering of the CMB by free electrons released during reionization at zr = 10.9 for a model with instantaneous reionization. By computing the likelihood of just the EE data as a function of τ we find τ = 0.10 ± 0.03. When the same EE data are used in the full six-parameter fit to all WMAP data (TT, TE, EE), we find τ = 0.09 ± 0.03. Marginalization over the foreground subtraction affects this value by δτ < 0.01. We see no evidence for B modes, limiting them to l(l + 1)C/2π = -0.04 ± 0.03 (μK)2. We perform a template fit to the E-mode and B-mode data with an approximate model for the tensor scalar ratio. We find that the limit from the polarization signals alone is r < 2.2 (95% CL), where r is evaluated at k = 0.002 Mpc-1. This corresponds to a limit on the cosmic density of gravitational waves of ΩGWh2 < 5 × 10-12. From the full WMAP analysis, we find r < 0.55 (95% CL) corresponding to a limit of ΩGWh2 < 1 × 10-12 (95% CL). The limit on r is approaching the upper bound of predictions for some of the simplest models of inflation, r ~ 0.3.

Sharper Focus for a Radially Polarized Light Beam

Abstract: We experimentally demonstrate for the first time that a radially polarized field can be focused to a spot size significantly smaller [$0.16(1){\ensuremath{\lambda}}^{2}$] than for linear polarization ($0.26{\ensuremath{\lambda}}^{2}$). The effect of the vector properties of light is shown by a comparison of the focal intensity distribution for radially and azimuthally polarized input fields. For strong focusing, a radially polarized field leads to a longitudinal electric field component at the focus which is sharp and centered at the optical axis. The relative contribution of this component is enhanced by using an annular aperture.

Macroscopic polarization in crystalline dielectrics : the geometric phase approach

Abstract: The macroscopic electric polarization of a crystal is often defined as the dipole of a unit cell. In fact, such a dipole moment is ill defined, and the above definition is incorrect. Looking more closely, the quantity generally measured is differential polarization, defined with respect to a "reference state" of the same material. Such differential polarizations include either derivatives of the polarization (dielectric permittivity, Born effective charges, piezoelectricity, pyroelectricity) or finite differences (ferroelectricity). On the theoretical side, the differential concept is basic as well. Owing to continuity, a polarization difference is equivalent to a macroscopic current, which is directly accessible to the theory as a bulk property. Polarization is a quantum phenomenon and cannot be treated with a classical model, particularly whenever delocalized valence electrons are present in the dielectric. In a quantum picture, the current is basically a property of the phase of the wave functions, as opposed to the charge, which is a property of their modulus. An elegant and complete theory has recently been developed by King-Smith and Vanderbilt, in which the polarization difference between any two crystal states---in a null electric field---takes the form of a geometric quantum phase. The author gives a comprehensive account of this theory, which is relevant for dealing with transverse-optic phonons, piezoelectricity, and ferroelectricity. Its relation to the established concepts of linear-response theory is also discussed. Within the geometric phase approach, the relevant polarization difference occurs as the circuit integral of a Berry connection (or "vector potential"), while the corresponding curvature (or "magnetic field") provides the macroscopic linear response.