Kinematical modeling of circular and elliptical polarization of the polarized light via screw transformation

In this paper, it is shown that the motion of a polarized light wave in an optical fiber has a special meaning that relates the scalar and vector part of the dual quaternion to the kinematics concept of a screw. We describe the circular and elliptical polarization of a light wave according to how the electric field vector varies in a projection onto a plane perpendicular to the propagation direction using the Clifford algebra of the dual quaternion. Also, we determine the circular-Rytov curve (CR ) and elliptical-Rytov curve (ER ), which described the paths traced out by the tip of the electric field vector as it propagates in space, related to the polarization state of the electric field ε. The elliptical and circular polarization states are expressed by using the four Stokes parameters and their matrix form. Furthermore, some motivating examples are given and visualized their images with the help of the MAPLE program.

Self-potential (SP) soil monitoring tool by numbers and vectors characteristic

<p>This paper attempts to provide a contribute to electric field monitoring on soil by Self-potential (SP) survey utilizing matrix determinant and eigenvalues. SP is connected to the electrical conductivity of soil that is an indirect measurement and correlates very well with several physical and chemical properties. The purpose of this method is to map the electrical potential to reveal one or several polarization mechanisms at play in the ground. In some cases, the self-potential signals are monitored with an electrodes network which provides the possibility to discriminate between various sources.</p><p>Our study provides synthetic and experiment cases that carried out a semi-quantitative method to estimate the variation of the electric field vector in the soil starting from the measurement of the SP. The experimental case is referred to a site located in the Campania Region in southern Italy. SP measurements can be performed by array dipoles oriented N-S, E-W and vertical direction. In this way, we can define the contribution of the electric field in both time and spatial domain. Now, if we denote with V(t) the potential difference between two electrodes, for each dipole, we will have 3 values  V<sub>x</sub>(t<sub>n</sub>), V<sub>y</sub>(t<sub>n</sub>) and V<sub>z</sub>(t<sub>n</sub>) relative to the dipoles in the three directions. Assuming that the electric currents associated with the potentials are continuous or in any case at very low frequency, we can with good approximation assume that the resulting electric field associated with such currents is conservative. Remembering that in the case of a conservative field the electric field vector, we can be expressed as a gradient of the scalar potential V. The SP data were obtained using an Arduino acquisition system with internal voltmeter impedance of 10 MOhm and resolution of 0.1 mV. In order to provide reliable SP measurements, the impedance of the voltmeter needs to be substantially higher than the impedance of the soil between the electrodes because of the small bias current used to measure the voltage. The electric potentials were measured between each electrode and a reference electrode was connected by ground. The electrode consisted of 8 electrodes spaced 1m and arranged in a cross array which form 6 dipoles. The cross array was orientated in N-S and E-W direction.</p><p>Because the SP depend on the electrical conductivity of the soil and therefore on the sources and the medium, any variation of the chemical-physical soil variation implies a variation of the SP. We calculated the determinant and the eigenvalues of the matrix whose columns consist of the components of the measured electric field and therefore, by such parameters it was possible to observe the variations of the electric field in the time domain. </p>

How to determine the shape of nuclear molecules with polarized gamma-rays

A method has been recently proposed to establish the geometry of the alpha-cluster arrangement in ^{12}12C making use of polarized gamma-rays. The ratio of intensities of scattered radiation at 90 degrees along and perpendicular to the initial direction of the electric field vector, called depolarization ratio, is a key quantity that allows to underpin the nature of totally symmetric modes of vibrations. This allows to connect with the underlying point-group structure and therefore to the geometric shape of the nuclear molecule. This method is reviewed for ^{12}12C and extended to other configurations, such as three unequal clusters and four identical clusters (e.g. ^{16}16O).