部分相干部分偏振电磁束通过光阑透镜的传输

基于广义斯托克斯参量,推导出了部分相干部分偏振高斯谢尔模型(GSM)电磁柬通过光阑透镜后交叉谱密度矩阵、光强、偏振度、偏振椭圆的方位角及椭偏角的解析表达式,并用以研究菲涅耳数、自相关和互相关长度以及束腰宽度对焦移和偏振特性的影响.对主要数值计算结果做了物理解释.     

部分相干部分偏振电磁束通过光阑透镜的传输

基于广义斯托克斯参量,推导出了部分相干部分偏振高斯谢尔模型(GSM)电磁束通过光阑透镜后交叉谱密度矩阵、光强、偏振度、偏振椭圆的方位角及椭偏角的解析表达式,并用以研究菲涅耳数、自相关和互相关长度以及束腰宽度对焦移和偏振特性的影响。对主要数值计算结果做了物理解释。     

Polarization ellipse and Stokes parameters of a stochastic electromagnetic Gaussian Schell-model beam propagating through a polarization grating

An analytical propagation formula for the cross-spectral density matrix of a stochastic electromagnetic Gaussian Schell-model (EGSM) beam after propagating through a polarization grating is derived with the help of a tensor method. The statistics properties, particularly the degree of polarization, polarization ellipse and Stokes parameters, of the EGSM beam on propagation after passing through a polarization grating are studied numerically. Our results clearly show that the statistics properties of the EGSM beam on propagation are closely determined by the initial parameters of the EGSM beam and the parameter of the polarization grating. The polarization grating provides one way for modulating the polarization properties of an EGSM beam.     

Experimental determination of electric cross-spectral density matrix and generalized Stokes parameters for a laser beam

We report an experimental method to determine the elements of the electric cross-spectral density matrix for laser light. For this purpose an additional setup consisting of mirrors and reflecting prisms is utilized with the conventional Young's interferometer to overcome existing experimental limitations. The generalized Stokes parameters, which are the characteristics of two spatial points of the electromagnetic field, are also obtained for a pair of points. The knowledge of these two quantities might be useful in determining the change in polarization properties of light in propagation and their effects in optical measurements.     

Evolution of the polarization of electromagnetic waves in weakly anisotropic inhomogeneous media — a comparison of quasi-isotropic approximations of the geometrical optics method and the Stokes vector formalism

The main methods describing polarization of electromagnetic waves in weakly anisotropic inhomogeneous media are reviewed: the quasi-isotropic approximation (QIA) of geometrical optics method that deals with coupled equations for electromagnetic field components, and the Stokes vector formalism (SVF), dealing with Stokes vector components, which are quadratic in electromagnetic field intensity. The equation for the Stokes vector evolution is shown to be derived directly from QIA, whereas the inverse cannot be true. Derivation of SVF from QIA establishes a deep unity of these two approaches, which happen to be equivalent up to total phase. It is pointed out that in contrast to QIA, the Stokes vector cannot be applied for a polarization analysis of the superposition of coherent electromagnetic beams. Additionally, the ability of QIA to describe a normal modes conversion in inhomogeneous media is emphasized. Presented at 9-th International Workshop on Nonlinear Optics Applications, NOA 2007, May 17–20, 2007, Świnoujście, Poland     

Determination of the amplitude and the phase of the elements of electric cross-spectral density matrix by spectral measurements

The amplitudes and the phases of the elements of electric cross-spectral density matrix are determined experimentally for a pair of points in the cross-section of an expanded laser beam. A modified version of the Young’s interferometer is used as an experimental tool, which separates the beams emerging from the double-slit widely and provides ease in insertion of polarizers and half wave rotators in individual beams. To determine these complex elements of the cross-spectral density matrix, the experimentally obtained values of the spectral densities at an off-axis point are put in the mathematical expressions derived by us using the spectral interference law. The four complex generalized Stokes parameters are also determined using the linear combinations of the matrix elements. This unique but simple experimental approach for determining both the two-point parameters might provide a means to investigate the polarization and the coherence properties of the random electromagnetic beams on propagation.     

部分相干刃型位错光束的谱Stokes奇点

利用交叉谱密度函数的传输公式,推导出部分相干刃型位错光束在自由空间中传输的解析表达式.结合谱Stokes参数,详细讨论了其Stokes场的奇点变化规律.结果表明,部分相干刃型位错光束在自由空间传输过程中存在谱s12,s23和s31奇点.改变刃型位错的离轴量、斜率、空间相关长度等光束参数以及随着传输距离的变化,会有谱Stokes奇点的移动、产生和湮没,也会有V点的产生和C点旋性的反转.     

Generalized Stokes parameters of random electromagnetic vortex beams propagating through atmospheric turbulence

By using the extended Huygens–Fresnel principle, the analytical expressions for the generalized Stokes parameters of random electromagnetic Gaussian Schell-model (GSM) vortex beams propagating through atmospheric turbulence are derived, and used to study the changes in spectral Stokes parameters of random electromagnetic GSM vortex beams in atmospheric turbulence and to compare the results of random electromagnetic GSM vortex-free beams. The influence of atmospheric turbulence on the spectral Stokes parameters is analyzed. The validity of our results is interpreted physically.     

An inverse problem in the theory of stochastic electromagnetic beams

The cross-spectral density matrix of an electromagnetic beam has been playing increasingly important role in studies of changes of spectra, of coherence and of polarization as the beam propagates. In this paper we derive solution to an inverse problem, which makes it possible to determine the cross-spectral density matrix of the beam in the source plane z=0, from the knowledge of the matrix in any cross-section z=z₀>0 in the half-space into which the beam propagates. We apply the result to the theory of so-called Stokes beams, which were introduced not long ago.     

Degree of polarization in near fields of thermal sources: effects of surface waves

We introduce the concept of degree of polarization for electromagnetic near fields. The approach is based on the generalized Stokes parameters that appear as expansion coefficients of the 3 x 3 coherence matrix in terms of the Gell-Mann matrices. The formalism is applied to optical near fields of thermally fluctuating half-space sources with particular interest in fields that are strongly polarized owing to resonant surface plasmons or phonons. This novel method is particularly useful when assessing the full vectorial characteristics of random evanescent fields, e.g., for near-field spectroscopy and polarization microscopy.     

Generalized Stokes parameters and polarization behavior of flat-topped array laser beam propagating through oceanic turbulence

In present paper, the analytical expression for the cross-spectral density of the phase-locked Partially Coherent Flat-Topped (PCFT) array beams propagating through oceanic turbulence based on the extended Huygens–Fresnel integral is derived. Then, the polarization behavior and generalized Stokes parameters of the phase-locked PCFT array beam propagating through oceanic turbulence using the cross-spectral density matrix elements have been achieved. In this paper, the case of the clearwater oceanic turbulence has been considered, i.e. it has been assumed that the light wave is not affected by suspended organic and inorganic impurities. Due to the above-mentioned reason and the turbulence importance, the impacts of oceanic turbulence have been scrutinized, while the effects of absorption and scattering have been ignored. The changes in the Stokes parameters, the fluctuation of Stokes parameters, and consequently the state of polarization (including the spectral degree of polarization, the orientation angle and the degree of ellipticity) of the phase-locked PCFT array beams for different turbulence conditions upon propagation have been investigated. The results may find possible applications in underwater communication.     

Spatial correlations and degree of polarization in homogeneous electromagnetic fields

We consider stationary electromagnetic fields modeled as superpositions of unpolarized and angularly uncorrelated plane waves and show that in anisotropic case the electric cross-spectral tensor is proportional to the imaginary part of the Green tensor. This is as for blackbody radiation, but here the field need not be in thermal equilibrium. We also evaluate the degree of polarization for a homogeneous but nonisotropic field for which the plane waves propagate within a cone of angles. The results are compared with the known polarization properties of blackbody radiation.     

Conditions for non-existence of static or stationary,Einstein–Maxwell,non-inheriting black-holes

We consider asymptotically-flat, static and stationary solutions of the Einstein equations representing Einstein–Maxwell space–times in which the Maxwell field is not constant along the Killing vector defining stationarity, so that the symmetry of the space-time is not inherited by the electromagnetic field. We find that static degenerate black hole solutions are not possible and, subject to stronger assumptions, nor are static, non-degenerate or stationary black holes. We describe the possibilities if the stronger assumptions are relaxed.     

Parameters characterizing electromagnetic wave polarization

In this paper, generalizations of the Stokes parameters and alternative characterizations of three-dimensional (3D) time-varying electromagnetic fields is introduced. One of these characteristics is the normal of the polarization plane, which, in many cases of interest, is parallel (or antiparallel) to the direction of propagation. Others are the two spectral density Stokes parameters which describe spectral intensity and circular polarization. The analysis is based on the spectral density tensor. This tensor is expanded in a base composed of the generators of the SU(3) symmetry group, as given by Gell-Mann and Y. Ne'eman [The Eight-fold Way (Benjamin, New York, 1964)] and the coefficients of this expansion are identified as generalized spectral density polarization parameters. The generators have the advantage that they obey the same algebra as the Pauli spin matrices, which is the base for expanding the 2D spectral density tensor with the Stokes parameters as coefficients. The polarization parameters introduced are formulated in the frequency domain, thereby further generalizing the theory to allow for wide-band electromagnetic waves in contrast to the traditional quasi-monochromatic formulation.     

Space–time structure of new physics with polarized beams at the linear collider

We approach the issue of the discovery of new physics at high energies associated with the proposed International Linear Collider in the presence of longitudinal as well as transverse electron and positron beam polarization. We determine the beam polarization dependence and the angular distribution of a particle of arbitrary spin in a one-particle inclusive final state produced in e⁺e^- collisions through the interference of γ or Z amplitude with the amplitude from new interactions having arbitrary space–time structure. We thus extend the results of Dass and Ross, proposed at the time of the discovery of neutral currents, to beyond the standard model currents. We also extend the case of e⁺e^- annihilation in the s-channel to the production of bosons due to t- and u-channel processes. Our work provides an approach to model-independent determination of the space–time structure of beyond the standard model interactions. We briefly discuss applications of the framework to popular extensions of the standard model, and demonstrate that our framework is general enough to account for certain results in the minimal supersymmetric standard model.     

Stokes parameters and polarization contrasts in Young's interference experiment

We derive a spectral interference law that governs the behavior of the four Stokes parameters in Young's two-pinhole experiment with a random electromagnetic beam. In addition to the visibility of intensity fringes, we introduce three new contrast parameters that describe the interference-induced changes in the field's state of partial polarization. The polarization modulation depends on the electric field correlations at the pinholes and is closely related to the two-point Stokes parameters. The results are expected to be particularly useful in polarization interferometry and electromagnetic coherence theory. The formalism is demonstrated with specific examples.     

Stability between foliations in general relativity

The aim of this paper is to study foliations that remain invariant under parallel transport along the integral curves of vector fields of another foliation. According to this idea, we define a new concept of stability between foliations. A particular case of stability (called regular stability) is studied, giving a useful characterization in terms of the Riemann curvature tensor. This characterization allows us to prove that there are no regularly self-stable foliations of dimension greater than 1 in the Schwarzschild and Robertson–Walker space–times. Finally, we study the existence of regularly self-stable foliations in other space–times, like pp-wave space–times.     

Measurement of the space–time interval between two events using the retarded and advanced times of each event with respect to a time-like world-line

Several recent studies have been devoted to investigating the limitations that standard quantum mechanics and/or quantum gravity might impose on the measurability of space–time observables. These analyses are often confined to the simplified context of 2D flat space–time and rely on a simple procedure for the measurement of space-like distances based on the exchange of light signals. We present a generalization of this measurement procedure applicable to all three types of space–time intervals between two events in space–times of any number of dimensions. We also present a preliminary account of an alternative measurement procedure that can be applied taking into account the gravitational field of the macroscopic measuring apparatus.     

On the physical interpretation of asymptotically flat gravitational fields

A problem in general relativity is how to extract physical information from solutions to the Einstein equations. Most often information is found from special conditions, e.g., special vector fields, symmetries or approximate symmetries. Our concern is with asymptotically flat space–times with approximate symmetry: the BMS group. For these spaces the Bondi four-momentum vector and its evolution, found at infinity, describes the total energy–momentum and the energy–momentum radiated. By generalizing the simple idea of the transformation of (electromagnetic) dipoles under a translation, we define (analogous to center of charge) the center of mass for asymptotically flat Einstein–Maxwell fields. This gives kinematical meaning to the Bondi four-momentum, i.e., the four-momentum and its evolution which is described in terms of a center of mass position vector, its velocity and spin-vector. From dynamical arguments, a unique (for our approximation) total angular momentum and evolution equation in the form of a conservation law is found. Third Award in the 2008 Essay Competition of the Gravity Research Foundation.     

Space–time inhomogeneity, anisotropy and gravitational collapse

We investigate the evolution of non-adiabatic collapse of a shear-free spherically symmetric stellar configuration with anisotropic stresses accompanied with radial heat flux. The collapse begins from a curvature singularity with infinite mass and size on an inhomogeneous space–time background. The collapse is found to proceed without formation of an even horizon to singularity when the collapsing configuration radiates all its mass energy. The impact of inhomogeneity on various parameters of the collapsing stellar configuration is examined in some specific space–time backgrounds.