Changes in statistics of the instantaneous Stokes parameters of a quasi-monochromatic electromagnetic beam on propagation

The changes in the probability density functions (PDFs) are discussed, of the instantaneous Stokes parameters of a quasi-monochromatic electromagnetic beam propagating in free space. Such changes may be caused by correlations between the components of the electric field at a pair of points in the source plane. When the fluctuations of the electric field are governed by Gaussian statistics the PDFs of the instantaneous Stokes parameters at any distance from the source are completely determined by the two-point correlation properties of the field in the source plane. These results can be used for synthesis of sources generating random beams with prescribed statistical properties. They also may find applications in remote sensing, tomography and communications with partially coherent and partially polarized light.     

Generalized stokes parameters of random electromagnetic beams

A generalization of the Stokes parameters of a random electromagnetic beam is introduced. Unlike the usual Stokes parameters, which depend on one spatial variable, the generalized Stokes parameters, depend on two spatial variables. They obey precise laws of propagation, both in free space and in any linear medium, whether deterministic or random. With the help of the generalized Stokes parameters, the changes in the ordinary Stokes parameters upon propagation can be determined. Numerical examples of such changes are presented. The generalized Stokes parameters contain information not only about the polarization properties of the beam but also about its coherence properties. We illustrate this fact by expressing the degree of coherence of the electromagnetic beam in terms of one of the generalized Stokes parameters.     

Weibull分布随机波的瞬态极化统计分析——相同形状参数情形

Weibull分布的雷达极化回波特征由三个分布参数来描述：波的强度、极化椭圆率角以及椭圆倾角.在瞬态极化理论的基础上,推导了三个分布参数的联合概率密度函数,标准Stokes矢量统计分布的联合概率密度函数及其边缘概率密度函数,并通过蒙塔卡罗方法进行了计算机仿真,结果验证了理论推导的正确性.Weibull分布随机极化电磁波瞬态极化统计特性的研究对高分辨条件下雷达目标的检测、识别和跟踪领域都有一定的理论指导意义. 关键词： Weibull分布 极化椭圆参数 标准Stokes矢量 统计     

Can two planar sources with the same sets of Stokes parameters generate beams with different degrees of polarization?

It is shown that two stochastic electromagnetic beams that propagate from the source plane z = 0 into the half-space z > 0 may have different degrees of polarization throughout the half-space, even though they have the same sets of Stokes parameters in the source plane. This fact is due to a possible difference in the coherence properties of the field in that plane, but other reasons are also possible. The result is illustrated by an example.     

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.     

Stokes parameters of optical singularities of random electromagnetic beams

In this paper,the relation between the spectral degree of coherence and degree of polarization of random electromagnetic beams is derived by the Stokes parameters.And the concept of polarization singularity is extended from spatially fully coherent beams to partially coherent electromagnetic beams.Theoretical analysis shows that correlation vortices are linearly polarized singularities.The results are illustrated by numerical examples.     

Scattering from a slightly random, one-dimensional metal surface: 45° linearly polarized incidence, backscattering enhancement and degree of polarization

The scattering of an electromagnetic wave from a slightly random metal surface which supports the surface plasmon mode at optical frequencies is studied theoretically by means of a stochastic functional approach. In order to investigate the Stokes matrix or the state of polarizations, as well as the intensity of the scattered waves, the rough surface is assumed to be one dimensional, and is illuminated by a+45° linearly polarized plane electromagnetic (light) wave whose plane of incidence is perpendicular to the grooves of the surface. The stochastic wave fields are represented in terms of the Wiener-Hermite functionals, and the approximate solutions of the Wiener kernels are obtained for both TM- and TE-polarized components, from which the Stokes matrix elements can be determined. The dressed or perturbed plasmon mode in the presence of surface roughness is obtained by a mass operator involved in the solutions, and the enhanced backscattering closely related to the plasmon mode is studied in connection with the enhanced peak width and the mass operator for the dressed plasmon mode. The Stokes parameters and the degree of polarization are calculated numerically from various polarized components of the incoherent scattering distribution. To clarify the surface plasmon's association with the scattering characteristics, calculations are made for two kinds of random surfaces, a random surface with a centred Gaussian spectrum and a random grating with twin spectral peaks at the plasmon spatial frequency.     

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.     

On the transformation of the stokes parameters for backscattering of electromagnetic waves

Expressions are derived for the interaction matrices which describe the transformation of the Stokes parameters for backscattering of a plane quasimonochromatic electromagnetic wave by an arbitrary statistical object or by an isotropic object. By means of the matrices that have been found the determination of the mutual correlation of the orthogonal components of the scattered field must be considered in an arbitrarily chosen polarization basis for arbitrary elliptic polarization of the incident wave. For the isotropic object the modulus and argument of the generalized correlation coefficient of the linear orthogonal components of the scattered field are obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 15, No. 4, pp. 601–610, April, 1972.The authors thank E. M. Kuchkov for his unfailing attention to the work.     

Point sources and rays in the phase-space representation of random electromagnetic fields

Random stationary electromagnetic fields can be modeled in terms of point sources disposed onto two distinct layers, named the radiant and the virtual layers. It allows describing the propagation of the power and the states of spatial coherence and polarization of the field by means of separate phase-space ray-maps. Spatial coherence of the field, correlation of the polarization angles and achievement of the Fresnel-Arago laws within the structured spatial coherence supports are the necessary conditions that determine the electromagnetic point sources in the virtual layer. The contributions of these sources produce two types of modulations on the electromagnetic field at the observation plane, one of them of scalar type is the interferometric power modulation, and the other one of vector type is de modulation of the polarization state provided by the radiant point sources, according to the Stokes' parameters. Some examples are presented.     

Contrasts of Stokes parameters in Young's interference experiment and electromagnetic degree of coherence

We analyze the modulation of the Stokes parameters in Young's two-pinhole interference experiment with a random electromagnetic beam. We demonstrate that the electromagnetic (spectral) degree of coherence put forward in Opt. Lett.29, 328 (2004) [or its space-time analog in Opt. Express 11, 1137 (2003)] is physically related to the contrasts of modulation in the four Stokes parameters. More explicitly, the electromagnetic degree of coherence is a measure of both the visibility of the intensity fringes and the modulation contrasts of the three polarization Stokes parameters. We also show that by using suitable wave plates the modulation in any Stokes parameter can be transformed into the form of intensity variation, and hence the electromagnetic degree of coherence can be obtained experimentally by four visibility measurements.     

On the problem of polarization characteristics of radio waves in a randomly inhomogeneous magnetoactive plasma

Expressions for the Stokes parameters when radio waves propagate in a turbulent magnetoactive plasma have been obtained using a refractive scattering method. The problem of the spatial coherence of polarized radiation is considered. Expressions for the correlation functions and fluctuation dispersions of the Stokes parameters are found in the case of saturated wave field fluctuation. It is shown that the fluctuation of the circular polarized component will be observed in the received radiation even if the circular polarization is absent in the radiation that is incident on the magnetoactive plasma slab. A method is proposed to define the preference orientation of the magnetic field in the inhomogeneous layer of space plasma, which is biased on the simultaneous measurement of the space correlation functions of the I, V Stokes parameter fluctuation and Faraday rotation of the radiation polarization plane from the source with known polarization characteristics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 8, pp. 1007–1013, August, 1996.This work was supported in part by the Russian Foundation for Fundamental Research under Project No. 96-02-18632.     

Propagation and parametric characterization of the polarization structure of paraxial radially and azimuthally polarized beams

Analytical expressions are provided for describing the free-space evolution of the polarization structure of paraxial beams whose electric-field vector at some transverse plane exhibits either a radially or an azimuthally polarized behavior. At each transverse plane, the polarization distribution across the beam profile is characterized by means of two sets of parameters, namely, the so-called (local) radial Stokes representation, and the (overall) percentage of the irradiance associated with the radial and azimuthal field components. The propagation laws for these sets of parameters are also shown. As an illustrative example, a radially polarized beam is analized whose wavefront contains a spiral phase factor.     

Optical parametric generation and phase matching in magneto-optic media

We derive the equations and main characteristics of optical parametric generation in magneto-optic media. The key performances are discussed in terms of Stokes parameters and conservation laws of electromagnetic linear and angular momentum.     

Cross-spectral purity of the Stokes parameters

We extend the concept of cross-spectral purity from the spectral density to the polarization properties of electromagnetic fields by considering the polarization Stokes parameters. We show that purity conditions similar to those in the case of electromagnetic cross-spectral purity can be derived for all the Stokes parameters. Furthermore, we introduce a situation of strict cross-spectral purity which leads to the equality of the degrees of coherence for electromagnetic fields in the space–time and space–frequency domains.     

Stokes beams formed by superposition of a completely unpolarized and a completely polarized Gaussian Schell-model beam

Analytic expressions and computed examples are given to elucidate the coherence and polarization properties of Stokes beams, i.e. beams formed by superposition of a completely unpolarized and a completely polarized electromagnetic Gaussian Schell-model beam. We found that superposition of such two beams cannot form a Stokes beam with a constant state of polarization on propagation. An additional constraint on the source plane parameters of the two Gaussian Schell-model beams is proposed. The resultant Stokes beam with a constant state of polarization on propagation is found to be a Gaussian Schell-model beam with the same variances as the two constituent Gaussian Schell-model beams. However, the modulus of the Gaussian intensity distributions across the source planes of these beams may be different.     

Correlation theory of quantized electromagnetic field I

A correlation matrix is defined which describes arbitrary order correlation effects of the electromagnetic field. Dynamical equations are derived which govern the space-time development of the correlation matrix of the quantized electromagnetic field in vacuo. With the help of these equations, propagation laws and non-linear conservation laws for the correlation matrix are obtained.The author wishes to thank Dr. J. Peina for stimulating discussions.     

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.     

Change in the optical properties of paper when exposed to the magnetic component of a high-frequency electromagnetic field

We have used laser Stokes polarimetry to study changes in the structure of paper for offset printing when exposed to a high-frequency electromagnetic field. We have shown that the effect of a high-frequency electromagnetic field on paper appears as a decrease in the structural ordering of the material and a change in the shape of the indicatrix of the reflected radiation power from an He-Ne laser at the wavelength 632.8 nm, a decrease in the bidirectional reflection and transmission coefficients of the paper. We have established that when the force lines of the magnetic component of the high-frequency electromagnetic field are oriented perpendicular to the plane of the sheet of paper, we observe a more substantial decrease in the anisotropy in the surface layer and within the interior (the volume) of the paper than when the lines of force are oriented parallel to the plane of the paper. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 4, pp. 421–426, July–August, 2007.     

复杂腔体本征电磁场空间分布的统计方法

 利用半经典近似方法分析了电大复杂腔体内电磁波传播的混沌特征,从而引入了3维矢量本征函数的随机平面波假设。根据电磁波传播的随机极化特征,利用统计方法推导出基于该假设本征电磁场空间分布的统计模型。应用数值方法对3维Sinai微波腔体进行模拟计算,其计算结果与统计模型符合较好。这些统计模型与腔体的具体细节特征无关。