Stokes parameters and degree of polarization of nonparaxial stochastic electromagnetic beams

On the basis of angular spectrum representation and the stationary-phase method, far-field expressions for generalized Stokes parameters of nonparaxial stochastic electromagnetic beams are derived, which permits us to study the changes in the ordinary Stokes parameters upon propagation, and the changes in the spectral degree of polarization of partially polarized nonparaxial stochastic electromagnetic beams. It is shown that the spectral degree of polarization changes across the section on beam propagation.     

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。     

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.     

Polarization analyzers operating in a wide spectral range

Different versions of practical realization of customary optical systems for full measurement of the polarization state of quasi-monochromatic partially polarized light are considered. They can be used to overcome measurement difficulties associated with the finite width of the spectral range being studied. The effect of changes in characteristics of optical and polarization elements over a spectral range on the character of polarization measurements is analyzed. Methods for elimination of chromatism or taking into account its effect on measurements are suggested. Relations for taking into account the effect of chromatism of a phase plate with constant thickness on measurement results are given. Operation of a classical four-channel scheme for studing quasi-monochromatic partially polarized light in the visible and near-IR regions is considered. For this system, expressions are derived which make possible determination of Stokes parameters taking into account the effect of a finite spectral range. A system using phase modulation of radiation by an electrooptical cell and measurement of the maximum and minimum intensities of the modulated signal is considered. Measurements are carried out by using a two-channel system. Expressions are derived which make possible determination of Stokes parameters for the system under consideration in the visible and near-IR spectral regions. A system for measuring the polarization state of radiation in the visible and near-IR regions and based on modulation of radiation by an electrooptical phase cell is described. Measurements are carried out for the fundamental modulation frequency and its harmonics using a two-channel scheme. Relations for determining Stokes parameters of the system are presented.     

Reconstruction of the probability density function by means of the degree of polarization for one-photon mixed states

In this paper the authors discuss an alternative way for reconstructing one-photon mixed states of a partially polarized optical field. The task is to represent the probability density distribution describing these kind of states with the Stokes parameters which also characterize the effective state of polarization. These parameters can be measured by means of the degree of polarization with an experimental setup containing a rotating linear polarizer and a circular polarizer. A thought experiment is presented which assumes that the measurement is undertaken on an analyzed beam coupled with a reference beam containing photons polarized in a well-known way. The method discussed in the paper is an alternative for the most commonly used quantum tomography approach.     

Stokes holography

A new technique, referred to as Stokes holography, is proposed and experimentally demonstrated for controlled synthesis of generalized Stokes parameters in 3D space using Stokes fringes. Stokes fringes are polarization fringes which permit to record and reconstruct complete wavefront. Full use of Stokes fringes in a single step is realized by scattering complex field and subsequently reconstructing using spatial averaging of the randomly scattered field. Mathematical formulations are derived and supported by experimental results of 3D object reconstruction in generalized Stokes parameters.     

Experimental verification of the electromagnetic spectral interference law using a modified version of the Young's interferometer

We present a method to verify the electromagnetic spectral interference law experimentally, which connects the combined two-beam usual Stokes parameters with the corresponding single beam usual Stokes parameters. Using polarizers and phase retarders in a modified version of the Young's interferometer, the usual Stokes parameters and the generalized Stokes parameters are determined for a laser beam. The experimentally determined single point (usual) Stokes parameters at an axial point in the observation plane for the combined beam are compared with their theoretically expected values obtained by putting the experimental data in the electromagnetic spectral interference law. A fairly good agreement is found between the two values. Not only does the proposed method provides a comparison between the two kinds of Stokes parameters but also validates the role of the generalized Stokes parameters as modulation parameters for the usual Stokes parameters.     

On the measurement of the generalized degree of polarization

On the basis of well-known methods to obtain the standard Stokes parameters, two simple experimental procedures are analysed to measure the so-called generalized degree of polarization, P, defined elsewhere [Opt. Commun., 149 (1998) 230]. After discussing the accuracy of the methods, the generalized degree of polarization of a non-uniformly polarized beam emerging from an optically pumped birefringent Nd:YAG rod optically pumped is experimentally investigated in terms of the pumped power.     

Polarization properties of polarized and partially coherent Electromagnetic Gaussian-Schell model pulse beams on slant path in turbulent atmosphere

This paper is based on the unified theory of coherence and polarization of stochastic electromagnetic beams and the extended Huygens–Fresnel principle, combined with the quadratic approximation of Rytov’s phase structure function and the generalized Stokes parameters. We have derived the novel expressions for the cross-spectral density matrix elements and the degree of cross-polarization of a class of elliptically polarized spatially and spectrally partially coherent Electromagnetic Gaussian-Schell model pulse (EGSMP) beams propagating through atmospheric turbulence along a slant path. Additionally, we calculate and analyze the effects of the turbulent intensity, the initial pulse duration, waist width of the beam, the spatial coherence length and temporal coherence length et al. on the polarization properties of fully polarized and partially coherent EGSMP beams. Finally, a comparison of the impact of those factors on the partially polarization beams is made. The results show that the influences of the turbulent intensity, the initial pulse duration, waist width of the beam, the spatial coherence length and temporal coherence length et al. on the polarization properties of fully polarized and partially coherent EGSMP beams are larger. While the effects of those parameters on the partially polarization and partially coherent EGSMP beams are smaller. It is noted that the results of this paper have established sound theoretical basis on the topic of improving performance of the laser system propagating through the atmospheric turbulence.     

Non-Gaussian fluctuations of Stokes parameters in scattering by small particles

Calculations are presented for second-order fluctuations of Stokes parameters that result from singly scattered, coherent, polarized radiation by an ensemble of small spheroidal particles which are randomly oriented in space. The form of the second-order non-Gaussian enhancements are obtained and discussed, but attention is also given to terms describing amplitude fluctuations that are present in the Gaussian scattering regime. These terms provide a generalized Siegert relationship for polarized radiation. The possibility of using measurements of fluctuations to characterize the particle shape is considered.     

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.     

Vector and tensor polarizations of light beams

Generalized Stokes vectors consisting of nine real parameters in terms of irreducible spherical and Cartesian tensor operators are considered to describe the 3D electromagnetic field. Vector and tensor polarization degrees are introduced to characterize the polarized beam. It is shown that the degree of a pure vector polarized light beam is less than 1, i.e., vector polarized light beam is only partially polarized. The geometrical interpretation of vector and tensor polarizations is presented.     

Stokes-parameters representation in terms of the radial and azimuthal field components: A proposal

A simple characterization of the polarization state of partially polarized beams is proposed on the basis of the Stokes parameters expressed in terms of the radial and azimuthal components of the field at each point of the beam cross-section. The main properties of the proposed Stokes representation are also shown, and its physical meaning is discussed.     

A generalized spherical harmonics solution for radiative transfer models that include polarization effects

A generalized spherical harmonics solution for all components (m ⩾ 0) in a Fourier representation of the Stokes vector basic to the scattering of polarized light is developed, and computational aspects of the solution are discussed in detail. The established solution is used in regard to two test problems to obtain numerical results, accurate, in general, to five significant figures, for the four Stokes parameters.     

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.     

基于斯托克斯参量的光弹性应力分布及成像方法研究

提出了一种基于斯托克斯参量测量的实时光弹性应力测量及其成像的新方法,对该方法的原理及参量测量方法进行了深入研究。根据分振幅斯托克斯参量测量原理设计一个实验系统,利用Equator-Poles(E-P)法定标系统,采用4个性能一致的光电探测器实现光束斯托克斯参量的快速实时测量。用实验系统测量单色平面偏振光通过光弹性样品后的斯托克斯参量,求得出射与入射偏振光的相位延迟量,再求得样品的应力值。运用该方法对有应力分布的平板玻璃和轴向受压有机玻璃进行测量并扫描成像,得到它们的应力分布图像。结果表明,该方法能够准确、快速和无损地测量光弹性样品任意位置的应力,实现对应力的实时测量。     

Degree of polarization of non-uniformly partially polarized beams: a proposal

Two overall parameters are proposed to characterize the degree of polarization and its uniformity across the transversal section of non-uniformly partially polarized beams. Such parameters can be measured according to the well-known standard methods used to obtain the Stokes parameters, with the addition of a CCD camera to determine the beam intensity at each point of the observation plane.     

The moon as a cosmic source of linearly polarized radio emission

We analyze parameters of the partially linearly polarized thermal radio emission from the Moon taking the effects of radiative heat transfer and surface roughness into account. The distributions of the Stokes parameters I, Q, and U over the visible lunar disk are considered. The polarization parameters of the integral radio emission as functions of the frequency and the Moon phase are obtained by integrating the Q and U distributions. We consider the possibility of using the Moon as a reference source of partially linearly polarized radiation for space-borne and ground-based projects aimed at studying polarization of the Galactic radio emission and the cosmic microwave background. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 7, pp. 593–606, July 2007.     

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.     

Ortho-Babinet polarization-interrogating filter: an interferometric approach to polarization measurement

A novel, interferometric, polarization-interrogating filter assembly and method for the simultaneous measurement of all four Stokes parameters across a partially polarized irradiance image in a no-moving-parts, instantaneous, highly sensitive manner is described. In the reported embodiment of the filter, two spatially varying linear retarders and a linear polarizer comprise an ortho-Babinet, polarization-interrogating (OBPI) filter. The OBPI filter uniquely encodes the incident ensemble of electromagnetic wave fronts comprising a partially polarized irradiance image in a controlled, deterministic, spatially varying manner to map the complete state of polarization across the image to local variations in a superposed interference pattern. Experimental interferograms are reported along with a numerical simulation of the method.