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.     

Can a light beam be considered to be the sum of a completely polarized and a completely unpolarized beam?

In a classic paper that may be regarded as the starting point of polarization optics, G. G. Stokes [Trans. Cambridge Philos. Soc.9, 399 (1852)] presented a theorem according to which any light beam is equivalent to the sum of two light beams, one of which is completely polarized and the other completely unpolarized. We show that Stokes' proof of this theorem is flawed. We present a condition for the theorem to be valid.     

Coherence properties of Stokes beams

A Stokes beam is a light beam which is expressible as a superposition of a completely polarized and a completely unpolarized beam. In this note we study coherence properties of a wide class of beams of this kind. The behaviors of the degree of coherence of a Stokes beam produced by a circular planar source are expressed in terms of Lommel functions and theoretical results are illustrated by computed examples.     

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.     

Experimental determination of two-point Stokes parameters for a partially coherent broadband light beam

The generalized Stokes parameters, which are two-point extensions of conventional Stokes parameters, are determined for a pair of points in the cross-section of a partially coherent broadband light beam. For this purpose, using a two-mirror and two-beam-splitter assembly, unpolarized, linearly polarized and partially polarized electromagnetic beams are generated. This simple experimental method for determining generalized Stokes parameters establishes an analogy with the experimental scheme of determining conventional Stokes parameters, which in succession contributes to appreciable reduction in uncertainty in the measurements.     

Polarization properties of vectorial nonparaxial Gaussian beams in the far field

The polarization properties of vectorial coherent nonparaxial Gaussian beams are studied. It is shown that, when the source of a nonparaxial Gaussian beam is completely polarized, the degree of polarization of the propagation field maintains a constant value of 1. However, when the source is completely unpolarized, the degree of polarization does not maintain a constant value of 0. In the far field, vectorial nonparaxial Gaussian beams can become partially polarized, except on the propagation axis, and are spatially nonuniform across a typical cross section of the beam even though the source field is completely unpolarized.     

双波长共焦衍射光学元件分析与设计

报道二维纯位相环带衍射光学透镜的研究。结果表明，在确定位置的像平面的光强分布呈现相当理想的光聚焦作用；同时以１．０６μｍ和０．６３２８μｍ两种波长为例，对双波长二维成像的环带衍射透镜进行分析计算，结果表明二种波长的光束都能聚焦于同一像平面。这种元件可方便地用于非可见激光中的对焦与光路调整。     

Scattering of an unpolarized Bessel beam by spheres

The scattering process of an unpolarized Bessel beam through spherical scatterers is investigated. We derive the analytical solutions of scattered fields of x-and y-polarized Bessel beams using a sphere, after which the dimensionless scattering function for an unpolarized Bessel beam is obtained. The dimensionless scattering function is applicable to spherical scatterers of any size on the beam axis or near it. Through numerical simulations, we demonstrate that extreme points exist in the direction or neighboring direction of the conical angle for spherical scatterers on the beam axis, whereas the existence of extreme points depends on the ratio between the spherical scatterers size and central spot size of the Bessel beam.     

基于焦散线方法的自加速光束设计

以艾里光束为代表的自加速光束是一类在自由空间中具有弯曲传播特性的新型特殊光束.这类光束因其具有无衍射、自加速和自修复等奇异特性引起了人们的广泛关注,有望应用于光学微粒操控、激光微加工、全光路由和超分辨成像等诸多领域.由于艾里光束只能沿着抛物线的轨迹传播,限制了其在实际应用中的灵活性,因而设计出能够沿着不同轨迹传播的自加速光束是这一研究领域的关键问题,而基于焦散线方法的自加速光束设计是解决该问题的有效途径之一.这一方法是将设计的传播轨迹与光学焦散线联系起来,通过分析形成该焦散线所需的光线簇构造出对应的初始场分布.基于该原理并经过不断发展,不同类型的自加速光束相继得以实现,并且借助维格纳函数还可以同时实现实空间和傅里叶空间的自加速光束设计,为自加速光束的应用提供了更多的可能性.本文对基于焦散线方法的自加速光束设计原理和进展进行全面介绍.     

Scintillation index of a stochastic electromagnetic beam propagating in random media

We study the behavior of the scintillation index (the normalized variance of fluctuating intensity) of a wide-sense statistically stationary, quasi-monochromatic, electromagnetic beam propagating in a homogeneous isotropic medium. In particular, we show that in the case when the beam is treated electromagnetically apart from the correlation properties of the medium in which the beam travels not only its degree of coherence but also its degree of polarization in the source plane can affect the values of the scintillation index along the propagation path. We find that, generally, beams generated by unpolarized sources have reduced level of scintillation, compared with beams generated by fully polarized sources, provided they have the same intensity distribution and the same state of coherence in the source plane. An example illustrating the theory is considered which examines how the scintillation index of an electromagnetic Gaussian Schell-model beam propagates in the turbulent atmosphere. These results may find applications in optical communications through random media and in remote sensing.     

Weak gravity-like force detector by “Atom interferometers”

We study nonlinear interaction of counter-propagating plane light waves in a semi-infinite isotropic lossless nonlinear Kerr medium and report existence of several regions of optical-polarization-multistability. The counter-propagating waves may be produced by normal reflection of an incident beam by a mirror in the nonlinear Kerr medium. We obtain nonlinear coupled differential equations for Stokes parameters of the two beams and solve them following the method of Prakash et al. [Mod. Phys. Lett. B 14, 47 (2000)] and the boundary conditions at the mirror. We find that, for the same incident intensity and for the same polarization state of the incident beam, output beam may exist in several stable polarization states.     

分振幅型全Stokes同时偏振成像系统波片相位延迟误差分析

分振幅型全Stokes同时偏振成像仪具有实时性好、空间分辨率高、精度高等优点,有很高的应用价值.分振幅型全Stokes同时偏振成像系统利用偏振分束器、1/2波片和1/4波片将入射光Stokes矢量调制在4幅图像中,可解析入射光Stokes矢量. 1/2波片和1/4波片的相位延迟误差对Stokes矢量测量精度有着不可忽略的影响.建立了包含上述两种误差的Stokes矢量测量误差方程,分析了1/2波片和1/4波片相位延迟耦合误差对自然光、0°/45°线偏光、左旋圆偏光等典型基态入射光的Stokes矢量测量误差的影响,推导了任意偏振态的Stokes矢量测量误差的表征方法.在邦加球球面和球内选取不同偏振度的Stokes矢量作为入射光进行仿真.结果表明, Stokes矢量测量误差和偏振度测量误差均随着入射光偏振度的增大而增大.选取入射光偏振度为1时的偏振测量精度评估系统.为满足2%的偏振测量精度, 1/2波片相位延迟误差应在±1.6°内, 1/4波片相位延迟误差应在±0.5°内.这对提高系统的偏振测量精度具有重要意义,为系统设计和研制提供了重要的理论指导.     

New multiplexed system for synchronous measurement of out-of-plane deformation and two orthogonal slopes

We propose a novel system for synchronous measurement of out-of-plane deformation and two orthogonal slopes using a single camera. The linearly polarized reference beam introduced by an optical fiber interferes with the unpolarized object beam to measure the out-of-plane deformation. A modified Mach—Zehnder interferometer is used to measure the two orthogonal slopes of the out-of-plane deformation. One of the object beams of the Mach—Zehnder interferometer is an unpolarized beam, and the other object beam is split into two orthogonal linearly polarized object beams by a polarizing prism. The two beams are orthogonally polarized. Hence, they will not interfere with each other. The two polarized beams respectively interfere with the unpolarized beam to simultaneously measure the two orthogonal slopes of the out-of-plane deformation. In addition, the imaging lens and apertures are respectively placed in three optical paths to independently control the carrier frequencies and shearing amounts. The effectiveness of this method can be proved by measuring two pressure-loaded circular plates.     

Polarization of completely coherent random electromagnetic beams

It is shown that the spectral degree of polarization rho(r, omega) of a fluctuating electromagnetic beam which is completely coherent throughout a domain D is necessarily the same at every point in D. It can take on any value in the range 0 < or = rho < or = 1. In particular, the fully coherent beam can be completely polarized or completely unpolarized throughout D.     

Spin-to-orbital angular momentum conversion and spin-polarization filtering in electron beams

We propose the design of a space-variant Wien filter for electron beams that induces a spin half-turn and converts the corresponding spin angular momentum variation into orbital angular momentum of the beam itself by exploiting a geometrical phase arising in the spin manipulation. When applied to a spatially coherent input spin-polarized electron beam, such a device can generate an electron vortex beam, carrying orbital angular momentum. When applied to an unpolarized input beam, the proposed device, in combination with a suitable diffraction element, can act as a very effective spin-polarization filter. The same approach can also be applied to neutron or atom beams.     

Incoherent light-induced self-organization of molecules

Although coherent light is usually required for the self-organization of regular spatial patterns from optical beams, we show that peculiar light-matter interaction can break this evidence. In the traditional method of recording laser-induced periodic surface structures, a light intensity distribution is produced at the surface of a polymer film by an interference between two coherent optical beams. We report on the self-organization followed by propagation of a surface relief pattern. It is induced in a polymer film by using a low-power and small-size coherent beam assisted by a high-power and large-size incoherent and unpolarized beam. We demonstrate that we can obtain large size and well-organized patterns starting from a dissipative interaction. Our experiments open new directions to improving optical processing systems.     

Preselection with certainty of photons in a singlet state from a set of independent photons

It is shown that one canpreselect with certainty photons in the singlet state from a set of completely unpolarized and independent photons which did not in any way directly interact with each other-without in any way affecting them. The result is based on an experiment which puts together two unpolarized photons from two independent singlet pairs, making them interfere in the fourth order at a beam splitter so as to preselect the singlet state of the other two photons from the pairs, although no polarization measurement has been carried out on the photons coming out from the beam splitter. One can obtain the expectation value for the correlated state of the former two unpolarized photons in the Hilbert space and therefore write down the singlet state for them, but one apparently cannotinfer the state within the Hilbert space. This might suggest that the Hilbert space is not amaximal model for quantum measurements.     

A generalized approach to beam wave interaction with a dielectric interface

New phenomena have been reported recently in connection with Gaussian beam interaction with a plane dielectric interface, namely, the deterioration of the reflected and refracted beams from shapes predicted by geometric optics, and the generation of higherorder components that cause angular beam deflection. Any bounded, symmetric beam, which is not necessarily Gaussian, can be comprised in terms of an angular spectrum of plane waves. Utilizing such a modal expansion, a model of the interaction process that seems to point out the generality of the phenomena involved for bounded symmetrical beams with any cross-section is presented. The procedure is applied to a Cauchy profile, and analytical results are given. Comparison with previous results obtained for the Gaussian beam and careful examination of the respective spectral functions demonstrate close correspondence between the results. This adds credence to the general approach presented here which can be applied to bounded symmetrical beams of general shape.     

Spirally polarized beams for polarimetry measurements of deterministic and homogeneous samples

The use of spirally polarized beams (SPBs) in polarimetric measurements of homogeneous and deterministic samples is proposed. Since across any transverse plane such beams present all possible linearly polarized states at once, the complete Mueller matrix of deterministic samples can be recovered with a reduced number of measurements and small errors. Furthermore, SPBs present the same polarization pattern across any transverse plane during propagation, and the same happens for the field propagated after the sample, so that both the sample plane and the plane where the polarization of the field is measured can be chosen at will. Experimental results are presented for the particular case of an azimuthally polarized beam and samples consisting of rotated retardation plates and linear polarizers.     

输入面纵向偏移诱导的强非局域非线性光传输特性变化

基于模式分解方法, 分析了输入面纵向偏移诱导的强非局域非线性光传输特性变化的普适性规律. 结果表明光束输入面移动后导致的影响包括: 光斑在每个周期内出现的位置和顺序的变化、 相同形状的光斑在输入面移动前后大小的差异以及波面曲率因子的演化. 这些性质可用一个简单的数学公式进行归纳; 利用这一公式可方便地由输入面移动前的任意光束解得到输入面纵向移动后的光束解. 关键词： 强非局域非线性 光束 输入面