Polarization singularity democracy: WYSIWYG

The canonical point singularity of elliptically polarized light is a C point, an isolated point of circular polarization surrounded by a field of polarization ellipses. The defining singular property of a C point is that the surrounding ellipses rotate about the point. It is shown that this rotation is seen only for a particular line of sight (LOS) and, conversely, that there exists a unique LOS for every ellipse along which the ellipse is seen as a singularity. It is also shown that changes in LOS can turn singularities into stationary points and vice versa. The democratic behavior of polarization singularities and stationary points is a consequence of the fundamental "what you see is what you get" property of ellipse fields. Simple experiments are proposed for observing this unusual property of elliptically polarized light.     

Hyperboloid structures formed by polarization singularities in coherent vector fields with longitudinal-transverse coupling

The propagation-dependent polarization vector fields are experimentally created from an isotropic microchip laser with a longitudinal-transverse coupling and entanglement of the polarization states. The experimental three-dimensional coherent vector fields are analytically reconstructed with a coherent superposition of orthogonal circularly polarized vortex modes. Each polarized component is found to comprise two Laguerre-Gaussian modes with different topological charges. With the analytical representation, the polarization singularities, on which the electric polarization ellipse is purely circular (C lines) or purely linear (L surfaces), are explored. The C line singularities are found to form an intriguing hyperboloidal structure.     

Experimental umbilic diabolos in random optical fields

The intensity of a random optical field consists of bright speckle spots (maxima) separated from dark areas (minima and optical vortices) by saddle points. We show that hidden in this complicated landscape are umbilic points--singular points at which the eigenvalues Lambda (+/-) of the Hessian matrix that measure the curvature of the landscape become degenerate. Although not observed previously in random optical fields, umbilic points are the most numerous of all special points, outnumbering maxima, minima, saddle points, and vortices. We show experimentally that the directions of principal curvature, the eigenvectors Psi (+/-), rotate about intensity umbilic points with positive or negative half-integer winding number, in accord with theory, and that Lambda (+) and Lambda (-) generate a double cone known as a diabolo. At optical vortices the curvature of the amplitude is singular, and we show from both theory and experiment that for this landscape Psi (+/-) rotate about vortex centers with a positive integer winding number. Diabolos can be classified as elliptic or hyperbolic, and we present initial results for the measured fractions of these two different types of umbilic diabolos.     

Polarization singularities in 2D and 3D speckle fields

The 3D structure of randomly polarized light fields is exemplified by its polarization singularities: lines along which the polarization is purely circular (C lines) and surfaces on which the polarization is linear (L surfaces). We visualize these polarization singularities experimentally in vector laser speckle fields, and in numerical simulations of random wave superpositions. Our results confirm previous analytical predictions [M. R. Dennis, Opt. Commun. 213, 201 (2002)] regarding the statistical distribution of types of C points and relate their 2D properties to their 3D structure.     

Emergent polarization singularities

Polarization singularities are shown to emerge spontaneously from the incoherent addition of uncorrelated optical fields that individually need not contain singularities. Examples of this phenomenon are given for both vector and ellipse fields. The incoherent addition of vector fields whose singularities have integer winding numbers is shown to yield fields whose singularities have half-integer winding numbers. These findings are used to make predictions about the singularities of the polarized component of the cosmic microwave background.     

Singularities in speckled speckle

Speckle patterns produced by random optical fields with two (or more) widely different correlation lengths exhibit speckle spots that are themselves highly speckled. Using computer simulations and analytic theory we present results for the point singularities of speckled speckle fields, namely, optical vortices in scalar (one polarization component) fields and C points in vector (two polarization components) fields. In single correlation length fields both types of singularities tend to be more or less uniformly distributed. In contrast, the singularity structure of speckled speckle is anomalous; for some sets of source parameters vortices and C points tend to form widely separated giant clusters, for other parameter sets these singularities tend to form chains that surround large empty regions. The critical point statistics of speckled speckle is also anomalous. In scalar (vector) single correlation length fields phase (azimuthal) extrema are always outnumbered by vortices (C points). In contrast, in speckled speckle fields, phase extrema can outnumber vortices and azimuthal extrema can outnumber C points by factors that can easily exceed 10(4) for experimentally realistic source parameters.     

Vector singularities of superposition of mutually incoherent orthogonally polarized beams

It is shown that, at an incoherent superposition of orthogonally polarized laser beams, a special type of singularities are formed in the cross section of a combined beam in place of the well-known singularities, such as optical vortices (for scalar fields); C points, at which the polarization is circular; and L lines, along which the polarization is linear (for coherent vector fields). These new singularities are U lines, along which the degree of polarization is zero and the state of polarization is undetermined, and P points, at which the degree of polarization is equal to unity and the state of polarization is determined by the nonzero component of the combined beam. Conditions of topological stability of U and P singularities are discussed, as well as peculiarities of the spatial distribution of the degree of polarization of the field in the vicinity of such singularities. First experimental results on the reconstruction of a vector skeleton formed by U and P singularities in combined speckle fields are presented.     

Topological structure in polarization resolved conoscopic patterns for nematic liquid crystal cells

We investigate the polarization structure of coherent light, produced by a convergent light beam transmitted through nematic liquid crystal (NLC) cells with different director configurations. Employing solutions to the transmission problem for the case when plane wave propagates through an anisotropic layer, we analyze the arrangement of the topological elements, such as polarization singularities (C points with circular polarization and L lines with linear polarization), saddle points and extrema of polarization azimuth. We observe transformations of the topological structure under the variation of the incident light ellipticity and represent it by corresponding trajectories of topological elements in three-dimensional space. For the cells with uniform and non-uniform director configuration we describe the processes of creation/annihilation of C point pairs, which can be controlled precisely in the case of the cell with non-uniform director. Our experimental measurements for the homeotropically oriented NLC cells are in good agreement with the theoretical predictions.     

Strong-field photoionization of intense laser fields by controlling optical singularities

The spatial features of a light field, such as in the form of the optical singularities, provide a new degree of freedom for the application of light fields in different areas of science and technology. However, although the exploration of structured light is growing rapidly, the investigation of strong-field photoionization using such light fields is noticeably lagging behind. Here, we present an experimental study that reveals the signatures of intense, structured light fields with controlled optical singularities in strong-field photoionization. The different types of optical singularities can be identified through photoionization observables,i.e., photoelectron momentum distributions(PMDs). By concurrently shifting the locations of the phase and polarization singularities, the focal electric field features can be designated, and subsequently, the photoionization appearances can be manipulated. In this process, the behaviors of the different intense optical singularities are clearly visualized by the PMDs. This work will advance both the strong-field science and singularity optics.     

Winding up of the wave-function phase by an insulator-to-superfluid transition in a ring of coupled Bose-Einstein condensates

We study phase transition from the Mott insulator to superfluid in a periodic optical lattice. Kibble-Zurek mechanism predicts buildup of winding number through random walk of BEC phases, with the step size scaling as a third root of transition rate. We confirm this and demonstrate that this scaling accounts for the net winding number after the transition.     

Linear Transformation of the Polarization Modes in Coiled Optical Spun-Fibers with Strong Unperturbed Linear Birefringence. I. Nonresonant Transformation

A linear transformation of orthogonal polarization modes in coiled optical spun-fibers with strong unperturbed linear birefringence, which causes the emergence of the dependences of the integrated elliptical birefringence and the ellipticity and azimuth of the major axis of the ellipse, as well as the polarization state of radiation (PSR), on the length of optical fiber has been considered. Optical spun-fibers are subjected to a strong mechanical twisting, which is frozen into the structure of the optical fiber upon cooling, in the process of being drawn out from the workpiece. Since the values of the local polarization parameters of coiled spunwaveguides vary according to a rather complex law, the calculations were carried out by numerical modeling of the parameters of the Jones matrices. Since the rotation speed of the axes of the birefringence is constant on a relatively short segment of a coiled optical spun-fiber in the accompanying torsion (helical) coordinate system, the so-called “Ginzburg helical polarization modes” (GHPMs)—two mutually orthogonal ellipses with the opposite directions of traversal, the axis of which rotate relative to the fixed coordinate system uniformly and unidirectionally—are approximately the local normal polarization modes of such optical fiber. It has been shown that, despite the fact that the unperturbed linear birefringence of the spun-fibers significantly exceeds the linear birefringence, which is caused by the winding on a coil, the integral birefringence of an extended segment of such a fiber coincides in order of magnitude with the linear birefringence, which is caused by the winding on the coil, and the integral polarization modes tend asymptotically to circular ones. It has been also shown that the values of the circular birefringence of twisted single-mode fibers, which were calculated in a nonrotating and torsion helical coordinate systems, differ significantly. It has been shown that the polarization phenomena occur in the process of linear transformation of local polarization modes, which lead to small quasi-harmonic oscillations of the birefringence integral parameters of the optical spun-fibers, which depend on their length, and the period of these oscillations is approximately equal to half of the effective period of polarization beating.     

Topological charge of (lattice) gauge fields

Using recently derived explicit formulae for the 2- and 3-cochains in SU(2) gauge theory, we are able to integrate the Chern-Simons density analytically. We arrive — in SU(2) — at a local algebraic expression for the topological charge, which is the sum of local winding numbers associated with the corners (lattice points) of the cells covering the manifold plus contributions from possible isolated gauge singularities which manifest themselves as “vortices” in the 1-, 2- or 3-cochains. Among others we consider hypercubic geometry — i.e. covering the manifold by hypercubes — which is of particular interest to lattice Monte Carlo applications. Finally, we extend our results to SU(3) gauge theory.     

四孔径衍射屏在近场形成的光强分布及拓扑荷

利用基尔霍夫衍射理论计算模拟了四圆孔径衍射屏在菲涅耳深区形成的衍射光场的强度、零值线和相位的分布,发现衍射光场亮斑关于中心呈对称分布,在距离衍射屏较近的观察面上,光强值为零的点组成光强零值线段,该线段上光强等值线的离心率都接近或等于1,其两侧的光强值变化非常剧烈。复振幅的实部和虚部零值线多为封闭的曲线,零值线交叉点的个数为偶数,并且正负相位奇异点的个数相等。特殊相位奇异点周围的相位不仅呈对称分布,而且该点的拓扑荷的值近似为零。随着光波的传播,在不同的观察面上光强零值线段逐渐变短,最终趋于一点。     

高阶贝塞尔-高斯脉冲光束相位奇点的演化

 推导出被光阑衍射高阶贝塞尔-高斯脉冲光束的场和光强分布的解析公式,对其相位奇点的演化特性做了计算和分析。结果表明,高阶贝塞尔-高斯脉冲光束经光阑衍射后,中心光涡旋始终存在,拓扑电荷守恒。随脉冲频率和脉冲宽度增加,等相位线均沿逆时针方向旋转,涡旋核随脉冲频率增加而减小,而脉冲宽度对涡旋核大小几乎无影响。等相位线随截断参数和传输距离的增加分别沿逆时针和顺时针方向旋转,涡旋核大小随截断参数增加而变化,随传输距离和光束阶数的增加而增大。     

Matrix-Based Polarization Analysis and Application of Semiconductor Optical Amplifiers

Employing the Mueller matrix method with polar decomposition, we analyse the polarization rotation (PR) effects in semiconductor optical amplifiers (SOAs) and demonstrate that the PR angle is linear to the birefringence dependent gain while the average PR coefficient is about 0.625 for the employed SOA. It is further evident that the current and optical intensity dependent PRs rotate reversely around the same axis. Thus we propose an optical-electric synchronous control scheme to obtain orthogonal polarization states with power-equalization, and implement it by a polarization-sensitive SOA. The polarization duration time is about 10 ns which is applicable to high-speed polarization state generation.     

Momentum-space polarization fields in two-dimensional photonic-crystal slabs: Physics and applications

In addition to non-radiative guided modes, two-dimensional photonic-crystal slabs support guided resonant ones which can radiate into free space. From the polarization states of these guided resonances, a polarization field on a photonic band can be constructed in momentum space. Momentum-space polarization fields display complicated configurations and patterns with different types of polarization singularities inside, shedding new light on the manipulations of light flows. In this review, we summarize the recent research progress on momentum-space polarization fields and singularities in two-dimensional photonic-crystal slabs, focusing on their unique optical properties and potential applications as well.     

聚偏氟乙烯分子链旋转时势能的变化

计算了聚偏氟乙烯分子链旋转时势能的变化.结果显示,当中心分子链旋转而其它链静止不动时,计算得到的势能曲线有4个很高的势垒,这些势垒来源于中心分子链和最近邻分子链中的氟原子对的“空间位阻”效应.这一结果与“六阱势”模型预言的势能变化存在准六度对称性相矛盾.计算结果表明,如果中心分子链和周围分子链同步旋转,势垒高度将极大地降低.另外,极化反转时晶格常数发生变化.最后得到的势垒高度约为7.5kJ/mol.与室温下的分子势运动的能量（约2.5kJ/mol）相比,这样的“浅”势阱不足以锁定分子偶极矩形成稳定的自发极 关键词：