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.     

The effect of spherical aberration on the phase singularities of focused dark-hollow Gaussian beams

The phase singularities of focused dark-hollow Gaussian beams in the presence of spherical aberration are studied. It is shown that the evolution behavior of phase singularities of focused dark-hollow Gaussian beams in the focal region depends not only on the truncation parameter and beam order, but also on the spherical aberration. The spherical aberration leads to an asymmetric spatial distribution of singularities outside the focal plane and to a shift of singularities near the focal plane. The reorganization process of singularities and spatial distribution of singularities are additionally dependent on the sign of the spherical aberration. The results are illustrated by numerical examples.     

Stokes singularity relations

Polarization singularities in paraxial vector optical fields are analyzed in terms of the phase singularities of complex Stokes scalar fields. Six independent relationships are obtained that connect the topological charges of these singularities on special closed contours with the charges of singularities that are enclosed by these contours. These relationships, which have been confirmed by experimental data and computer simulations, imply topological polarization correlations of an infinite range.     

Singularities and spectral changes of Gaussian beams focused by a lens with spherical aberration

We address the effect of the truncation parameter and spherical aberration (SA) on the singularity transformation and spectral behavior of the polychromatic Gaussian beams focused by an aperture lens with SA in detail. The numerical simulation results, based on the derived equations of the intensity and the spectral density, are given. It is found that the axial singularities vanished with the change of the truncated parameter. The intensity and drastic spectral change fade away with an annihilation process of the phase singularities, and the drastic spectral change does not disappear immediately at the moment the phase singularity annihilates. The singularities in the focal region will redistribute with the increment of SA coefficient, some singularities will vanish, some will spilt into two new singularities, and other off-axial singularities will appear and split into two new singularities as well. When SA coefficient changed, we can find that the axial singularities disappear as well with the decreasing value of truncation parameter. These new splitted singularities due to the change of SA coefficient will converge into one singularity again and disappear gradually.     

Vortex solitons with inhomogeneous polarization in nonlocal self-focusing nonlinear media

Both azimuthally and radially polarized vortex solitons are investigated to be able to exist in highly nonlocal nonlinear media. We get exactly analytical solutions of azimuthally polarized vortex solitons with only polarization singularities and radially polarized vortex solitons with both phase singularities and polarization singularities. Both azimuthally and radially polarized vortex solitons can exist in nonlocal self-focusing nonlinear media with proper modulation of the beam power and the degree of nonlocality. Contrary to those of radially polarized counterparts in local Kerr media, the topological charge can be any integer. When the topological charge m ≠ 0, both phase singularities and polarization singularities work. When m = 0, the polarization singularities work. Azimuthally polarized vortex solitons with polarization singularities corresponds to the linearly polarized vortex solitons with single charge. Our results show that polarization singularities work the same way as phase singularities in some sense.     

String theory and cosmological singularities

In general relativity space-like or null singularities are common: they imply that ‘time’ can have a beginning or end. Well-known examples are singularities inside black holes and initial or final singularities in expanding or contracting universes. In recent times, string theory is providing new perspectives of such singularities which may lead to an understanding of these in the standard framework of time evolution in quantum mechanics. In this article, we describe some of these approaches.      

On the genericity of spacetime singularities

We consider here the genericity aspects of spacetime singularities that occur in cosmology and in gravitational collapse. The singularity theorems (that predict the occurrence of singularities in general relativity) allow the singularities of gravitational collapse to be either visible to external observers or covered by an event horizon of gravity. It is shown that the visible singularities that develop as final states of spherical collapse are generic. Some consequences of this fact are discussed.      

A cascade of singular field patterns in Young’s interference experiment

We analyze Young’s interference experiment for the case that two correlated, linearly polarized beams are used. It is shown that even when the incident fields are partially coherent, there are always correlation singularities (pairs of lines where the fields are completely uncorrelated) on the observation screen. These correlation singularities evolve in a non-trivial manner into dark lines (phase singularities in the paraxial approximation). The latter in turn each unfold into a triplet of polarization singularities, namely an L-line and two C-lines of opposite handedness.     

The effect of astigmatism on the phase singularities of focused beams

The phase singularities of plane beams focused by an aperture lens with astigmatism are studied. Numerical calculation results are given to illustrate the dependence of phase singularities of focused plane beams on the astigmatic coefficient and the Fresnel number. It is shown that as the Fresnel number gradually increases, the phase singularities shift not only towards the z-axis but also towards the geometrical focal plane in the presence of astigmatism, whereas the phase singularities move along the focal plane and always line in the focal plane for the astigmatism-free case. With increasing astigmatic coefficient, the phase singularities shift not only towards the z-axis but also far away from the geometrical focal plane.     

Influence of the comatic aberration of an apertured lens on the focused polychromatic Gaussian beams

The focusing of polychromatic Gaussian beams by an apertured lens with comatic aberration is investigated in this paper. We study the influence of the comatic aberration and truncation parameter on the intensity distribution at the focal plane, and singularities and spectral behavior near the focal plane in detail. The simulation results show that the maximum intensity at the focal plane will shift and split with the gradual increment of comatic aberration. We also find that the decrease of truncation parameter will counteract the influence of comatic aberration, which leads to the intensity variation. Furthermore, the singularity transformation and spectral anomalies are discussed. It is found that with the increment of comatic aberration, some singularities are split into several new singularities, and by combining some of these new singularities with other singularities near the focal plane, they vanish or form new singularities with the continuing increase of comatic aberration. The decreasing value of truncation parameter will cause similar phenomena.     

Foliation analysis of gravitation singularities

Gravitation singularities are examined as singularities of space-time foliations which represent critical points of real functions on a space-time.     

Mixture steering law design for control moment gyroscopes

Focusing on the singularities of a spacecraft using control moment gyros(CMGs)to do the large angle maneuvers,a new mixture steering law is proposed to avoid the singularities.According to this method,if the CMGs are far away from the singularity,the Moore-Penrose pseudo-inverse steering law(MP)is used directly.If the CMGs are close to the singularity,instead of solving the inverse matrix,a set of optimal gimbal angles are sought for the singular measurement to reach the maximum,which can avoid the singularities.Simulations show that the designed steering law enables the spacecraft to carry out the large angle maneuver and avoid the singularities simultaneously.     

Dynamic behavior of composite spectral Stokes singularities in?superimposed partially coherent beams beyond the paraxial approximation

The composite spectral Stokes singularities are introduced to describe polarization singularities in superimposed partially coherent beams beyond the paraxial approximation. Based on the vector Rayleigh–Sommerfeld diffraction integrals, the dynamic behavior of composite spectral Stokes singularities in the free-space propagation is studied and illustrated by numerical examples. A comparison with the previous work is also made.     

LETTER: Quantum Singularity of Quasiregular Spacetimes

Some of the mildest singularities in classical general relativity are shown to be singular quantum mechanically as well. A class of the mild, topological singularities known as quasiregular singularities remains singular when probed by quantum wave packets. These static spacetimes possessing dislocations and disclinations are quantum-mechanically singular since the spatial portion of the wave operator is not essentially self-adjoint and thus the evolution of a test quantum wave packet is not uniquely determined by the initial wave function.     

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.     

Gravitational singularities and disruption of causality

Basic aspects of describing gravitational singularities as singularities of causal space-time layering are considering. The relationship between disruption of causality and the existence of singularities is studied. It is shown that under certain conditions disruption of causality may prevent the development of a gravitational singularity.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 41–45, April, 1985.     

Polarization singularities in Young's two-slit experiment

Young's interference experiment is regarded as a two-slit diffraction phenomenon, the polarization singularities in Young's two-slit configuration illuminated with two linearly, orthogonally polarized Gaussian vortex beams are studied. It is shown that generally, there exist L-lines (linearly polarization) and polarization singularities including C-points (circular polarization), S₂₃ and S₃₁ singularities even though the parameters of two beams are the same. The pair creation-annihilation and motion of polarization singularities take place upon propagation, or by varying a control parameter, such as the amplitude ratio of two beams or obscure ratio of slits etc. For a special case of the illumination with two linearly, orthogonally polarized Gaussian vortex-free beams, polarization singularities, in particular, C-points may occur if a parameter of two beams is not equal.     

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.     

Singularities,trapped sets,and cosmic censorship in asymptotically flat space-times

We show that space-time is future asymptotically predictable from a regular partial Cauchy provided that singularities are causally preceded by trapped sets. Future asymptotic predictability is a formal statement of cosmic censorship in asymptotically flat space-times. A regular partial Cauchy surface means that singularities in gravitational collapse can arise only from regular initial data. Our result confirms a supposition by Hawking that singularities forced by singularity theorems cannot be naked.     

经光阑衍射的平顶涡旋光束位相奇点的演化特性

推导出了平顶涡旋光束通过有光阑ABCD光学系统的传输解析式,并以光阑透镜和矩形光阑系统为例,与平顶光束比较研究了截断参量、相对离轴距离和光束阶数对衍射场中位相奇点演化特性的影响.数值计算表明,平顶涡旋光束通过上述光学系统均存在位相奇点,即使源处涡旋被光阑阻拦时,衍射场中也会出现位相奇点;而平顶光束通过光阑透镜系统存在刃型位错,随着截断参量增大,会发生刃型位错的演化和湮灭现象,且平顶光束通过矩形光阑系统没有发现位相奇点.