Phase singularities and coherence vortices in linear optical systems

It is demonstrated for a time-invariant linear optical system that there exists a definite connection between the optical vortices (phase singularities of the field amplitude) which appear when it is illuminated by spatially coherent light and the coherence vortices (phase singularities of the field correlation function) which appear when it is illuminated by partially coherent light. Optical vortices are shown to evolve into coherence vortices when the state of coherence of the field is decreased. Examples of the connection are given. Furthermore, the generic behavior of coherence vortices in linear optical systems is described.     

散斑场相位涡旋及其传播特性的实验研究

用CCD记录散斑场和参考光的干涉图样, 利用傅里叶变换法实现了散斑场复振幅以及相位分布的实验提取, 在复振幅实部零值线和虚部零值线切点处出现一种新的相位奇点, 与两条零值线交点处的传统相位奇点周围单调螺旋变化的相位分布不同, 绕切点一周的相位具有先增大后减小几乎呈对称性分布的特性, 为了解释这种新的相位奇点,提出了准孪生相位涡旋的概念. 在理论研究散斑场强度的纵向自相关函数的基础上, 实验观察散斑场相位涡旋的传播, 发现在光强纵向相关长度范围内的不同传播距离处的观察面上, 复振幅实部和虚部随机变化而涡旋的 关键词： 相位涡旋 散斑 干涉     

Measurement of the spatial coherence function of undulator radiation using a phase mask

A measurement of the horizontal coherence function of 7.9 keV radiation from an undulator beam line at the Advanced Photon Source is reported. X-ray diffraction from a phase-shifting mask was used, and the coherence function was measured as a function of the width of beam-conditioning slits in the beam line. The coherence distribution is found to be best described by a Lorentzian function.     

Experimental investigation of local properties and statistics of optical vortices in random wave fields

We present the first direct experimental evidence of the local properties of optical vortices in a random laser speckle field. We have observed the Berry anisotropy ellipse describing the anisotropic squeezing of phase lines close to vortex cores and quantitatively verified the Dennis angular momentum rule for its phase. Some statistics associated with vortices, such as density, anisotropy ellipse eccentricity, and its relation to zero crossings of real and imaginary parts of the random field, are also investigated by experiments.     

块状介质超连续谱相位的相干特性

 块状介质超连续谱由一系列复杂的非线性过程产生。用两路飞秒泵浦光聚焦到熔石英玻璃上得到两束独立的超连续谱,实验上观察到它们形成的稳定干涉条纹;改变两路泵浦光的时间延迟,得到共线超连续谱形成的频率梳。实验证明,块状介质超连续谱的产生保持了泵浦光的相位锁定关系,泵浦光能量抖动和介质的缺陷都不会对超连续谱的相位带来明显的扰动。     

块状介质超连续谱相位的相干特性

块状介质超连续谱由一系列复杂的非线性过程产生。用两路飞秒泵浦光聚焦到熔石英玻璃上得到两束独立的超连续谱,实验上观察到它们形成的稳定干涉条纹;改变两路泵浦光的时间延迟,得到共线超连续谱形成的频率梳。实验证明,块状介质超连续谱的产生保持了泵浦光的相位锁定关系,泵浦光能量抖动和介质的缺陷都不会对超连续谱的相位带来明显的扰动。     

Measurement of spatial coherence through diffraction from a transparent mask with a phase discontinuity

We describe a robust method by which the spatial coherence from all pairs of points along a line may be simultaneously acquired from an image formed by diffraction from a phase discontinuity. In contrast to other methods, this approach can accurately reveal weak correlations in the tails of a coherence function.     

Transverse laser-mode structure determination from spatial coherence measurements: Experimental results

We demonstrate experimentally the feasibility of a certain coherence-theoretic algorithm for determining the relative modal weights of a laser beam that consists of multiple Hermite-Gaussian transverse modes. A computer-controlled Young's two-pinhole interferometer with a linear CCD array is used for the coherence measurements. The required scaling parameter (beam width) is obtained iteratively by library routines. Numerical simulations on the stability of the algorithm in the presence of experimental noise are also presented.     

Relationship between spectral properties and spatial coherence properties in one-dimensional free fields

Some consequences of a recently derived relationship between the spectral properties and the spatial coherence properties of a stationary optical field are studied for the case when the field is one-dimensional. It is found that the spectrum may be determined from the knowledge of the spatial coherence of the field at all pairs of points that lie within an interval whose length is at least as great as the coherence length of the light.     

Experimental observation of phase coherence in bilayer systems in the absence of a magnetic field

A high narrow peak of differential interlayer tunneling conductance is observed in the absence of a magnetic field at low temperatures in heterostructures with two closely spaced electron layers. The analysis of experimental results suggests that this peak is a consequence of the interlayer phase coherence, which arises in the system owing to the Bose condensation of interlayer excitons, i.e., pairs formed by electrons and holes belonging to different layers, in accordance with the recent theoretical predictions.     

Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering

We report a method for generation of arbitrary shape and array of optical vortices by use of a superposition of coherent elementary vortices based on helical phase spatial filtering in spatial frequency domain. In this method, a helical phase spatial filter (HPSF) is placed in the spatial frequency plane of a 4-f imaging processing system. We demonstrated that the output field distribution represents the convolution between the input field and an elementary vortex field introduced by the HPSF, which results in a special shape or array of optical vortices determined by the “degenerate” properties of coherent elementary vortices and the distribution formats of the input field.     

Symmetry breaking of optical vortices: birth and annihilation of singularities in the evanescent field

The interaction of optical vortices (or phase singularities, or screw dislocations) with ordinary matter is treated with a simple approach. Using the total internal reflection phenomenon and the superposition of four plane waves incident on a material with a refractive index lower than the original propagating medium, we are able to show the birth and annihilation of optical vortices in an evanescent field with curved topological features. Until now, this phenomenon has been explored only in free space propagation. By a suitable tuning process involving the incident angles and the amplitudes of the incident plane waves, it is possible to create unusual topological features of optical vortices in the vicinity of the material. We believe that this work can open new aspects of curved optical vortex manipulation in near-field optics.     

High-resolution phase imaging of phase singularities in the focal region of a lens

Subwavelength-resolution phase images of phase dislocations at the focal region of a 20x , 0.4-N.A. lens have been obtained by use of an optical fiber interferometer with a tapered probe in one arm. A phase-stepping algorithm is used to determine a quantitative value of the phase at each point in the scan, clearly showing the presence of edge dislocations between the Airy rings of the diffraction pattern near the lens focus, as well as four isolated screw-type singularties caused by astigmatism in the lens.     

Creation and annihilation of phase singularities in a focal field

It is well known that uniform illumination of a lens leads to a focal field with a pattern of dark Airy rings in the focal plane, whereas this is not the case for Gaussian illumination. We show theoretically and experimentally that in the transition between the two cases the Airy rings, being phase singularities, reorganize themselves by means of a creation-annihilation process leading to new dark rings outside the focal plane.     

Optimisation using measured Green's function for improving spatial coherence in acoustic measurements

Aberrating materials can degrade acoustic measurements by distorting the acoustic wavefront and causing acoustic speckle (as opposed to speckle noise which is a manifestation of coherent backscatter). The amplitude and phase fluctuations associated with acoustic speckle can introduce considerable measurement uncertainty which is difficult to deal with. This paper demonstrates a new technique which optimises the spatial distribution of the generation of the ultrasound to compensate for the aberration. This technique uses experimentally measured Green's functions to allow the calculation of the field resulting from the generation wavefront during optimisation. The technique is used to improve the accuracy of velocity measurements in a steel sample using 82 MHz SAW waves. This is achieved by optimising for improved spatial coherence in the measurement region which suppresses the speckle noise. Experimental evidence of acoustic aberration arising from grain structure is shown for steel and aluminium and the measured Green's function optimisation technique is shown to overcome the resulting acoustic speckle. The technique was performed using the Adaptive Optical Scanning Acoustic Microscope (AOSAM) at Nottingham University, UK.