Observation of Gouy phase anomaly with an interferometer

The intensity variation of bright and dark fringes in Young's double slit experiment shows that a light beam propagating through the focus of a lens experiences a phase shift (called the Gouy phase shift [Gouy CR. Acad Sci Paris 1890;110:1251]) with respect to its plane wave counterpart. The additional phase change of π introduced on focusing the light beam and then further propagating it in one arm of the interferometer changes a bright fringe into a dark fringe and vice-versa. We have, thus, made direct visualization of the Gouy phase shift by a simple experiment.     

Gouy phase compensation in quasi-phase matching

In any focussed nonlinear interaction the focus induced phase shift, known as the Gouy phase shift, provides an imperfection in phase matching for any linearly invariant material. However, using an appropriately designed quasi-phase matched structure it is theoretically possible to compensate for the deleterious effects of the Gouy phase shift, allowing a symmetric frequency response and tighter optimal focussing than in a uniform material.     

Gouy phase and visibility in the double-slit experiment

We study a matter wave double-slit experiment with unequal aperture widths in order to evaluate the effect of the Gouy phase on the visibility/predictability. While the predictability changes as one increases the width of one of the slits, the visibility receives a contribution from the Gouy phase at a specific point in the detection screen. Consequently such apparatus constitutes a simple device for measuring the Gouy phase of matter waves. We illustrate it numerically for neutrons.     

Propagation of optical vortex solitons due to the Gouy phase in strongly nonlocal nonlinear media

In this paper,we present a study on the propagation of the symmetrical optical vortices formed by two collinear Laguerre-Gauss solitons in strongly nonlocal nonlinear media.The optical vortices,which move along the beam axis as the light propagates,result in a rotation of the beam’s transverse profile.This physical reason of the rotation is the Gouy phase acquired by the component beams.     

超连续谱干涉方法测量古依相移

利用两束超连续光干涉得到的信号,测量了透镜焦点附近飞秒激光脉冲的古依(Gouy)相移。根据得到的光谱干涉信号,利用傅里叶变换得到相对相位值。激光光束在聚焦透镜后的束腰半径可以由成像方法测得。根据测量得到的激光光束束腰半径,用非线性拟合的方法得到了古依相移曲线,拟合曲线与实验结果符合得非常好。给出了古依相位在焦点前后1 mm区域内的移动量。     

强非局域介质中基于古依相位的旋转涡旋光孤子

利用强非局域非线性介质中傍轴光束传输的修正Snyder-Mitchell模型讨论了两束共线(即光束中心和传输方向都相同)拉盖尔-高斯型光孤子(CLGS)构成的涡旋光孤子传输过程。在一定条件下,涡旋光束在传输过程中,光束截面光斑发生旋转现象,但光束的束宽保持不变,称之为旋转涡旋光孤子。涡旋光孤子旋转的现象可以通过叠加光场中的古依相位来解释。结果展现了几个旋转涡旋光孤子在传输过程中的旋转现象和强非局域介质中多环形旋转涡旋光孤子的传输。     

光束在左手材料中的强度和相位旋转特性

建立了左手材料中拉盖尔高斯光束传输模型,通过研究拉盖尔高斯光束的相位分布来分析光束的强度旋转特性。具体分析了光束参数模式、Gouy相、频率和色散对光束强度和相位旋转特性的影响。研究发现:方位角相差是导致光束强度旋转的主要原因;负折射率引起的逆的Gouy相移将会导致光束强度反转;在正常色散区左手材料中光束的强度和相位旋转方向是相同的,而在反常色散区,左手材料中光束的强度和相位旋转方向是相反的。     

Sufficient Condition for Validity of Quantum Adiabatic Theorem

In this paper,we attempt to give a sufficient condition of guaranteeing the validity of the proof of the quantum adiabatic theorem.The new sufficient condition can clearly remove the inconsistency and the counterexample of the quantum adiabatic theorem pointed out by Marzlin and Sanders.     

计算电容中Fabry-Perot干涉仪测量位移的相位修正方法

计算电容是复现电学阻抗单位的基准装置, 利用计算电容值和量子霍尔电阻值可以准确计算出精细结构常数α. 计算电容的本质是通过高准确度地测量屏蔽电极的位移, 实现对电容量值的测量. 因此, 基于Fabry-Perot干涉仪的精密电极位移测量系统是计算电容装置中最为核心和关键的部分. 在Fabry-Perot干涉仪测位移过程中, 由于高斯激光束存在轴向Gouy相位, 该附加相位将会引起相邻干涉条纹对应位移的变化(大于或者小于λ/2), 导致位移的测量值与实际值存在偏差. 本文阐述了高斯激光场的传播特性, 利用高斯激光束在自由空间和透过薄透镜复振幅的变换关系, 建立了计算电容装置中Fabry-Perot干涉仪透射光束的传输模型; 通过对不同腔长的Fabry-Perot干涉仪透射光场相位的分析, 获得了高斯激光束轴向Gouy相位修正与传输距离的关系. 结果表明, 当腔长从111.3 mm移动至316.3 mm时, 在接收距离为560 mm的情况下, 高斯光束轴向Gouy 相位引起的位移修正的绝对值最小为0.7 nm, 其相对相位修正量|δL|/|ΔL| = 3.4×10^-9.     

Phase anomaly and phase singularities of the field in the focal region of high-numerical aperture systems

The phase behavior of the three Cartesian components of the electric field in the focal region of a high-numerical aperture focusing system is studied. The Gouy phase anomaly and the occurence of phase singularities are examined in detail. It is found that the three field components exhibit different behaviors.     

菲涅耳衍射公式误差相位的讨论

根据波动光学的理论,对菲涅耳近场衍射公式误差相位的影响进行了分析。以单缝衍射为例,讨论了误差相位与计算精度的联系。结合菲涅耳线波带片焦面光强分布的计算,对比了菲涅耳衍射公式与基尔霍夫衍射公式的计算结果,说明在不满足误差相位近似条件下使用菲涅耳衍射公式带来的影响。最后对影响波带片焦面光强分布的几个因素进行了讨论。     

Array illumination with minimal non-uniformity based on generalized phase contrast

The generalized phase contrast method (GPC) has been previously shown to be an efficient technique for generating array illumination and is thus highly suitable for such applications as dynamic multiple beam trapping and optical micromanipulation. However, projected arrays usually exhibit intensity roll-offs that may be undesirable for some applications. We show that the uniformity of GPC-generated array illuminations can be improved using intuitive corrections to the input spatial phase modulation, by increasing or decreasing it to respectively raise or lower the intensity of the corresponding output spots to improve uniformity. This is combined with matching corrections to the phase shift introduced by the phase contrast filter. Results from numerical experiments show that the array illumination uniformity error improves from over 40% to less than 1% while maintaining the efficiency prior to implementing corrections.     

Polarization phase shifting in digital holographic microscopy

In the present work we have made use of polarization phase shifting in digital holographic microscopy (DHM) for three dimensional phase profiling of transmissive and reflecting microscopic samples. The Mach–Zehnder arrangement with proper polarizing elements (polarizer-masked cube beam splitter, quarter wave plate and a linear polarizer) is used for recording the phase-shifted digital holograms. The suggested procedure is simple and accurate and obviates the need of piezo devices for phase shifting. The phase profile of the specimen is reconstructed from the holograms by using standard phase shifting algorithms.     

In-line phase contrast for weakly absorbing materials with a microfocus x-ray source

For weakly absorbing materials, image contrast can be enhanced by phase contrast in formation. The effectiveness of the in-line phase contrast technique relies on its ability to record intensity data which contain information on the x-ray's phase shift. Four kinds of approaches to the relationship between intensity distribution and phase shift are reviewed and discussed. A micro-focal x-ray source with high geometrical magnification is used to acquire phase contrast images. A great improvement on image quality is shown and geometrical parameters are modified for comparison between different imaging positions.     

X射线菲涅耳波带板成像和投影式相衬成像的数值模拟比较

通过解析分析和数值模拟,比较了钛K线（4.5 keV）与铜K线（8.0 keV）等X射线源背光透视物体情况下,菲涅耳波带板直接成像与投影式相衬成像对被透视物体的空间分辨能力。结果表明,波带板成像可实现优于1 m的高空间分辨能力,而且使用较大尺度背光源更有利于成像。对于高透射或弱吸收的透视物体,波带板难以成像,可采用投影式相衬成像实现m级空间分辨。计入了以前文献没有考虑到的更高阶影响后,解析给出了点光源照射下相衬像的强度分布与对比度。模拟了微焦点X射线源照射存在厚度起伏的薄膜靶以及密度空间调制靶的相衬成像,点光源情况下模拟结果和解析结果相符。讨论了光源大小、成像距离等参数对相衬成像对比度和空间分辨能力的影响,结果表明,通过减小光源尺度和调节物体到探测面的距离,空间分辨能力可优化到1～4 m。     

Pruning-induced phase transition observed by a scattering method

In hyperbolic systems, transient chaos is associated with an underlying chaotic saddle in phase space. The structure of the chaotic saddle of a class of piecewise linear, area-preserving, two-dimensional maps with overall constant Lyapunov exponents has been observed by a scattering method. The free energy obtained in this way displays a phase transition at <0 in spite of the fact that no phase transition occurs in the free energy dedcued from the spectrum of Lyapunov exponents. This is possible because pruning introduces a second effective scaling exponent by creating, at each level of the approximation, particular small pieces in the incomplete Cantor set approximating the saddle. The second scaling arises for a subset of values of the control parameter that is dense in the parameter interval.     

Maps of intervals with indifferent fixed points: Thermodynamic formalism and phase transitions

We develop the thermodynamic formalism for a large class of maps of the interval with indifferent fixed points. For such systems the formalism yields onedimensional systems with many-body infinite-range interactions for which the thermodynamics is well defined but Gibbs states are not. (Piecewise linear systems of this kind yield the soluble, in a sense, Fisher models.) We prove that such systems exhibit phase transitions, the order of which depends on the behavior at the indifferent fixed points. We obtain the critical exponent describing the singularity of the pressure and analyze the decay of correlations of the equilibrium states at all temperatures. Our technique relies on establishing and exploiting a relation between the transfer operators of the original map and its suitable (expanding) induced version. The technique allows one also to obtain a version of the Bowen-Ruelle formula for the Hausdorff dimension of repellers for maps with indifferent fixed points, and to generalize Fisher results to some nonsoluble models.Meyerhoff Visiting Professor, on leave from the Center for Transport Theory and Mathematical Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061.     

Superpositions of multifractals: Generators of phase transitions in the generalized thermodynamic formalism

We investigate the superposition of multifractals in the generalized thermodynamic formalism. It is shown analytically that phase transitions of first and second order are obtained and that the topology of the corresponding critical lines endows bicritical behavior. We demonstrate that these phase transitions can be observed in the spectrum of fractal dimensions and in the spectra of related quantities. Therefore, the obtained results are of importance for the interpretation of experimental systems.