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。     

Imaging the Gouy phase shift in photonic jets with a wavefront sensor

A wavefront sensor is used as a direct observation tool to image the Gouy phase shift in photonic nanojets created by micrometer-sized dielectric spheres. The amplitude and phase distributions of light are found in good agreement with a rigorous electromagnetic computation. Interestingly the observed phase shift when travelling through the photonic jet is a combination of the awaited π Gouy shift and a phase shift induced by the bead refraction. Such direct spatial phase shift observation using wavefront sensors would find applications in microscopy, diffractive optics, optical trapping, and point spread function engineering.     

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。     

Focusing and phase compensation of paraxial beams by a left-handed material slab

On the basis of angular spectrum representation, a formalism describing paraxial beams propagating through an isotropic left-handed material (LHM) slab is presented. The treatment allows us to introduce the ideas of beam focusing and phase compensation by LHM slab. Because of the negative refractive index of LHM slab, the inverse Gouy phase shift and the negative Rayleigh length of paraxial Gaussian beam are proposed. It is shown that the phase difference caused by the Gouy phase shift in right-handed material (RHM) can be compensated by that caused by the inverse Gouy phase shift in LHM. If certain matching conditions are satisfied, the intensity and phase distributions at object plane can be completely reconstructed at the image plane.     

Physical origin of the Gouy phase shift

We show explicitly that the well-known Gouy phase shift of any focused beam originates from transverse spatial confinement, which, through the uncertainty principle, introduces a spread in the transverse momenta and hence a shift in the expectation value of the axial propagation constant. A general expression is given for the Gouy phase shift in terms of expectation values of the squares of the transverse momenta. Our result also explains the phase shift in front of the Kirchhoff diffraction integral.     

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.     

Generalized eikonal treatment of the Gouy phase shift

We use a generalized refractive index that includes diffraction effects to show that the Gouy phase shift can be seen as an intensity averaged optical path difference between the generalized eikonal and the geometrical eikonal. This approach generalizes previous treatments to include the effects of phase distortion and confirms the role of transverse spatial confinement in the Gouy shift.     

The Gouy phase shift of the highly focused radially polarized beam

The Gouy phase shift in the focal field of high-NA focused radially polarized beam has been investigated in detail. Analytical expression for the Gouy phase shift can be derived using tilted wave interpretation, which provides a reasonable prediction compared to vectorial diffraction numerical simulation. Using this method, irregular wave spacing in the vicinity of the focus can be revealed.     

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 for full-aperture spherical and cylindrical waves

We investigate the Gouy phase shift for full-aperture waves converging to a focal point from all directions in two and three dimensions. We find a simple interpretation for the Gouy phase in this situation and show that it has a dramatic effect on reshaping sharply localized pulses.     

负折射率平板透镜系统中的光束聚焦及相位补偿特性

利用平面角谱理论,建立厄米-高斯光束和拉盖尔-高斯光束在负折射率平板透镜系统中的傍轴传输模型,研究负折射率平板透镜中厄米-高斯光束和拉盖尔-高斯光束强度聚焦及相位补偿特性。结果发现:负折射率平板透镜产生的反向Gouy相移可以补偿空气中Gouy相移导致的相差,因而在满足相位匹配条件下,光束在物平面和像平面之间的相差为零;当强度聚焦和相位匹配条件同时满足的条件下,光束在物平面强度和相位分布可在像平面实现完全重构。     

Revisiting Gouy phase

The aim of this paper is to highlight the added value of the generalized Gouy phase shift introduced by Siegman. Although suited for optical systems study, including those more complex than free space, we note that it did not meet the use that it deserves so far. The analysis of the whole of the ideas and analytical approaches associated to the important concept of the Gouy phase proves its effectiveness.

Usually, the resonance condition is systematically built on the basis of the equivalent empty cavity. Unfortunately, this approach does not cover some of the useful parameters of the real resonator. By means of the generalized Gouy phase and the self-consistent complex parameter q, we derive here a new approach for the calculation of the resonance condition for the real cavity. Moreover, the use of the generalized Gouy phase clearly simplifies the study of resonators, while making it possible to avoid the use of the Huygens’ Fresnel integral.     

波动方程深度偏移的局部裂步Fourier传播算子

针对裂步Fourier传播算子在速度强横向变化介质中的不足,将算子的框架展开方法应用于Fourier传播算子中的相移算子,提出了一种波场传播的局部裂步Fourier传播算子,并把它应用于波动方程叠前深度偏移成像.这个局部裂步Fourier传播算子是由相空间(空间-波数)-频率域的相移算子和空间-频率域的窗口时移算子两部分组成.与波数-频率域的空间全局性相移算子不同,相空间-频率域的相移算子具有很好的空间局部性.通过在国际标准的SEG-EAGE二维盐丘模型的波动方程叠前深度偏移成像数值试验,证明局部Fourier传播算子不仅具有很好的稳定性,而且还特别适用于速度强横向变化介质.     

一种适于自适应光学的旋转软刀口波面传感器的研究

利用傅里叶光学理论,证明了一种新型波面传感器——旋转软刀口波面传感器的概念.在经典刀口法的刀口区,以渐变透过率代替突变透过率函数,在光瞳象面上可获得反映光瞳面位置待测波面位相梯度及位相梯度方向的调制信号.文中给出了实验结果和讨论.     

Phase-Space Analysis of Wavefront Coding Imaging Systems

We explore the use of the Radon-Wigner transform, which is associated with the fractional Fourier transform of the pupil function, for determining the point spread function （PSF） of an incoherent defocused optical system. Then we introduce these phase-space tools to analyse the wavefront coding imaging system. It is shown that the shape of the PSF for such a system is highly invariant to the defocus-related aberrations except for a lateral shift. The optical transfer function of this system is also investigated briefly from a new understanding of ambiguity function.     

The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields

One of the most poorly understood subjects in physical optics is the origin of the Gouy phase (sometimes called “the phase anomaly near focus”). This is evident from the large number of publications on the subject, many of which attribute it to quite different causes. In this paper we show that the Gouy phase anomaly can be clearly understood from elementary properties of normal congruences of light rays and from the relationship between geometrical optics and physical optics. We also show that the Gouy phase anomaly may be regarded as a degenerate case of a rapid π/2 phase change that is found to occur at each focal line of an astigmatic pencil of rays. The intensity distribution in the region of the phase changes is also presented. Furthermore, symmetry relations for both the phase anomaly and the intensity distribution are derived.     

Acceleration of femtosecond pulses to superluminal velocities by Gouy phase shift

The phase and the group velocities are calculated in a three-dimensional neighbourhood of the focus of an aberration-free lens illuminated by a spatially Gaussian beam. The Gouy phase shift caused by the diffraction results in superluminal pulse propagation on the optical axis within the Rayleigh range.     

Observing quantum correlation of photons in Laguerre-Gauss modes using the Gouy phase

The effect of the Gouy phase, which is one of the geometrical phases of photons, is observed through quantum correlation in Laguerre-Gaussian (LG) modes. In an experiment, the relative phase of two different LG modes of measurement basis states is manipulated via the Gouy phase, and the observed coincidence count rates agree well with theoretical predictions. This result suggests that the Gouy phase can be used as a new tool to manipulate multidimensional photonic quantum states.     

Comment on "Generation of 10(11) contrast 50 TW laser pulses"

We argue for a different physical interpretation of the results given in the recent Letter by Chvykov et al. [Opt. Lett.31, 1456 (2006)] in which a double nonlinear crystal scheme for cross-polarized wave generation is analyzed. We discuss the most important factors that explain the origin of the two-crystal scheme's increased efficiency, namely, the Kerr lensing effect and a Gouy phase shift. The position and orientation of the second crystal relative to the first one are unambiguously defined; related effects are illustrated by already published works on the subject.     

Optical transfer function analysis of circular-pupil wavefront coding systems with separable phase masks

This paper proposes a simple method to achieve the optical transfer function of a circular pupil wavefront coding system with a separable phase mask in Cartesian coordinates.Based on the stationary phase method,the optical transfer function of the circular pupil system can be easily obtained from the optical transfer function of the rectangular pupil system by modifying the cut-off frequency and the on-axial modulation transfer function.Finally,a system with a cubic phase mask is used as an example to illustrate the way to achieve the optical transfer function of the circular pupil system from the rectangular pupil system.