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 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.     

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.     

复动量格林函数方法对n-α散射研究

在复动量表象下引入格林函数,建立了复动量格林函数方法.把这种方法应用于n-α散射系统,计算其散射相移.提取n-α系统的共振态并研究共振态对能级密度、相移和散射截面的贡献.在不引入任何非物理参数的前提下,离散化薛定谔积分方程得到束缚态、共振态和连续谱.通过分析散射态物理量可以更好地理解共振态以及非共振连续谱态.在n-α系统中的成功应用,证明了该方法的正确性.     

Generalized Bloch's theorem for viscous metamaterials: Dispersion and effective properties based on frequencies and wavenumbers that are simultaneously complex

It is common for dispersion curves of damped periodic materials to be based on real frequencies as a function of complex wavenumbers or, conversely, real wavenumbers as a function of complex frequencies. The former condition corresponds to harmonic wave motion where a driving frequency is prescribed and where attenuation due to dissipation takes place only in space alongside spatial attenuation due to Bragg scattering. The latter condition, on the other hand, relates to free wave motion admitting attenuation due to energy loss only in time while spatial attenuation due to Bragg scattering also takes place. Here, we develop an algorithm for 1D systems that provides dispersion curves for damped free wave motion based on frequencies and wavenumbers that are permitted to be simultaneously complex. This represents a generalized application of Bloch's theorem and produces a dispersion band structure that fully describes all attenuation mechanisms, in space and in time. The algorithm is applied to a viscously damped mass-in-mass metamaterial exhibiting local resonance. A frequency-dependent effective mass for this damped infinite chain is also obtained.     

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.     

In situ spatial mapping of Gouy phase slip for high-detail attosecond pump-probe measurements

Attosecond pump-probe experiments routinely utilize extreme ultraviolet (XUV) and IR fields, with relative phase being the variable parameter. However, the Gouy phase slip between the focused IR and XUV pulses inevitably leads to a certain amount of phase averaging and loss of accuracy. By using ion imaging, we establish a one-to-one mapping between the local phase slip and the spatial coordinates of the focal volume, thus performing in situ characterization of the Gouy phase of a complex beam and its role in ionization of He and Xe. We demonstrate that spatially discriminated ion imaging enhances the contrast of a phase-dependent XUV+IR ionization signal. We utilize our technique to unmask a weak ionization asymmetry, thus opening pathways for further high-precision attosecond studies.     

Thermodynamic geometry for a non-extensive ideal gas

A generalized entropy arising in the context of superstatistics is applied to an ideal gas. The curvature scalar associated to the thermodynamic space generated by this modified entropy is calculated using two formalisms of the geometric approach to thermodynamics. By means of the curvature/interaction hypothesis of the geometric approach to thermodynamic geometry it is found that as a consequence of considering a generalized statistics, an effective interaction arises but the interaction is not enough to generate a phase transition. This generalized entropy seems to be relevant in confinement or in systems with not so many degrees of freedom, so it could be interesting to use such entropies to characterize the thermodynamics of small systems.     

Fractional Gouy phase

In general, the total Gouy phase shift has the form n pi, where n need not be an integer. As a result of the Fourier transforming property of a lens, the Gouy phase is found to be related to the types of discontinuities at the upper or lower range of the pupil function Q(c) resulting from the asymptotic order of the Fourier transform. The sign of the Gouy phase is also related to the slope of the pupil function. The oscillations of the Gouy phase shift arise from the strength of the nondominant discontinuity.     

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.     

Variation of the carrier-envelope phase of few-cycle laser pulses owing to the Gouy phase: a solid-state-based measurement

The carrier-envelope phase of a laser pulse has recently become an important quantity in extreme nonlinear optics. Because of the topological Gouy phase, it changes while the pulse propagates through the focus of a lens. This variation is measured by a simple solid-state-based approach. The experimental results are analyzed by comparison with simple analytical model calculations.     

Generalization of the stabilization method for green functions and quantum resonances

The stabilization method provides an efficient approach to many problems in atomic and molecular dynamics. Real avoided crossings and smoothing techniques provide the relevant information to compute real density of states. The aim of this letter is to present an extension of the stabilization method that allows for a direct determination of full Green functions and resonance energies. The method is based on the use of optical potentials and perturbation theory. Real avoided crossings of the original stabilization method become complex and resonance energies appear to stabilize in the complex-energy plane. A numerical illustration is presented for a simple model of shape resonance. Accurate results are obtained with a small number of real square-integrable functions as in the original stabilization method. The computational efficiency of the approach and its generality are emphasized.     

Manifestation of the Gouy phase in vector-vortex beams

Experimental measurements of the twirl and changes in the anisotropy of the constant intensity ellipse, and the rotation of the polarization singular lemon pattern a generalized vector-vortex beam experiences around the two foci due to the converging and diverging conical waves and in between, are presented and interpreted as being due to the universal form of the Gouy phase, φ(G)=mπ/2.     

On the mass,width and coupling constants of the <Emphasis Type="Italic">f</Emphasis><Subscript><Emphasis Type="Italic">0</Emphasis></Subscript>(980)

Using the pole approach we determine the mass and width of the f ₀ (980); in particular, we analyze the possibility that two nearby poles are associated to it. We restrict our analysis to a neighborhood of the resonance, using data for the phase shift and inelasticity, and the invariant mass spectrum of the decays. The formalism we use is based on unitarity and a generalized ver sion of the Breit-Wigner parameterization. We find that a single pole describes the f ₀ (980), the precise position depending upon the data used. As a byproduct, values for the and coupling constants are obtained. Received: 6 June 2002 / Revised version: 21 October 2002 / Published online: 3 March 2003     

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.     

Complex resonance and complex-frequency spectroscopy

The response of a medium to radiation with a complex frequency corresponding to an exponential time decrease in the radiation amplitude has been analyzed. The effect of complex resonance has been demonstrated when the real and imaginary parts of the complex radiation frequency approach the real and imaginary parts of the complex frequency of damping natural oscillations of medium oscillators. In resonance itself, the absolute value of the refractive index is divergent and radiation is completely reflected from the medium boundary. It has been shown that scanning of not only the real part, but also the imaginary part of the probe radiation frequency expands the capabilities of spectroscopy and makes it possible to, e.g., distinguish resonances even with coinciding (real) frequencies and close (of the same order of magnitude) widths.     

On the solutions of the hypernetted chain equation inside the gas-liquid coexistence region

We present a detailed study of the solutions of the hypernetted chain integral equation inside the gas-liquid coexistence region for simple Lennard-Jones fluids. The study is performed by means of a hybrid Newton-Raphson algorithm extended to cope with complex solutions. In this way, we have unequivocally confirmed that the origin of the well-known HNC singular behavior inside the coexistence curve is linked to the onset of complex solutions. As density is increased starting from the vapor phase along isotherms inside the coexistence region, another singularity is encountered (very likely linked with the existence of a complex multiple solution point), and correlations start to diverge. Therefore, with the numerical approach here presented it is not feasible to join the liquid and vapor phases through an analytically continuous path of real and complex solutions. Finally, a study of the transition from the mean spherical approximation behavior (characterized by the presence of a spinodal divergence) to the peculiar hypernetted chain sort of singularity is also presented.     

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.     

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。