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 shift for few-cycle laser pulses

We measured for the first time the influence of the Gouy effect on focused few-cycle laser pulses. The carrier-envelope phase is shown to undergo a smooth variation over a few Rayleigh distances. This result is of critical importance for any application of ultrashort laser pulses, including high-harmonic and attosecond pulse generation, as well as phase-dependent effects.     

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.     

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.     

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.     

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.     

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.     

Heavy-ion scattering at low energies: First-order correction to the eikonal phase shift

The first-order non-eikonal correction has been applied to calculate heavy-ion reaction cross sections at low energies. The numerical investigations show that, for many heavy-ion systems, reaction cross sections and elastic scattering angular distributions thus calculated, are in good agreement with the optical model calculations.     

The Gouy phase of Airy beams

The phase behavior of Airy beams is studied, and their Gouy phase is defined. Analytic expressions for the idealized, infinite-energy type beam are derived. They are shown to be excellent approximations for finite-energy beams generated under typical experimental conditions.     

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.     

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.     

Focal transformation and the Gouy phase shift of converging one-cycle surface acoustic waves excited by femtosecond laser pulses

We studied the changes of the pulse shape and the phase of the spectral components in converging-surface acoustic wave pulses. These pulses were excited with a femtosecond laser by a thermoelastic mechanism. To produce converging acoustic pulses, the laser beam was focused with an axicon in a circle on the surface of an aluminum sample. During propagation through the focus, the shape of the pulses of the normal surface velocity changed from two to three polar. The absolute value of the phase of the spectral components experienced a change close to pi/2 rad (Gouy phase shift) after passage of the focal region. These observations were confirmed by analytical and numerical calculations based on the two-dimensional wave equation for surface acoustic waves.     

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 shift and temporal reshaping of focused single-cycle electromagnetic pulses

We discuss exact solutions of Maxwell's equations that describe the evolution of single-cycle electromagnetic pulses. The solutions are applied to recent observations of the diffraction transformation of terahertz pulses. In particular, we elucidate the role of the Gouy shift in the temporal reshaping and polarity reversals of single-cycle terahertz pulses.     

Tuning of ring laser by varying the Gouy phase

Tuning a ring laser by using the Gouy phase is explored. We find a sensitive capability by moving a lens in the ring cavity. Application of the effect to ring laser gyro is discussed.     

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.     

利用Gouy位相对丙酮分子反应分支比进行调控

在532 nm和177 nm双色激光场的作用下,实现了对丙酮分子电离解离产物产额的调制. 进一步,当激光焦点位置与分子束中心位置有一定偏离时,由于Gouy位相的影响,使得不同产物调制曲线之间产生位相差,实现了不同反应通道分支比的调控. 在不同激光焦点与分子束中心相对位置处测得的不同位相差与根据特定反应通道模型进行的理论预期符合的很好,从而说明了丙酮分子的反应控制机制为：532 nm三光子处发生解离产生乙酰基和甲基碎片被进一步电离,三光子处的激发态分子可以继续吸收两个基频光子而发生电离.     

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.     

Accurate Gouy phase measurement in an astigmatic optical cavity

We present measurements of the Gouy phase accumulation for the fundamental mode of an astigmatic Fabry–Perot cavity over 70?% of its stability range. The method is based on simultaneous measurement of the resonant frequencies of the fundamental mode and the $\text{TEM}_{11}$ Hermite–Gauss mode of the cavity. We achieve an uncertainty of $2.7\times 10^{-6}$ ?rad, which, in the context of displacement metrology, is sufficient to enable measurements over 50?mm with relative uncertainty below $10^{-10}$ .