Gouy Phase Research Articles

Realization of multi-transverse-mode squeezed optical frequency combs with Gouy phase compensation

Multimode quantum light fields significantly enhance quantum state manipulation and communication capabilities by expanding the dimensionality of the Hilbert space. In this work, we elaborately design a non-horizontal cavity suitable for a Gouy phase-compensated synchronously pumped optical parametric oscillator. By injecting an optical frequency comb in HG10 mode into the cavity as the seed, we demonstrate the simultaneous generation of a bright squeezed optical frequency comb in HG10 mode and a vacuum squeezed optical frequency comb in HG01 mode. The coexistence of amplitude quadrature squeezed fields in these two orthogonal first-order Hermite-Gaussian transverse modes also suggest the presence of quadrature entanglement between the two first-order Laguerre-Gaussian modes, LG0 + 1 and LG0 - 1. This research underscores the capability of one-step generation of multi-transverse-mode squeezed optical frequency combs using a single cavity, marking a significant stride in the realm of quantum optics.

Transfer Matrix Method with Gouy Phase Shift correction applied to a High Numerical Aperture fiber-to-fiber optical coupling analysis

In this paper, we present the transmittance and reflectance study of the optical coupling between two High Numerical Aperture (HNA) fibers using a new model based on the Transfer Matrix Method (TMM). The TMM is corrected by the effects of the Gouy phase shift and the mode overlap is used in the material between the fibers to calculate the coupling loss. The coupling is also simulated using the Eigenmode Expansion (EME) method, and these numerical results are compared with experimental ones. The Gaussian beam nonparaxial field equations are used to evaluate the phase of the light in the coupling region and to obtain the effective refractive index of the wave between the fiber facets. Our TMM approach produced results close to experimental ones. Our model is, at least, two orders of magnitude faster than a commercial solver, and easy to coding; highlighting this approach’s importance as a transmittance/reflectance simulation tool.

Gouy Phase Induced Optical Skyrmion Transformation in Diffraction Limited Scale

AbstractOptical skyrmions are topologically stable quasiparticles that can be constructed with electric field, spin angular momentum, polarization Stokes vector, pseudospin, etc. In this letter, both theoretical and experimental studies are carried out to reveal the role of Gouy phase in the topology transformation during the tight focusing of Stokes skyrmions. The Stokes skyrmionic beam can be constructed by superposing two orthogonally polarized components with orthogonal spatial modes. The Gouy phase produced in the focused field depends on the orbital angular momentum carried by the high order mode component of the incident Stokes skyrmionic beam. While the beam size of the focused field is diffraction limited, the variation of the Stokes vectors in the skyrmion topology is in the sub‐diffraction limited scale. The presented results shed light on the understanding of the topology transformation between the incident and the tightly focused fields, paving the way for engineering the optical skyrmions in micro‐nano scale and their applications in information processing, quantum technology, metrology, etc.

Controllable helical collapse caused by a nonlinearity-related Gouy phase shift

Controllable helical collapse caused by a nonlinearity-related Gouy phase shift

Experimental Verification of the Gouy Phase for Higher-Order Hermite-Gaussian Beams

The Gouy phase is related to the axial phase shift experienced by any focused light beam with respect to a reference plane wave when passing through its focus. Generally, the Gouy phase ΦG for a higher-order Hermite-Gaussian (HG) beam is this for the fundamental Gaussian beam multiplied by a factor, which is the sum of the mode indices of the HG beam plus unity. Although this result is a paradigm in optics, we are not aware of its experimental verification. In this paper, we present experimental results obtained with a single-lens interferometer for higher-order HG modes generated using spatial light modulator. The retrieved Gouy phase ΦG is found in a very good quantitative agreement with the mentioned theoretical result.

Bessel–Bessel–Gaussian vortex laser beams

Abstract We obtain and investigate Bessel–Bessel–Gaussian vortex beams (BBG beams) with the complex amplitude being equal to a product of the Gaussian function with two Bessel functions, whose arguments are expressed as complicated radicals including the cylindrical coordinates and a free parameter that defines the shape of the intensity distribution. If this parameter is small, the intensity has the shape of an inhomogeneous ring. For larger values of this parameter, the intensity has the shape of two arcs or ‘crescents’, oriented by their concave sides to each other. The complex amplitude of such beams is derived in explicit form for an arbitrary distance from the waist. We demonstrate that the BBG beams rotate upon propagation anomalously fast: at a distance much shorter than the Rayleigh length, the intensity distribution is already rotated by almost 45°, whereas typically, the rotation angle of vortex Gaussian beams is equal to the Gouy phase. It is also shown that the parameter of the BBG beam allows controlling its topological charge (TC): when the parameter value is positive and increases, the beam TC also increases stepwise by an even number. Besides, we study two other similar vortex BBG beams: either with four local intensity maxima, lying on the Cartesian coordinates axes, or with one intensity maximum with a crescent shape, whose center is on the horizontal axis. The derived three new families of asymmetric vortex laser beams, whose complex amplitude is described by explicit analytical expressions at an arbitrary distance from the waist, extend the variety of laser beams that can be used for manipulating and rotating microparticles, free space data transmission, and in quantum informatics.

Ultrafast structured light through nonlinear frequency generation in an optical enhancement cavity.

The generation of shaped laser beams, or structured light, is of interest in a wide range of fields, from microscopy to fundamental physics. There are several ways to make shaped beams, most commonly using spatial light modulators comprised of pixels of liquid crystals. These methods have limitations on the wavelength, pulse duration, and average power that can be used. Here we present a method to generate shaped light that can be used at any wavelength from the UV to IR, on ultrafast pulses, and a large range of optical powers. By exploiting the frequency difference between higher-order modes, a result of the Gouy phase, and cavity mode matching, we can selectively couple into a variety of pure and composite higher-order modes. Optical cavities are used as a spatial filter and then combined with sum-frequency generation in a nonlinear crystal as the output coupler to the cavity to create ultrafast, frequency comb structured light.

Generating Optical Vortex Array Laser Beams of Superimposing Hermite–Gaussian Beams with a Dual–Phase Modulation Digital Laser System

This study presents an efficient and practical intra-cavity approach for selectively generating vortex array laser beams employing a dual-phase modulation digital laser system, which has not yet been completed in single-phase modulation digital laser. The stable optical vortex array laser beams were formed by superimposing cavity Hermite–Gaussian (HG) eigenmodes. In particular, when the selected cavity HG modes shared the same Gouy phase, the resulting optical vortex beam could preserve its light field pattern, thereby maintaining the optical vortex properties in the near and far fields. Numerical results demonstrated that employing dual-phase modulation could establish optimal boundary conditions for the selection of HG modes within the cavity, successfully generating various vortex array laser beams. The experimental validation of the proposed method confirmed the ability to select optical vortex array lasers solely by controlling the loaded phase of the dual-phase modulation digital laser. These results demonstrate the ability of digital lasers to generate and dynamically control optical vortex array lasers.

Gouy phase and quantum interference with cross-Wigner functions for matter-waves

The Gouy phase is essential for accurately describing various wave phenomena, ranging from classical electromagnetic waves to matter waves and quantum optics. In this work, we employ phase-space methods based on the cross-Wigner transformation to analyze spatial and temporal interference in the evolution of matter waves characterized initially by a correlated Gaussian wave packet. First, we consider the cross-Wigner of the initial wave function with its free evolution, and second for the evolution through a double-slit arrangement. Different from the wave function which acquires a global Gouy phase, we find that the cross-Wigner acquires a Gouy phase difference due to different evolution times. The results suggest that temporal like-Gouy phase difference is important for an accurate description of temporal interference. Furthermore, we propose a technique based on the Wigner function to reconstruct the cross-Wigner from the spatial intensity interference term in a double-slit experiment with matter waves.

Generation of Propagation-Dependent OAM Self-Torque with Chirped Spiral Gratings

The application of non-uniform spiral gratings to control the structure, topological parameters and propagation of orbital angular momentum (OAM) beams was studied experimentally with coherent near-infrared light. Adapted digital spiral grating structures were programmed into the phase map of a high-resolution liquid-crystal-on-silicon spatial light modulator (LCoS-SLM). It is shown that characteristic spatio-spectral anomalies related to Gouy phase shift can be used as pointers to quantify rotational beam properties. Depending on the sign and gradient of spatially variable periods of chirped spiral gratings (CSGs), variations in rotation angle and angular velocity were measured as a function of the propagation distance. Propagation-dependent self-torque is introduced in analogy to known local self-torque phenomena of OAM beams as obtained by the superposition of temporally chirped or phase-modulated wavepackets. Applications in metrology, nonlinear optics or particle trapping are conceivable.

Strong-field photoelectron holography in the subcycle limit

Strong-field photoelectron holography is promising for the study of electron dynamics and structure in atoms and molecules, with superior spatiotemporal resolution compared to conventional electron and X-ray diffractometry. However, the application of strong-field photoelectron holography has been hindered by inter-cycle interference from multicycle fields. Here, we address this challenge by employing a near-single-cycle field to suppress the inter-cycle interference. We observed and separated two distinct holographic patterns for the first time. Our measurements allow us not only to identify the Gouy phase effect on electron wavepackets and holographic patterns but also to correctly extract the internuclear separation of the target molecule from the holographic pattern. Our work leads to a leap jump from theory to application in the field of strong-field photoelectron holography-based ultrafast imaging of molecular structures.

Design of optical telescopes for laser field wavefront reconstruction in gravitational-wave detectors

Pick-off beams in Interferometric Gravitational Wave Detectors are often used to derive information on the field circulating in the interferometer. In order to retrieve the wavefront of the field at some chosen location, an optical system has to be deployed so to image the desired field characteristics to an optical bench and ultimately to suitable sensors. In this paper, we detail the requirements in terms of Gouy Phase and ABCD matrix for such an optical system to provide the correct information. We show also that by designing the optical system with adequate Gouy Phase evolution, the same kind of transformation holds true not only for the fundamental Gaussian mode, but also for both even and odd Higher Order Modes (HOMs) of the main interferometer beam. This is important because these HOMs are excited by the aberrations of the optical elements in the interferometer, and carry the information one is interested to. Simulations with two tools (Finesse and Zemax OpticsStudio®) are provided to confirm the analytical results obtained using Gaussian modes expansion of a generic field.

Temperature effects in narrow-linewidth optical cavity control with a surrogate quasi-second-harmonic field

Fabry–Perot cavities are widely used in precision interferometric applications. Various techniques have been developed to achieve the resonance condition via the direct interrogation of the cavity with the main laser field of interest. Some use cases, however, require a surrogate field for cavity control. In this study, we construct a bichromatic cavity to study the surrogate control approach, where the main and the surrogate fields are related by the second-harmonic generation with nonlinear optics. We experimentally verify the temperature dependence of the differential reflection phase of a dielectric coating design optimized for the surrogate control approach of the optical cavities of the light-shining-through-a-wall experiment Any Light Particle Search II and develop a comprehensive cavity model for quasi-second-harmonic resonances that considers also other important factors, such as the Gouy phase shift, for a detailed analysis of the surrogate control approach.

Gouy phase effects on photocurrents in plasmonic nanogaps driven by single-cycle pulses.

The investigation of optical phenomena in the strong-field regime requires few-cycle laser pulses at field strengths exceeding gigavolts per meter (GV/m). Surprisingly, such conditions can be reached by tightly focusing pJ-level pulses with nearly octave spanning optical bandwidth onto plasmonic nanostructures, exploiting the field-enhancement effect. In this situation, the Gouy phase of the focused beam can deviate significantly from the monochromatic scenario. Here, we study the effect of the Gouy phase of a pulse exploited to drive coherent strong-field photocurrents within a plasmonic gap nanoantenna. While the influence of the specific Gouy phase profile in the experiment approaches the monochromatic case closely, this scheme may be utilized to identify more intricate phase profiles at sub-diffraction scale. Our results pave the way for Gouy phase engineering at picojoule (pJ) pulse energy levels, enabling the optimization of strong-field optical phenomena.

Optimization of the reflection in the optical coupling between high numerical aperture fibers and photonic integrated circuits

The optical coupling in silicon Photonic Integrated Circuits (PICs) remains one of the main topics in the improvement of the performance of these devices. Highly demanding parameter specifications, such as loss, reflection, and bandwidth, drive the continuous search for optimization. The use of High Numerical Aperture Fibers (HNA fibers) to couple light in small diameter mode edge couplers, is one of the existing technologies that address the coupling challenge. We demonstrate, using Eigenmode Expansion (EME) and Transfer Matrix Method (TMM) simulations, that the Optical Return Loss (ORL) of this coupling approach can be made as low as −45 dB for both Transverse Electric (TE) and Transverse Magnetic (TM) polarizations, simultaneously. The results from our TMM model agree well with a commercial solver one and are faster (six orders of magnitude) and more computationally efficient. It is shown that the refractive index in the TMM should be corrected to compensate for the Gouy phase shift in the non-guided sections of the optical coupling. Additionally, the reflection pattern, as a function of the gap between the fiber and the PIC, provides a way to control the distance of the fiber to avoid packaging-related problems.

Peak positive pressure matters in acoustic droplet vaporization

We demonstrate the significance of the positive pressure component of an ultrasound wave in acoustic droplet vaporization. Theory and acoustic simulations reveal that the distorted compression part of the incoming wave, which includes a broad spectrum of frequencies above the fundamental, presents a pronounced shift in phase when focusing within the droplet and crossing the focal point. The extent of this so-called Gouy phase shift is sufficient to change the sign of the compression phase of the wave, actively creating a tension region in the droplet bulk in the same location where we experimentally observe vapor nucleation. A sign reversal of the rarefaction component of the ultrasound wave is, on the other hand, not expected. The extent of distortion of the incoming ultrasound wave can influence the occurrence of droplet vaporization, even at constant peak negative pressure, which may partially explain the broad range of vaporization threshold values reported in literature. The results suggest that vaporization can be achieved exploiting ultrasound waves with high peak positive pressures and reduced peak negative pressures.

Propagation properties of elegant modified Bessel Gaussian beams.

A kind of optical beam with a radially parabolic propagating manner and intensity decay inversely proportional to propagating distance in the far field is investigated. The initial complex amplitudes of this kind of beam have the form of a Gaussian function multiplied by a m/2-order modified Bessel function and a helical phase factor with topological charge m. The arguments for Bessel and Gauss parts in the propagating solutions of these beams are complex and symmetric as elegant Laguerre and Hermite Gaussian beams. As a result, the beams can be referred to as elegant modified Bessel Gauss (EMBG) beams. Similar to non-diffractive beams such as Bessel and Airy beams, the EMBG beams also carry infinite power due to a transversely slowly decaying tail of complex amplitude. The EMBG beams demonstrate intermediate propagating properties between non-diffractive and finite-power beams. Unlike non-diffractive beams that never spread their power and finite-power beams that always diverge in a linear manner and spread their power by inversely square law in the far field, the EMBG beams demonstrate a far-field parabolic propagating manner and decay their power by inversely linear law. In addition, the EMBG beams have total Gouy phase, which is only half of that of elegant Laguerre Gauss beams with the same topological charge, and have far-field intensity distributions regardless of the beam waist radius in the initial plane. The propagating and focusing properties of EMBG beams represent an intermediate status between the non-diffractive and finite-power beams.

Procedure for automated low uncertainty assessment of empty cavity mode frequencies in Fabry-Pérot cavity based refractometry.

A procedure for automated low uncertainty assessment of empty cavity mode frequencies in Fabry-Pérot cavity based refractometry that does not require access to laser frequency measuring instrumentation is presented. It requires a previously well-characterized system regarding mirror phase shifts, Gouy phase, and mode number, and is based on the fact that the assessed refractivity should not change when mode jumps take place. It is demonstrated that the procedure is capable of assessing mode frequencies with an uncertainty of 30 MHz, which, when assessing pressure of nitrogen, corresponds to an uncertainty of 0.3 mPa.

Three-dimensional nanoscale vortex line visualization and chiral nanostructure fabrication of tightly focused multi-vortex beams via direct laser writing

Optical singularity is pivotal in nature and has attracted wide interest from many disciplines nowadays, including optical communication, quantum optics, and biomedical imaging. Visualizing vortex lines formed by phase singularities and fabricating chiral nanostructures using the evolution of vortex lines are of great significance. In this paper, we introduce a promising method based on two-photon polymerization direct laser writing (2PP-DLW) to record the morphology of vortex lines generated by tightly focused multi-vortex beams (MVBs) at the nanoscale. Due to Gouy phase, the singularities of the MVBs rotate around the optical axis and move towards each other when approaching the focal plane. The propagation dynamics of vortex lines are recorded by 2PP-DLW, which explicitly exhibits the evolution of the phase singularities. Additionally, the MVBs are employed to fabricate stable three-dimensional chiral nanostructures due to the spiral-forward property of the vortex line. Because of the obvious chiral features of the manufactured nanostructures, a strong vortical dichroism is observed when excited by the light carrying orbital angular momentum. A number of applications can be envisioned with these chiral nanostructures, such as optical sensing, chiral separation, and information storage.

Lagging propagation phase of spatially structured beams

The structured beams especially with spatially varying phase distribution have attracted tremendous attention in both physics and engineering. Recently, studies have shown that the transverse spatial confinement of optical fields or photons leads to a modification of the group velocity but the phase velocity of propagating structured beams is revealed insufficiently in the experiments. In this work, we provide the theoretical model and experimental observation of propagation phase of structured beams. The analysis suggests that the spatially structured beams with a definite axial component of wavevector kr carry a so called “lagging propagation phase”, which can be considered as a generalized Gouy phase that originally appears within a focal region. Taking the higher-order Bessel beam as an example, the propagation phase difference is demonstrated by mapping to the rotating angle of intensity patterns superposed with different radial and angular phase gradients. Physically, the lagging propagation phase may provide an interpretation for the dynamic evolution of complex structured beams or interfering fringes upon propagation such as the vortex knots or braids. From the application aspect, the lagging propagation phase would facilitate a promising way for structured beams in optical sensing and metrology.