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This study theoretically and experimentally investigates the phase structure of radiation emitted from an elliptically polarized undulator. Analytic expressions for the emitted electromagnetic fields are fully derived and the radiation's phase structure is found to change according to polarization. When the polarization is circular, a helical structure is observed; however, when the polarization changes from circular to elliptical, a phase structure comprising several orbital angular momentum modes is observed. Herein, phase gradients of the undulator's radiation are measured using a double-slit interferometer. A sampling moiré method is used to accurately extract the phase difference on the transverse plane from the observed interference fringe. The measured phase gradients of the first and second harmonics reveal a similar change to the calculated results. However, under circular polarization, the change exhibited by the third harmonic is smaller than the calculated value. This phase gradient reduction is due to the split in phase singularities and is attributed to both the fluctuation in the undulator's peak magnetic fields and the radiation emitted from the entrance and exit of those magnetic fields.

The acoustic scattering of targets in shallow-sea waveguides exhibits complex features such as multipath propagation and intricate echo components, with its acoustic field properties remaining incompletely understood. This study employs a hybrid method combining normal modes and scattering functions to numerically model the acoustic scattering of targets in waveguide channels. We analyze the coupling mechanisms of multipath acoustic waves and derive precise predictive formulas for the bright–dark interference fringe patterns in range–frequency spectra based on the physical mechanisms governing acoustic field interference. By tracking the peak trajectories of these interference fringes in range–frequency spectra, we investigate the variations of the waveguide invariant with frequency, range, and depth, revealing statistical patterns of the waveguide invariant in target–waveguide coupled scattering fields under different water depths. The results demonstrate that, under constant channel conditions, waveguide properties exhibit a weak correlation with target material characteristics. In shallow water environments, waveguide invariant values display broader distributions with higher probability density peaks, whereas increasing water depth progressively narrows the distribution range and monotonically reduces the peak magnitudes of the probability density function. Experimental validation via scaled elastic target echo testing confirms the observed trends of waveguide invariant variation with water depth.

Phase shift plays a vital role in the analysis of interference and manipulation of polarization behavior in interferometric techniques. The Sagnac interferometer (SI) is initially studied due to its ability to withstand external environmental factors, including noise, temperature, and other interferences. However, the real impact of these factors is not demonstrated. To address this, comparative studies are conducted involving both mathematical theories, simulations, and physical experiments of Sagnac and Mach-Zehnder interferometers (MZI), both utilizing a phase shift. The purpose is to explore the SI advantages over the MZI in a series of experiments with both interferometers to validate the superior configuration. Numerical simulations of the total electric field are performed at the output of these interferometers. By adjusting the orientation of a half-wave plate from 45 and 135 degrees at a step of 90 degrees, the interference fringe pattern and respective signal are generated. These simulation parameters are then implemented experimentally, and the results from both approaches are carefully analyzed and compared. It is shown that the light reflection through the SI setup makes it more tolerant to noise compared to the MZI. Consequently, these results confirm that the image intensity and pixel level of the SI are higher than that of the MZI, potentially leading to greater brightness for the simplified image analysis.

Matter-wave interference experiments provide a direct confirmation of the quantum superposition principle, a hallmark of quantum theory, and thereby constrain possible modifications to quantum mechanics1. By increasing the mass of the interfering particles and the macroscopicity of the superposition2, more stringent bounds can be placed on modified quantum theories such as objective collapse models3. Here, we report interference of a molecular library of functionalized oligoporphyrins4 with masses beyond 25,000 Da and consisting of up to 2,000 atoms, by far the heaviest objects shown to exhibit matter-wave interference to date. We demonstrate quantum superposition of these massive particles by measuring interference fringes in a new 2-m-long Talbot–Lau interferometer that permits access to a wide range of particle masses with a large variety of internal states. The molecules in our study have de Broglie wavelengths down to 53 fm, five orders of magnitude smaller than the diameter of the molecules themselves. Our results show excellent agreement with quantum theory and cannot be explained classically. The interference fringes reach more than 90% of the expected visibility and the resulting macroscopicity value of 14.1 represents an order of magnitude increase over previous experiments2.

Free-electron lasers generate high-brilliance coherent radiation at wavelengths spanning from the infrared to the X-ray domains. The recent development of short-wavelength seeded free-electron lasers now allows for unprecedented levels of control on longitudinal coherence, opening new scientific avenues such as ultra-fast dynamics on complex systems and X-ray nonlinear optics. Although those devices rely on state-of-the-art large-scale accelerators, advancements on laser-plasma accelerators, which harness gigavolt-per-centimetre accelerating fields, showcase a promising technology as compact drivers for free-electron lasers. Using such footprint-reduced accelerators, exponential amplification of a shot-noise type of radiation in a self-amplified spontaneous emission configuration was recently achieved. However, employing this compact approach for the delivery of temporally coherent pulses in a controlled manner has remained a major challenge. Here we present the experimental demonstration of a laser-plasma accelerator-driven free-electron laser in a seeded configuration, where control over the radiation wavelength is accomplished. Furthermore, the appearance of interference fringes, resulting from the interaction between the phase-locked emitted radiation and the seed, confirms longitudinal coherence. Building on our scientific achievements, we anticipate a navigable pathway to extreme-ultraviolet wavelengths, paving the way towards smaller-scale free-electron lasers, unique tools for a multitude of applications in industry, laboratories and universities.Researchers demonstrate a laser-plasma accelerator-driven free-electron laser in a seeded configuration, where control over the radiation wavelength and longitudinal coherence are achieved.

The concept of gauge field is a cornerstone of modern physics and the synthetic gauge field has emerged as a new way to manipulate particles in many disciplines. In optics, several schemes of Abelian synthetic gauge fields have been proposed. Here, we introduce a new platform for realizing synthetic SU(2) non-Abelian gauge fields acting on two-dimensional optical waves in a wide class of anisotropic materials and discover novel phenomena. We show that a virtual non-Abelian Lorentz force arising from material anisotropy can induce light beams to travel along Zitterbewegung trajectories even in homogeneous media. We further design an optical non-Abelian Aharonov–Bohm system which results in the exotic spin density interference effect. We can extract the Wilson loop of an arbitrary closed optical path from a series of gauge fixed points in the interference fringes. Our scheme offers a new route to study SU(2) gauge field related physics using optics. In optics, schemes have been proposed to realize synthetic gauge fields, but are restricted to the Abelian type. Here, the authors demonstrate synthetic SU(2) non-Abelian gauge fields in anisotropic media, which allows the study of novel optical phenomena not found in Abelian synthetic gauge field systems.

Distance measurements are commonly performed by phase detection based on a lock-in strategy. Super-resolution fluorescence microscopy is still striving to perform axial localization but through entirely different strategies. Here we show that an illumination modulation approach can achieve nanometric axial localization precision without compromising the acquisition time, emitter density or lateral localization precision. The excitation pattern is obtained by shifting tilted interference fringes. The molecular localizations are performed by measuring the relative phase between each fluorophore response and the reference modulated excitation pattern. We designed a fast demodulation scheme compatible with the short emission duration of single emitters. This modulated localization microscopy offers a typical axial localization precision of 6.8 nm over the entire field of view and the axial capture range. Furthermore, the interfering pattern being robust to optical aberrations, a nearly uniform axial localization precision enables imaging of biological samples by up to several micrometres in depth.Adapting the amplitude-modulated light detection and ranging approach to super-resolution microscopy offers a typical axial localization precision of 6.8 nm over the entire field of view and the axial capture range, enabling imaging of biological samples by up to several micrometres in depth.

We report on a universal method to measure the genuine indistinguishability ofnphotons—a crucial parameter that determines the accuracy of optical quantum computing. Our approach relies on a low-depth cyclic multiport interferometer withN=2nmodes, leading to a quantum interference fringe whose visibility is a direct measurement of the genuinen-photon indistinguishability. We experimentally demonstrate this technique for an eight-mode integrated interferometer fabricated using femtosecond laser micromachining and four photons from a quantum dot single-photon source. We measure a four-photon indistinguishability up to0.81±0.03. This value decreases as we intentionally alter the photon pairwise indistinguishability. The low-depth and low-loss multiport interferometer design provides an original path to evaluate the genuine indistinguishability of resource states of increasing photon number.

Optical trapping in air of dielectric micro-spheres is reported using a dual fiber optical tweezers. The spheres are trapped on the interference fringes created by the two counter-propagating optical trapping beams. The use of polarization maintaining fibers allowed us to obtain very high and reproducible trapping efficiencies.

We introduce an axial localization with repetitive optical selective exposure (ROSE-Z) method for super-resolution imaging. By using an asymmetric optical scheme to generate interference fringes, a <2 nm axial localization precision was achieved with only ~3,000 photons, which is an approximately sixfold improvement compared to previous astigmatism methods. Nanoscale three-dimensional and two-color imaging was demonstrated, illustrating how this method achieves superior performance and facilitates the investigation of cellular nanostructures.ROSE-Z achieves axial interference through an asymmetrical optical scheme, yielding 2 nm axial localization precision with ~3,000 photons and a single objective, which offers improved multicolor three-dimensional localization microscopy for cellular structures.