Ultra-sensitive measurement of transverse displacements with linear photonic gears

Engineering quantum states from a spatially structured quantum eraser

Quantum interference is a central resource in many quantum-enhanced tasks, from computation to communication. While usually occurring between identical photons, it can also be enabled by performing projective measurements that render the photons indistinguishable, a process known as quantum erasing. Structured light forms another hallmark of photonics, achieved by manipulating the degrees of freedom of light, and enables a multitude of applications in both classical and quantum regimes. By combining these ideas, we design and experimentally demonstrate a simple and robust scheme that tailors quantum interference to engineer photonic states with spatially structured coalescence along the transverse profile, a type of quantum mode with no classical counterpart. To achieve this, we locally tune the distinguishability of a photon pair by spatially structuring the polarization and creating a structured quantum eraser. We believe that these spatially engineered multiphoton quantum states may be of significance in fields such as quantum metrology, microscopy, and communication.

Nanoradian-scale precision in light rotation measurement via indefinite quantum dynamics

The manipulation and metrology of light beams are pivotal for optical science and applications. In particular, achieving ultrahigh precision in the measurement of light beam rotations has been a long-standing challenge. Instead of using quantum probes like entangled photons, we address this challenge by incorporating a quantum strategy called "indefinite time direction" into the parameterizing process of quantum parameter estimation. Leveraging this quantum property of the parameterizing dynamics allows us to maximize the utilization of orbital angular momentum resources for measuring ultrasmall angular rotations of beam profile. Notably, a nanoradian-scale precision of light rotation measurement is lastly achieved in the experiment, which is the highest precision by far to our best knowledge. Furthermore, this scheme holds promise in various optical applications due to the diverse range of manipulable resources offered by photons.

Measuring the Tensorial Flow of Mosaic Vector Beams in Disordered Media

Optical beams with nonuniform polarization offer enhanced capabilities for information transmission, boasting increased capacity, security, and resilience. These beams possess vectorial features that are spatially organized within localized three-dimensional regions, forming tensors that can be harnessed across a spectrum of applications spanning quantum physics, imaging, and machine learning. However, when subjected to the effect of the transmission channel, the tensorial propagation leads to a loss of data integrity due to the entanglement of spatial and polarization degrees of freedom. The challenge of quantifying this spatial-polarization coupling poses a significant obstacle to the utilization of vector beams in turbulent environments, multimode fibers, and disordered media. Here, we introduce and experimentally investigate mosaic vector beams, which consist of localized polarization tesserae that propagate in parallel, demonstrating accurate measurement of their behavior as they traverse strongly disordered channels and decoding their polarization structure in single-shot experiments. The resultant transmission tensor empowers polarization-based optical communication and imaging in complex media. These findings also hold promise for photonic machine learning, where the engineering of tensorial flow can enable optical computing with high throughput.

Structured-Light 3D Imaging Based on Vector Iterative Fourier Transform Algorithm

Quasi-continuous-phase metasurfaces overcome the side effects imposed by high-order diffraction on imaging and can impart optical parameters such as amplitude, phase, polarization, and frequency to incident light at sub-wavelength scales with high efficiency. Structured-light three-dimensional (3D) imaging is a hot topic in the field of 3D imaging because of its advantages of low computation cost, high imaging accuracy, fast imaging speed, and cost-effectiveness. Structured-light 3D imaging requires uniform diffractive optical elements (DOEs), which could be realized by quasi-continuous-phase metasurfaces. In this paper, we design a quasi-continuous-phase metasurface beam splitter through a vector iterative Fourier transform algorithm and utilize this device to realize structured-light 3D imaging of a target object with subsequent target reconstruction. A structured-light 3D imaging system is then experimentally implemented by combining the fabricated quasi-continuous-phase metasurface illuminated by the vertical-cavity surface-emitting laser and a binocular recognition system, which eventually provides a new technological path for the 3D imaging field.

Optical ranging and vibration sensing based on the lagging propagation phase of structured beams

Recently, studies have shown that the spatial confinement on waves or photons with beam shaping techniques would modify the propagation speed of optical fields including both group and phase velocities. Particularly, for the monochromatic spatially structured beams, the reduced longitudinal wave vector enables the phase velocity to be superluminal, causing a lagging propagation phase. In this Letter, we propose a novel, to the best of our knowledge, scheme for optical ranging and vibration sensing with the lagging propagation phase of structured beams. We experimentally demonstrate the extraction of displacement from the rotating angles of interfering fringes of superposed Gaussian and higher-order Bessel beams with lagging propagation phase difference. The measuring range is 0.2 m with the limitation of the tested moving stage, but it can be extended to tens of meters in principle. The measuring resolution can reach sub-millimeters, which can be further improved by carefully designing the probe beam and using a finer camera. The results may provide potential applications in position sensing and monitoring.

Full Spatial Characterization of Entangled Structured Photons

Vector modes are fully polarized modes of light with spatially varying polarization distributions, and they have found widespread use in numerous applications such as microscopy, metrology, optical trapping, nanophotonics, and communications. The entanglement of such modes has attracted significant interest, and it has been shown to have tremendous potential in expanding existing applications and enabling new ones. However, due to the complex spatially varying polarization structure of entangled vector modes (EVMs), a complete entanglement characterization of these modes remains challenging and time consuming. Here, we have used a time-tagging event camera to demonstrate the ability to completely characterize the entanglement of EVMs. Leveraging the camera's capacity to provide independent measurements for each pixel, we simultaneously characterize the entanglement of approximately 2.6×10^{6} modes between a bipartite EVM through measuring only 16 observables in polarization. We reveal that EVMs can naturally generate various polarization-entangled Bell states. This achievement is an important milestone in high-dimensional entanglement characterization of structured light, and it could significantly impact the implementation of related quantum technologies. The potential applications of this technique are extensive, and it could pave the way for advancements in quantum communication, quantum imaging, and other areas where structured entangled photons play a crucial role.

High-precision two-dimensional displacement metrology based on matrix metasurface

A long-range, high-precision, and compact transverse displacement metrology is of crucial importance in both industries and scientific researches. However, it is a great challenge to measure arbitrary two-dimensional (2D) displacement with angstrom-level precision and hundred-micrometer range. Here, we demonstrated a prototype of high-precision 2D-displacement metrology with matrix metasurface. Light passing through the metasurface is diffracted into three beams in horizontal (H), vertical (V), and diagonal (D) linear polarization. 2D transverse displacement of the metasurface relative to the incident light beam is retrieved from the interferential optical powers arisen from coherent superposition between H-polarized and D-polarized beams or V-polarized and D-polarized beams. We experimentally demonstrate that arbitrary displacement in 2D plane can be determined with high precision down to 0.3 nm in a large range of 200 micrometers. Our work broadens the application scope of metasurface and paves the way for development of ultrasensitive optical 2D displacement metrology.

High-precision laser beam lateral displacement measurement based on differential wavefront sensing

Accurately lateral displacement measurement is essential for a vast of non-contact sensing technologies. Here, we introduce a high-precision lateral displacement measurement method based on differential wavefront sensing (DWS). Compared to the conventional differential power sensing (DPS) method, the DWS method based on phase readout has the potential to achieve a higher resolution. The beam lateral displacement can be obtained by the curvature distribution of the wavefront on the surface of the detector. According to the theoretical model of the DWS method, the sensitivity of the lateral displacement can be greatly improved by increasing the wavefront curvature of the measured laser beam by means of lenses. An optical system for measuring the lateral displacement of the laser beam is built and calibrated by a high-precision hexapod. The experimental results show that the DWS-based lateral displacement measurement achieves a resolution of 40 pm/Hz1/2 (at 1-10 Hz) with a linear range of about 40 µm, which is consistent with the theoretical model. This technique can be applied to high-precision multi-degree-of-freedom interferometers.

Measuring picometre-level displacements using speckle patterns produced by an integrating sphere

As the fields of optical microscopy, semiconductor technology and fundamental science increasingly aim for precision at or below the nanoscale, there is a burgeoning demand for sub-nanometric displacement and position sensing. We show that the speckle patterns produced by multiple reflections of light inside an integrating sphere provide an exceptionally sensitive probe of displacement. We use an integrating sphere split into two independent hemispheres, one of which is free to move in any given direction. The relative motion of the two hemispheres produces a change in the speckle pattern from which we can analytically infer the amplitude of the displacement. The method allows a noise floor of 5 pm/[Formula: see text] ([Formula: see text]) above 30 Hz in a facile implementation, which we use to measure oscillations of 17 pm amplitude ([Formula: see text]) with a signal to noise ratio of 3.

High-precision micro-displacement sensing based on an optical filter and optoelectronic oscillators

High-precision micro-displacement sensing based on an optical filter and optoelectronic oscillators (OEOs) is proposed and experimentally demonstrated. In this scheme, an optical filter is utilized to separate the carriers of the measurement and reference OEO loops. Through the optical filter, the common path structure can be consequently achieved. The two OEO loops share all optical/electrical components, except for the micro-displacement to be measured. Measurement and reference OEOs are alternately oscillated by using a magneto-optic switch. Therefore, self-calibration is achieved without additional cavity length control circuits, greatly simplifying the system. A theoretical analysis of the system is developed, and this analysis is then demonstrated with experiments. Regarding the micro-displacement measurements, we achieved a sensitivity of 312.058 kHz/mm and a measurement resolution of 356 pm. The measurement precision is less than 130 nm over a measurement range of 19 mm.

Ultrasensitive and long-range transverse displacement metrology with polarization-encoded metasurface

A long-range, high-precision, and compact transverse displacement metrology method is of crucial importance in many research areas. Recent schemes using optical antennas are limited in efficiency and the range of measurement due to the small size of the antenna. Here, we demonstrated the first prototype polarization-encoded metasurface for ultrasensitive long-range transverse displacement metrology. The transverse displacement of the metasurface is encoded into the polarization direction of the outgoing light via the Pancharatnam-Berry phase, which can be read out directly according to the Malus law. We experimentally demonstrate nanometer displacement resolution with the uncertainty on the order of 100 picometers for a large measurement range of 200 micrometers with the total area of the metasurface being within 900 micrometers by 900 micrometers. The measurement range can be extended further using a larger metasurface. Our work opens new avenues of applying metasurfaces in the field of ultrasensitive optical transverse displacement metrology.