Laguerre-Gaussian mode sorter

Interferometric focal planes

We propose arrays of integrated interferometers to characterize the mutual intensity on focal planes. While focal coherence measurement does not increase the aperture-limited spatial bandpass, it can increase Shannon information capacity relative to irradiance measurement by increasing the number of degrees of freedom per Nyquist sample. We describe a sampling model for interferometric measurement using arrays of 2-port Mach-Zehnder interferometers and show within this model that interferometric focal planes enable more accurate estimation of prototypical scene parameters.

Tsang's resolution enhancement method for imaging with focused illumination

A widely tested approach to overcoming the diffraction limit in microscopy without disturbing the sample relies on substituting widefield sample illumination with a structured light beam. This gives rise to confocal, image scanning, and structured illumination microscopy methods. On the other hand, as shown recently by Tsang and others, subdiffractional resolution at the detection end of the microscope can be achieved by replacing the intensity measurement in the image plane with spatial mode demultiplexing. In this work, we study the combined action of Tsang's method with image scanning. We experimentally demonstrate superior lateral resolution and enhanced image quality compared to either method alone. This result paves the way for integrating spatial demultiplexing into existing microscopes, contributing to further pushing the boundaries of optical resolution.

Sparse intensity sampling for ultrafast full-field reconstruction in low-dimensional photonic systems

Phase-sensitive measurements usually utilize interferometric techniques to retrieve the optical phase. However, when the feature space of an electromagnetic field is inherently low dimensional, most field parameters can be extracted from intensity measurements only. However, even the fastest of the previously published intensity-only methods have too high a computational complexity to be applicable at high data rates and, most importantly, require data from CCD cameras, which are generally slow. This paper shows how a few intensity measurements taken from properly placed photodetectors can be used to reconstruct the complex-valued field fully in systems with low-dimensional feature space. The presented method allows full-field characterization in few-mode fibers and does not employ a reference beam. This result is 3 orders of magnitude faster than the fastest previously published result and uses 3 orders of magnitude fewer photodetectors, allowing retrieval of mode amplitudes and phases relative to the fundamental mode using only several photodetectors. This approach enables ultrafast applications of intensity-only mode decomposition method, including pulse-to-pulse laser beam characterization, providing an essential tool for experimental exploration of the modal dynamics in spatiotemporal modelocked systems. It can also be applied to ultrafast sensing in few-mode fibers and for coherent mode division-multiplexed receivers using quadratic detectors only.

Broadband uniform-efficiency OAM-mode detector

The high-dimensional basis of orbital angular momentum (OAM) has several added and unique advantages for photonic quantum technologies compared to the polarization basis, which is only two-dimensional. However, one of the major roadblocks in implementing OAM-based applications with their full potentials is the absence of an ideal OAM-mode detector. Despite the plethora of efforts in the last three decades, currently, there is no OAM detector that can detect a broad OAM-mode spectrum, has uniform detection-efficiency over all the modes, measures the true spectrum, and works for an arbitrary quantum state without the need for any previous information. Here, we experimentally demonstrate just such an OAM detector. We report detection of pure and mixed OAM states with fidelities more than 98% and with measurement times of only a few minutes for dimensionalities up to 100. We expect our work to substantially boost the OAM-based photonic quantum technology efforts.

Three-dimensional Stacking of Phase Plates for Advanced Electron Beam Shaping

Tuneable phase plates for free electrons are a highly active area of research. However, their widespread implementation, similar to that of spatial light modulators in light optics, has been hindered by both conceptual and technical challenges. A specific technical challenge involves the need to minimize obstruction of the electron beam by supporting films and electrodes. Here, we describe numerical and analytical mathematical frameworks for three-dimensional stacks of phase plates that can be used to provide near-arbitrary electron beam shaping with minimal obstruction.

Orbital angular momentum coherent state beams

Paraxial propagation through isotropic, homogeneous, linear media exhibits invariance under rotations around the propagation axis, a symmetry described by the su(2) Lie algebra. We explore a family of paraxial beams that exploit this symmetry, constructed as linear superpositions of Laguerre-Gaussian beams (LGBs), serving as optical analogs of generalized SU(2) Lie group coherent states. A single complex parameter controls a smooth transition between Laguerre-Gaussian and Hermite-Gaussian beams (HGBs), producing intermediate beams that blend the characteristics of both families. Our beams exhibit propagation-invariant properties, up to a scaling factor, a highly desirable feature for optical applications. Experimental validation via digital holography demonstrates the practical feasibility of our approach.

Orbital angular momentum multiplexing holography based on multi-plane light conversion

Orbital angular momentum (OAM), with its unique orthogonality, is widely applied in optical holographic encryption and information storage. Theoretically, the topological charge of OAM holography is infinite. However, in practice, it is restricted by the Nyquist-Shannon sampling theorem and experimental equipment, resulting in a relatively small number of practically usable channels. We propose an OAM holography technique based on multi-plane light conversion (MPLC) to increase the number of multiplexed channels in OAM holography. In contrast to conventional OAM holographic designs, the present design employs a limited number of phase planes to achieve multi-channel coaxial OAM multiplexing holograms. In the experiment, we using four MPLC phase planes to reconstruct six coaxial OAM holograms, the peak signal-to-noise ratio (PSNR) value of the reconstructed holograms exceeds 20 dB, and the crosstalk between multiple modes is less than -19 dB. This mitigates the crosstalk problem of multiple images and provides what we believe to be a new way to realize large-capacity and high-quality optical holography encryption and information storage.

Automated discovery of experimental designs in super-resolution microscopy with XLuminA

Driven by human ingenuity and creativity, the discovery of super-resolution techniques, which circumvent the classical diffraction limit of light, represent a leap in optical microscopy. However, the vast space encompassing all possible experimental configurations suggests that some powerful concepts and techniques might have not been discovered yet, and might never be with a human-driven direct design approach. Thus, AI-based exploration techniques could provide enormous benefit, by exploring this space in a fast, unbiased way. We introduce XLuminA, an open-source computational framework developed using JAX, a high-performance computing library in Python. XLuminA offers enhanced computational speed enabled by JAX's accelerated linear algebra compiler (XLA), just-in-time compilation, and its seamlessly integrated automatic vectorization, automatic differentiation capabilities and GPU compatibility. XLuminA demonstrates a speed-up of 4 orders of magnitude compared to well-established numerical optimization methods. We showcase XLuminA's potential by re-discovering three foundational experiments in advanced microscopy, and identifying an unseen experimental blueprint featuring sub-diffraction imaging capabilities. This work constitutes an important step in AI-driven scientific discovery of new concepts in optics and advanced microscopy.

Optimization and realignment of OAM mode excitation in ring-core optical fibers using machine learning

Light beams carrying orbital angular momentum (OAM) in free space or within optical fibers have a wide range of applications in optics; however, exciting these modes with both high purity and low loss generally requires demanding optimization of excitation conditions in a high dimensional space. Furthermore, mechanical drift can significantly degrade the mode purity over time, which may limit practical deployment of OAM modes in concrete applications. Here, combining an iterative wavefront matching approach and a genetic algorithm, we demonstrate rapid and automated excitation of OAM modes with optimized purity and reduced loss. Our approach allows for systematic computational realignment of the system enabling drift compensation over extended durations. Our experimental results indicate that OAM purity can be optimized and maintained over periods exceeding 24 h, paving the way for the applications of stable OAM beams in optics.

Laser harmonic generation with independent control of frequency and orbital angular momentum

The non-linear optical process of laser harmonic generation (HG) enables the creation of high quality pulses of UV or even X-ray radiation, which have many potential uses at the frontiers of experimental science, ranging from lensless microscopy to ultrafast metrology and chiral science. Although many of the promising applications are enabled by generating harmonic modes with orbital angular momentum (OAM), independent control of the harmonic frequency and OAM level remains elusive. Here we show, through a theoretical approach, validated with 3D simulations, how unique 2-D harmonic progressions can be obtained, with both frequency and OAM level tuned independently, from tailored structured targets in both reflective and transmissive configurations. Through preferential selection of a subset of harmonic modes with a specific OAM value, a controlled frequency comb of circularly polarised harmonics can be produced. Our approach to describe HG, which simplifies both the theoretical predictions and the analysis of the harmonic spectrum, is directly applicable across the full range of HG mechanisms and can be readily applied to investigations of OAM harmonics in other processes, such as OAM cascades in Raman amplification, or the analysis of harmonic progressions in nonlinear optics.

Reaching the precision limit with tensor-based wavefront shaping

Perturbations in complex media, due to their own dynamical evolution or to external effects, are often seen as detrimental. Therefore, a common strategy, especially for telecommunication and imaging applications, is to limit the sensitivity to those perturbations in order to avoid them. Here, instead, we consider enhancing the interaction between light and perturbations to produce the largest change in the output intensity distribution. Our work hinges on the use of tensor-based techniques, presently at the forefront of machine learning explorations, to study intensity-based measurements where its quadratic relationship to the field prevents the use of standard matrix methods. With this tensor-based framework, we can identify the maximum-information intensity channel which maximizes the change in its output intensity distribution and the Fisher information encoded in it about a given perturbation. We further demonstrate experimentally its superiority for robust and precise sensing applications. Additionally, we derive the appropriate strategy to reach the precision limit for intensity-based measurements, leading to an increase in Fisher information by more than four orders of magnitude compared to the mean for random wavefronts when measured with the pixels of a camera.

Temporally and longitudinally tailored dynamic space-time wave packets

In general, space-time wave packets with correlations between transverse spatial fields and temporal frequency spectra can lead to unique spatiotemporal dynamics, thus enabling control of the instantaneous light properties. However, spatiotemporal dynamics generated in previous approaches manifest themselves at a given propagation distance yet are not arbitrarily tailored longitudinally. Here, we propose and demonstrate a new versatile class of judiciously synthesized wave packets whose spatiotemporal evolution can be arbitrarily engineered to take place at various predesigned distances along the longitudinal propagation path. Spatiotemporal synthesis is achieved by introducing a 2-dimensional spectrum comprising both temporal and longitudinal wavenumbers associated with specific transverse Bessel-Gaussian fields. The resulting spectra are then employed to produce wave packets evolving in both time and axial distance - in full accord with the theoretical analysis. In this respect, various light degrees of freedom can be independently manipulated, such as intensity, polarization, and transverse spatial distribution (e.g., orbital angular momentum). Through a temporal-longitudinal frequency comb spectrum, we simulate the synthesis of the aforementioned wave packet properties, indicating a decrease in relative error compared to the desired phenomena as more spectral components are incorporated. Additionally, we experimentally demonstrate tailorable spatiotemporal fields carrying time- and longitudinal-varying orbital angular momentum, such that the local topological charge evolves every ∼1 ps in the time domain and 10 cm axially. We believe our space-time wave packets can significantly expand the exploration of spatiotemporal dynamics in the longitudinal dimension. Such wave packets might potentially enable novel applications in light-matter interactions and nonlinear optics.

Coherent beam combining of optical vortices

We experimentally demonstrate the power scaling of optical vortices using the coherent beam combining technique, encompassing topological charges ranging from ℓ = 1 to ℓ = 5 realized on the basis of a Yb-doped fiber short-pulsed laser system. The combining efficiency varies from 83.2 to 96.9% depending on the topological charge and beam pattern quality generated by the spatial light modulators. This work is a proof of concept for using a coherent beam combining technique to surpass the physical power/energy limitation of any single source of optical vortices, regardless of the generation methods employed. These results open a pathway to power scaling of optical vortices with diverse applications in science and industry by utilizing advances in light-matter interactions.

Simultaneous generation of first- to fourth-order OAM modes based on a cascaded preset-twist long-period fiber grating

We propose and demonstrate the simulation and fabrication of an all-fiber orbital angular momentum (OAM) mode converter capable of generating first- to fourth-order modes simultaneously, which is realized by inscribing a cascaded preset-twist long-period fiber grating (CPT-LPFG) in a six-mode fiber utilizing a CO2 laser. A new segmented Runge-Kutta method is proposed to simulate the preset-twist long-period fiber gratings. By calculating the twist angle and relative coupling coefficient for each pitch and then solving the coupled mode equations utilizing the Runge-Kutta algorithm. The simulation illustrates that the preset-twist method significantly improves the coupling coefficient of higher-order modes, thereby reducing coupling difficulty. In the experiment, by twisting the fiber at an angle of 1080° and fabricating cascaded gratings with periods of 745 μm, 310 μm, 204 μm, and 146 μm, it is feasible to generate first- to fourth-order OAM modes simultaneously, at wavelengths of 1635 nm, 1548 nm, 1460 nm, and 1334 nm, respectively. The insertion loss is less than 1 dB, and the mode purity is over 90 %. To the best of our knowledge, this is the first time that first- to fourth-order OAM modes are simultaneously generated utilizing a single long-period fiber grating.

Enhancing multi-plane light conversion orbital angular momentum multiplexer performance via error analysis

We present what we believe to be a novel orbital angular momentum (OAM) multiplexing apparatus capable of handling topological charges ranging from l = 0 to ±3 through multi-plane light conversion (MPLC) across four phase planes. Nevertheless, the fabricating process of MPLC devices is prone to errors that cannot be avoided. Our investigation primarily delves into the repercussions of misalignment and etching inaccuracies on the device's phase, with the assistance of a spatial light modulator. The scrutiny of fabrication errors associated with the device offers valuable insights for refining the fabricating of MPLC devices. The OAM multiplexing device converts the phase of MPLC onto a glass substrate through four etching steps, corresponding to a depth of 0-775 nm. OAM multiplexing/demultiplexing crosstalk based on MPLC is less than -20 dB and -18 dB, respectively. The insertion loss of the OAM mode generated by the OAM multiplexing device coupled to the few-mode fiber is less than 7 dB. In a communication experiment, we demonstrated multiplexed three OAM channels carrying 10 Gbit/s OOK signals over a 5 km few-mode fiber using two MPLC devices. Both the bit error rate curve and constellation diagram demonstrate the excellent performance of MPLC-based OAM multiplexing devices in communication networks.

Spatiotemporal optical vortices with controllable radial and azimuthal quantum numbers

Optical spatiotemporal vortices with transverse photon orbital angular momentum (OAM) have recently become a focal point of research. In this work we theoretically and experimentally investigate optical spatiotemporal vortices with radial and azimuthal quantum numbers, known as spatiotemporal Laguerre-Gaussian (STLG) wavepackets. These 3D wavepackets exhibit phase singularities and cylinder-shaped edge dislocations, resulting in a multi-ring topology in its spatiotemporal profile. Unlike conventional ST optical vortices, STLG wavepackets with non-zero p and l values carry a composite transverse OAM consisting of two directionally opposite components. We further demonstrate mode conversion between an STLG wavepacket and an ST Hermite-Gaussian (STHG) wavepacket through the application of strong spatiotemporal astigmatism. The converted STHG wavepacket is de-coupled in intensity in space-time domain that can be utilized to implement the efficient and accurate recognition of ultrafast STLG wavepackets carried various p and l . This study may offer new insights into high-dimensional quantum information, photonic topology, and nonlinear optics, while promising potential applications in other wave phenomena such as acoustics and electron waves.

Memory-less scattering imaging with ultrafast convolutional optical neural networks

The optical memory effect in complex scattering media including turbid tissue and speckle layers has been a critical foundation for macroscopic and microscopic imaging methods. However, image reconstruction from strong scattering media without the optical memory effect has not been achieved. Here, we demonstrate image reconstruction through scattering layers where no optical memory effect exists, by developing a multistage convolutional optical neural network (ONN) integrated with multiple parallel kernels operating at the speed of light. Training this Fourier optics-based, parallel, one-step convolutional ONN with the strong scattering process for direct feature extraction, we achieve memory-less image reconstruction with a field of view enlarged by a factor up to 271. This device is dynamically reconfigurable for ultrafast multitask image reconstruction with a computational power of 1.57 peta-operations per second (POPS). Our achievement establishes an ultrafast and high energy-efficient optical machine learning platform for graphic processing.

Free-standing microscale photonic lantern spatial mode (De-)multiplexer fabricated using 3D nanoprinting

Photonic lantern (PL) spatial multiplexers show great promise for a range of applications, such as future high-capacity mode division multiplexing (MDM) optical communication networks and free-space optical communication. They enable efficient conversion between multiple single-mode (SM) sources and a multimode (MM) waveguide of the same dimension. PL multiplexers operate by facilitating adiabatic transitions between the SM arrayed space and the single MM space. However, current fabrication methods are forcing the size of these devices to multi-millimeters, making integration with micro-scale photonic systems quite challenging. The advent of 3D micro and nano printing techniques enables the fabrication of freestanding photonic structures with a high refractive index contrast (photopolymer-air). In this work we present the design, fabrication, and characterization of a 6-mode mixing, 375 µm long PL that enables the conversion between six single-mode inputs and a single six-mode waveguide. The PL was designed using a genetic algorithm based inverse design approach and fabricated directly on a 7-core fiber using a commercial two-photon polymerization-based 3D printer and a photopolymer. Although the waveguides exhibit high index contrast, low insertion loss (-2.6 dB), polarization dependent (-0.2 dB) and mode dependent loss (-4.4 dB) were measured.

Low-loss and compact photonic lantern based on a step-index double cladding fiber

The fulfilment of the adiabatic criterion is indispensable for the realization of a low-loss photonic lantern (PL), concurrently imposing a stringent restriction on the taper transition length of the PL. Here, by relaxing the adiabatic criterion, a low-loss and compact PL based on a step-index double cladding fiber (SI-DCF) is theoretically proposed and experimentally demonstrated. The use of SI-DCF can reduce the mode field diameter (MFD) expansion ratio during the tapering processing and greatly decrease the taper transition length required for adiabatic tapering. We initially evaluate the variation of both MFD and effective refractive index (RI) along the fiber tapering based on three types of fiber structures, including the modified standard single-mode fiber (SSMF), the graded-index fiber (GIF), and the proposed SI-DCF. In comparison with the commonly used fiber geometry, the SI-DCF can reduce the MFD expansion ratio from 77.73% to 38.81%, leading to more than half reduction of the tapering length for both 3-mode and 6-mode PLs. Then, two kinds of SI-DCF with different core diameters are fabricated to realize a 3-mode PL. The fabricated PL possesses a 1.5 cm tapering length and less than 0.2 dB insertion loss (IL). After splicing with the commercial few-mode fiber, the PL has an average IL of 0.6 dB and more than 13 dB LP11 mode purity over the C-band. Finally, a transfer matrix measurement indicates that the fabricated PLs have a mode coupling of less than -10 dB at 1550 nm.

Empowering high-dimensional optical fiber communications with integrated photonic processors

Mode-division multiplexing (MDM) in optical fibers enables multichannel capabilities for various applications, including data transmission, quantum networks, imaging, and sensing. However, high-dimensional optical fiber systems, usually necessity bulk-optics approaches for launching different orthogonal fiber modes into the optical fiber, and multiple-input multiple-output digital electronic signal processing at the receiver to undo the arbitrary mode scrambling introduced by coupling and transmission in a multi-mode fiber. Here we show that a high-dimensional optical fiber communication system can be implemented by a reconfigurable integrated photonic processor, featuring kernels of multichannel mode multiplexing transmitter and all-optical descrambling receiver. Effective mode management can be achieved through the configuration of the integrated optical mesh. Inter-chip MDM optical communications involving six spatial- and polarization modes was realized, despite the presence of unknown mode mixing and polarization rotation in the circular-core optical fiber. The proposed photonic integration approach holds promising prospects for future space-division multiplexing applications.

Ternary logic in the optical controlled-SWAP gate based on Laguerre-Gaussian modes of light

The need set by a computational industry to increase processing power, while simultaneously reducing the energy consumption of data centers, became a challenge for modern computational systems. In this work, we propose an optical communication solution, that could serve as a building block for future computing systems, due to its versatility. The solution arises from Landauer's principle and utilizes reversible logic, manifested as an optical logical gate with structured light, here represented as Laguerre-Gaussian modes. We introduced a phase-shift-based encoding technique and incorporated multi-valued logic in the form of a ternary numeral system to determine the similarity between two images through the free space communication protocol.

Nanostructure-based orbital angular momentum encryption and multiplexing

The orthogonality among the OAM modes provides a new degree of freedom for optical multiplexing communications. So far, traditional Dammann gratings and spatial light modulators (SLMs) have been widely used to generate OAM beams by modulating electromagnetic waves at each pixel. However, such architectures suffer from limitations in terms of having a resolution of only a few microns and the bulkiness of the entire optical system. With the rapid development of the electromagnetic theory and advanced nanofabrication methods, artificial nanostructures, especially optical metasurfaces, have been introduced which greatly shrink the size of OAM multiplexing devices while increasing the level of integration. This review focuses on the study of encryption, multiplexing and demultiplexing of OAM beams based on nanostructure platforms. After introducing the focusing characteristics of OAM beams, the interaction mechanism between OAM beams and nanostructures is discussed. The physical phenomena of helical dichroism response and spatial separation of OAM beams achieved through nanostructures, setting the stage for OAM encryption and multiplexing, are reviewed. Afterward, the further advancements and potential applications of nanophotonics-based OAM multiplexing are deliberated. Finally, the challenges of conventional design methods and dynamic tunable techniques for nanostructure-based OAM multiplexing technology are addressed.

Multi-dimensional cylindrical vector beam (de)multiplexing through cascaded wavelength- and polarization-sensitive metasurfaces

Cylindrical vector beams (CVBs) exhibit great potential for multiplexing communication, owing to their mode orthogonality and compatibility with conventional wavelength multiplexing techniques. However, the practical application of CVB multiplexing communication faces challenges due to the lack of effective spatial polarization manipulation technologies for (de)multiplexing multi-dimensional physical dimensions of CVBs. Herein, we introduce a wavelength- and polarization-sensitive cascaded phase modulation strategy that utilizes multiple coaxial metasurfaces for multi-dimensional modulation of CVBs. By leveraging the spin-dependent phase modulation mechanism, these metasurfaces enable the independent transformation of the two orthogonal polarization components of CVB modes. Combined with the wavelength sensitivity of Fresnel diffraction in progressive phase modulation, this approach establishes a high-dimensional mapping relationship among CVB modes, wavelengths, spatial positions, and Gaussian fundamental modes, thereby facilitating multi-dimensional (de)multiplexing involving CVB modes and wavelengths. As a proof of concept, we theoretically demonstrate a 9-channel multi-dimensional multiplexing system, successfully achieving joint (de)multiplexing of 3 CVB modes (1, 2, and 3) and 3 wavelengths (1550 nm, 1560 nm, and 1570 nm) with a diffraction efficiency exceeding 80%. Additionally, we show the transmission of 16-QAM signals across 9 channels with the bit-error-rates below 10-5. By combining the integrability of metasurfaces with the high-dimensional wavefront manipulation capabilities of multilevel modulation, our strategy can effectively address the diverse demands of different wavelengths and CVB modes in optical communication.

Structured light enhanced machine learning for fiber bend sensing

The intricate optical distortions that occur when light interacts with complex media, such as few- or multi-mode optical fiber, often appear random in origin and are a fundamental source of error for communication and sensing systems. We propose the use of orbital angular momentum (OAM) feature extraction to mitigate phase-noise and allow for the use of intermodal-coupling as an effective tool for fiber sensing. OAM feature extraction is achieved by passive all-optical OAM demultiplexing, and we demonstrate fiber bend tracking with 94.1% accuracy. Conversely, an accuracy of only 14% was achieved for determining the same bend positions when using a convolutional-neural-network trained with intensity measurements of the output of the fiber. Further, OAM feature extraction used 120 times less information for training compared to intensity image based measurements. This work indicates that structured light enhanced machine learning could be used in a wide range of future sensing technologies.

Multiplication of orbital angular momentum via multi-plane light conversion

The multiplication of orbital angular momentum (OAM) modes using optical coordinate transformation is useful for OAM optical networks, but the scalability of this scheme is limited by the ray model. Here, we propose an alternative scheme for the scalable multiplication of OAM modes based on modified multi-plane light conversion (MPLC) that can extend azimuthal and radial indices of OAM modes supported by the multipliers and unlock a new degree of freedom for radial high-order OAM states that has been restricted in the zero order. The multiplication for 20 OAM modes with radial index p = 0 and 10 OAM modes with radial index p = 1 is performed in simulation and experiment. The 3-dB optical bandwidth corresponding to the purity of OAM modes covers the entire C-band experimentally. This novel, to the best of our knowledge, approach to manipulating OAM states provides valuable insights and flexible strategies for high-capacity OAM optical communication and high-dimensional optical quantum information processing.

Spatiotemporal diffractive deep neural networks

A spatiotemporal diffractive deep neural network (STD2NN) is proposed for spatiotemporal signal processing. The STD2NN is formed by gratings, which convert the signal from the frequency domain to the spatial domain, and multiple layers consisting of spatial lenses and space light modulators (SLMs), which conduct spatiotemporal phase modulation. An all-optical backpropagation (BP) algorithm for SLM phase tuning is proposed, with the gradient of the loss function computed by the inner product of the forward propagating optical field and the backward propagating conjugated error field. As a proof of concept, a spatiotemporal word "OPTICA" is generated by the STD2NN. Afterwards, a spatiotemporal optical vortex (STOV) beam multiplexer based on the STD2NN is demonstrated, which converts the spatially separated Gaussian beams into the STOV wave-packets with different topological charges. Both cases illustrate the capability of the proposed STD2NN to generate and process the spatiotemporal signals.

Ultrahigh-fidelity spatial mode quantum gates in high-dimensional space by diffractive deep neural networks

While the spatial mode of photons is widely used in quantum cryptography, its potential for quantum computation remains largely unexplored. Here, we showcase the use of the multi-dimensional spatial mode of photons to construct a series of high-dimensional quantum gates, achieved through the use of diffractive deep neural networks (D2NNs). Notably, our gates demonstrate high fidelity of up to 99.6(2)%, as characterized by quantum process tomography. Our experimental implementation of these gates involves a programmable array of phase layers in a compact and scalable device, capable of performing complex operations or even quantum circuits. We also demonstrate the efficacy of the D2NN gates by successfully implementing the Deutsch algorithm and propose an intelligent deployment protocol that involves self-configuration and self-optimization. Moreover, we conduct a comparative analysis of the D2NN gate's performance to the wave-front matching approach. Overall, our work opens a door for designing specific quantum gates using deep learning, with the potential for reliable execution of quantum computation.

Fan-in/fan-out for heterogeneous 19-core fibers based on metasurfaces with nonuniform phase plates

In space-division-multiplexed transmission systems, it is essential to realize fan-in/fan-out devices that connect the cores between multicore fibers and single-mode fibers. In this Letter, we propose a metasurface-based fan-in/fan-out device with nonuniform phase plates for heterogeneous 19-core fibers across the full C band. Our results show that an average insertion loss of 0.85 dB and a maximum crosstalk of -25.5 dB can be achieved at 1550 nm. Across the C band, the insertion loss and crosstalk are better than 2.78 dB and -19.96 dB, respectively. The proposed concept can flexibly handle various fiber configurations without additional complexity.

Information multiplexing from optical holography to multi-channel metaholography

Holography offers a vital platform for optical information storage and processing, which has a profound impact on many photonic applications, including 3D displays, LiDAR, optical encryption, and artificial intelligence. In this review, we provide a comprehensive overview of optical holography, moving from volume holography based on optically thick holograms to digital holography using ultrathin metasurface holograms in nanophotonics. We review the use of volume holograms for holographic multiplexing through the linear momentum selectivity and other approaches and highlight the emerging use of digital holograms that can be implemented by ultrathin metasurfaces. We will summarize the fabrication of different holographic recording media and digital holograms based on recent advances in flat meta-optics and nanotechnology. We highlight the rapidly developing field of metasurface holography, presenting the use of multi-functional metasurfaces for multiplexing holography in the use of polarization, wavelength, and incident angle of light. In the scope of holographic applications, we will focus on high bandwidth metasurface holograms that offer the strong sensitivity to the orbital angular momentum of light. At the end, we will provide a short summary of this review article and our perspectives on the future development of the vivid holography field.

Resource-Efficient High-Dimensional Entanglement Detection via Symmetric Projections

We introduce two families of criteria for detecting and quantifying the entanglement of a bipartite quantum state of arbitrary local dimension. The first is based on measurements in mutually unbiased bases and the second is based on equiangular measurements. Both criteria give a qualitative result in terms of the state's entanglement dimension and a quantitative result in terms of its fidelity with the maximally entangled state. The criteria are universally applicable since no assumptions on the state are required. Moreover, the experimenter can control the trade-off between resource-efficiency and noise-tolerance by selecting the number of measurements performed. For paradigmatic noise models, we show that only a small number of measurements are necessary to achieve nearly-optimal detection in any dimension. The number of global product projections scales only linearly in the local dimension, thus paving the way for detection and quantification of very high-dimensional entanglement.

Vector vortex beams sorting of 120 modes in visible spectrum

Polarization (P), angular index (l), and radius index (p) are three independent degrees of freedom (DoFs) of vector vortex beams, which have found extensive applications in various domains. While efficient sorting of a single DoF has been achieved successfully, simultaneous sorting of all these DoFs in a compact and efficient manner remains a challenge. In this study, we propose a beam sorter that simultaneously handles all the three DoFs using a diffractive deep neural network (D2NN), and demonstrate the robust sorting of 120 Laguerre-Gaussian (LG) modes experimentally in the visible spectrum. Our proposed beam sorter underscores the considerable potential of D2NN in optical field manipulation and promises to enhance the diverse applications of vector vortex beams.

Referenceless characterization of complex media using physics-informed neural networks

In this work, we present a method to characterize the transmission matrices of complex scattering media using a physics-informed, multi-plane neural network (MPNN) without the requirement of a known optical reference field. We use this method to accurately measure the transmission matrix of a commercial multi-mode fiber without the problems of output-phase ambiguity and dark spots, leading to up to 58% improvement in focusing efficiency compared with phase-stepping holography. We demonstrate how our method is significantly more noise-robust than phase-stepping holography and show how it can be generalized to characterize a cascade of transmission matrices, allowing one to control the propagation of light between independent scattering media. This work presents an essential tool for accurate light control through complex media, with applications ranging from classical optical networks, biomedical imaging, to quantum information processing.

Nanophotonic Materials for Twisted-Light Manipulation

Twisted light, an unbounded set of helical spatial modes carrying orbital angular momentum (OAM), offers not only fundamental new insights into structured light-matter interactions, but also a new degree of freedom to boost optical and quantum information capacity. However, current OAM experiments still rely on bulky, expensive, and slow-response diffractive or refractive optical elements, hindering today's OAM systems to be largely deployed. In the last decade, nanophotonics has transformed the photonic design and unveiled a diverse range of compact and multifunctional nanophotonic devices harnessing the generation and detection of OAM modes. Recent metasurface devices developed for OAM generation in both real and momentum space, presenting design principle and exemplary devices, are summarized. Moreover, recent development of whispering-gallery-mode-based passive and tunable microcavities, capable of extracting degenerate OAM modes for on-chip vortex emission and lasing, is summarized. In addition, the design principle of different plasmonic devices and photodetectors recently developed for on-chip OAM detection is discussed. Current challenges faced by the nanophotonic field for twisted-light manipulation and future advances to meet these challenges are further discussed. It is believed that twisted-light manipulation in nanophotonics will continue to make significant impact on future development of ultracompact, ultrahigh-capacity, and ultrahigh-speed OAM systems-on-a-chip.

Extending orbital angular momentum multiplexing to radially high orders for massive mode channels in fiber transmission

Orbital angular momentum (OAM) beams with different angular indices l have the potential to greatly increase communication capacity. However, the finite aperture of optical systems limits the value of the angular index. In order to fully use the orthogonal mode channels supported in the fiber for high-capacity communications, we propose extending the radial indices p of OAM modes as an additional multiplexing dimension. In this paper, we introduce spatially discrete multiple phase planes to multiplex the angular and radial OAM modes simultaneously. Due to the orthogonal property of the central symmetric OAM modes, a two-dimensional (2D) input Gaussian beams array can be converted to coaxial OAM modes through Cartesian to log-polar coordinate transformation by inverse design. For a proof-of-concept demonstration, a 10-mode multiplexer for high-order radial OAM modes was designed using five phase planes. The fabricated multiplexer generated high-quality multiplexed OAM modes with a loss of less than 5.4 dB. The multiplexed OAM modes were coupled into a specially designed ring-core fiber by mode-field matching, achieving stable mode transmission in 2 km fiber. The approach provides a scalable technology to increase the number of transmission channels and could lead to the practical applications of OAM multiplexing in communication.

Single-wavelength polarization- and mode-division multiplexing free-space optical communication at 689 Gbit/s in strong turbulent channels

We experimentally demonstrated, for, it is believed, the first time, high-capacity polarization- and mode-division multiplexing free-space optical transmission with adequate strong turbulence resiliency. A compact spatial light modulator-based polarization multiplexing multi-plane light conversion module was employed to emulate strong turbulent links. By employing advanced successive interference cancellation multiple-input multiple-output decoder and redundant receive channels, the strong turbulence resiliency was significantly improved in a mode-division multiplexing system. As a result, we achieved a record-high line rate of 689.2 Gbit/s, channel number of 10, and net spectral efficiency of 13.9 bit/(s Hz) in a single-wavelength mode-division multiplexing system with strong turbulence.

Tolerance to aberration and misalignment in a two-point-resolving image inversion interferometer

Image inversion interferometry can measure the separation of two incoherent point sources at or near the quantum limit. This technique has the potential to improve upon current state-of-the-art imaging technologies, with applications ranging from microbiology to astronomy. However, unavoidable aberrations and imperfections in real systems may prevent inversion interferometry from providing an advantage for real-world applications. Here, we numerically study the effects of realistic imaging system imperfections on the performance of image inversion interferometry, including common phase aberrations, interferometer misalignment, and imperfect energy splitting within the interferometer. Our results suggest that image inversion interferometry retains its superiority to direct detection imaging for a wide range of aberrations, so long as pixelated detection is used at the interferometer outputs. This study serves as a guide for the system requirements needed to achieve sensitivities beyond the limits of direct imaging, and further elucidates the robustness of image inversion interferometry to imperfections. These results are critical for the design, construction, and use of future imaging technologies performing at or near the quantum limit of source separation measurements.

Multiplane Diffractive Acoustic Networks

Acoustic holograms are able to control pressure fields with high spatial resolution, enabling complex fields to be projected with minimal hardware. This capability has made holograms attractive tools for applications, including manipulation, fabrication, cellular assembly, and ultrasound therapy. However, the performance benefits of acoustic holograms have traditionally come at the cost of temporal control. Once a hologram is fabricated, the field it produces is static and cannot be reconfigured. Here, we introduce a technique to project time-dynamic pressure fields by combining an input transducer array with a multiplane hologram, which is represented computationally as a diffractive acoustic network (DAN). By exciting different input elements in the array, we can project distinct and spatially complex amplitude fields to an output plane. We numerically show that the multiplane DAN outperforms a single-plane hologram, while using fewer total pixels. More generally, we show that adding more planes can increase the output quality of the DAN for a fixed number of degrees of freedom (DoFs; pixels). Finally, we leverage the pixel efficiency of the DAN to introduce a combinatorial projector that can project more output fields than there are transducer inputs. We experimentally demonstrate that a multiplane DAN could be used to realize such a projector.

Simultaneously Sorting Overlapping Quantum States of Light

The efficient manipulation, sorting, and measurement of optical modes and single-photon states is fundamental to classical and quantum science. Here, we realize simultaneous and efficient sorting of nonorthogonal, overlapping states of light, encoded in the transverse spatial degree of freedom. We use a specifically designed multiplane light converter to sort states encoded in dimensions ranging from d=3 to d=7. Through the use of an auxiliary output mode, the multiplane light converter simultaneously performs the unitary operation required for unambiguous discrimination and the basis change for the outcomes to be spatially separated. Our results lay the groundwork for optimal image identification and classification via optical networks, with potential applications ranging from self-driving cars to quantum communication systems.

High-efficiency interface between multi-mode and single-mode fibers

Multi-mode fibers (MMFs) and single-mode fibers (SMFs) are widely used in optical communication networks. MMFs are the practical choice in terms of cost in applications that require short distances. Beyond that, SMFs are necessary because of the modal dispersion in MMFs. Here, we present a method capable of interfacing an MMF with an SMF using a re-programmable multi-plane light conversion scheme (MPLC). We demonstrate that only three phase modulations are necessary to achieve MMF-SMF coupling efficiencies from 30% to 70%, i.e., an insertion loss from 5 dB to 1.5 dB, for MMFs with core diameters up to 200 μm. We show how the obtained coupling efficiency can be recovered if the output field of the MMF changes entirely, e.g., through strong deformation of the fiber, by simple monitoring of the field. Furthermore, we test the influence of the resolution of both essential devices (field reconstruction and MPLC) on coupling efficiencies. We find that commercially available devices with increased speed and efficiency, such as wavefront sensors and deformable mirrors, are sufficient for establishing an MMF-SMF interface that auto-corrects any decoupling in the kilohertz regime.

Efficient dispersion modeling in optical multimode fiber

Dispersion remains an enduring challenge for the characterization of wavelength-dependent transmission through optical multimode fiber (MMF). Beyond a small spectral correlation width, a change in wavelength elicits a seemingly independent distribution of the transmitted field. Here we report on a parametric dispersion model that describes mode mixing in MMF as an exponential map and extends the concept of principal modes to describe the fiber's spectrally resolved transmission matrix (TM). We present computational methods to fit the model to measurements at only a few, judiciously selected, discrete wavelengths. We validate the model in various MMF and demonstrate an accurate estimation of the full TM across a broad spectral bandwidth, approaching the bandwidth of the best-performing principal modes, and exceeding the original spectral correlation width by more than two orders of magnitude. The model allows us to conveniently study the spectral behavior of principal modes, and obviates the need for dense spectral measurements, enabling highly efficient reconstruction of the multispectral TM of MMF.

Using an acousto-optic modulator as a fast spatial light modulator

High-speed spatial light modulators (SLM) are crucial components for free-space communication and structured illumination imaging. Current approaches for dynamical spatial mode generation, such as liquid crystal SLMs or digital micromirror devices, are limited to a maximum pattern refresh rate of 10 kHz and have a low damage threshold. We demonstrate that arbitrary spatial profiles in a laser pulse can be generated by mapping the temporal radio-frequency (RF) waveform sent to an acousto-optic modulator (AOM) onto the optical field. We find that the fidelity of the SLM performance can be improved through numerical optimization of the RF waveform to overcome the nonlinear effect of AOM. An AOM can thus be used as a 1-dimensional SLM, a technique we call acousto-optic spatial light modulator (AO-SLM), which has 50 µm pixel pitch, over 1 MHz update rate, and high damage threshold. We simulate the application of AO-SLM to single-pixel imaging, which can reconstruct a 32×32 pixel complex object at a rate of 11.6 kHz with 98% fidelity.

Why optics needs thickness

This study shows why and when optical systems need thickness as well as width or area. Wave diffraction explains the fundamental need for area or diameter of a lens or aperture to achieve some resolution or number of pixels in microscopes and cameras. This work demonstrates that if we know what the optics is to do, even before design, we can also deduce the minimum required thickness. This limit comes from diffraction combined with a concept called overlapping nonlocality C that can be deduced rigorously from just the mathematical description of what the device is to do. C expresses how much the input regions for different output regions overlap. This limit applies broadly to optics, from cameras to metasurfaces, and to wave systems generally.

Optical mode conversion via spatiotemporally modulated atomic susceptibility

Light is an excellent medium for both classical and quantum information transmission due to its speed, manipulability, and abundant degrees of freedom into which to encode information. Recently, space-division multiplexing has gained attention as a means to substantially increase the rate of information transfer by utilizing sets of infinite-dimensional propagation eigenmodes such as the Laguerre-Gaussian "donut" modes. Encoding in these high-dimensional spaces necessitates devices capable of manipulating photonic degrees of freedom with high efficiency. In this work, we demonstrate controlling the optical susceptibility of an atomic sample can be used as powerful tool for manipulating the degrees of freedom of light that pass through the sample. Utilizing this tool, we demonstrate photonic mode conversion between two Laguerre-Gaussian modes of a twisted optical cavity with high efficiency. We spatiotemporally modulate the optical susceptibility of an atomic sample that sits at the cavity waist using an auxiliary Stark-shifting beam, in effect creating a mode-coupling optic that converts modes of orbital angular momentum l = 3 → l = 0. The internal conversion efficiency saturates near unity as a function of the atom number and modulation beam intensity, finding application in topological few-body state preparation, quantum communication, and potential development as a flexible tabletop device.

High-capacity free-space optical communications using wavelength- and mode-division-multiplexing in the mid-infrared region

Due to its absorption properties in atmosphere, the mid-infrared (mid-IR) region has gained interest for its potential to provide high data capacity in free-space optical (FSO) communications. Here, we experimentally demonstrate wavelength-division-multiplexing (WDM) and mode-division-multiplexing (MDM) in a ~0.5 m mid-IR FSO link. We multiplex three ~3.4 μm wavelengths (3.396 μm, 3.397 μm, and 3.398 μm) on a single polarization, with each wavelength carrying two orbital-angular-momentum (OAM) beams. As each beam carries 50-Gbit/s quadrature-phase-shift-keying data, a total capacity of 300 Gbit/s is achieved. The WDM channels are generated and detected in the near-IR (C-band). They are converted to mid-IR and converted back to C-band through the difference frequency generation nonlinear processes. We estimate that the system penalties at a bit error rate near the forward error correction threshold include the following: (i) the wavelength conversions induce ~2 dB optical signal-to-noise ratio (OSNR) penalty, (ii) WDM induces ~1 dB OSNR penalty, and (iii) MDM induces ~0.5 dB OSNR penalty. These results show the potential of using multiplexing to achieve a ~30X increase in data capacity for a mid-IR FSO link.

Generation of OAM-carrying space-time wave packets with time-dependent beam radii using a coherent combination of multiple LG modes on multiple frequencies

Space-time (ST) wave packets, in which spatial and temporal characteristics are coupled, have gained attention due to their unique propagation characteristics, such as propagation invariance and tunable group velocity in addition to their potential ability to carry orbital angular momentum (OAM). Through experiment and simulation, we explore the generation of OAM-carrying ST wave packets, with the unique property of a time-dependent beam radius at various ranges of propagation distances. To achieve this, we synthesize multiple frequency comb lines, each assigned to a coherent combination of multiple Laguerre-Gaussian (LG_ℓ,p) modes with the same azimuthal index but different radial indices. The time-dependent interference among the spatial modes at the different frequencies leads to the generation of the desired OAM-carrying ST wave packet with dynamically varying radii. The simulation results indicate that the dynamic range of beam radius oscillations increases with the number of modes and frequency lines. The simulated ST wave packet for OAM of orders +1 or +3 has an OAM purity of >95%. In addition, we experimentally generate and measure the OAM-carrying ST wave packets with time-dependent beam radii. In the experiment, several lines of a Kerr frequency comb are spatially modulated with the superposition of multiple LG modes and combined to generate such an ST wave packet. In the experiment, ST wave packets for OAM of orders +1 or +3 have an OAM purity of >64%. In simulation and experiment, OAM purity decreases and beam radius becomes larger over the propagation.

Full mode power spectrum for Laguerre-Gauss beams in strong Kolmogorov turbulence

We analyze the effects of atmospheric turbulence on the mode power spectrum of beams carrying orbital angular momentum represented by Laguerre-Gauss (LG) modes. For an input (p,m) LG mode, i.e. pump, we calculate the power transferred to other modes (p',m') due to turbulence. Our analysis is validated against split-step beam propagation simulations and shows agreement into the strong turbulence regime. These results have applications for the design and characterization of free-space laser communication systems.

Sorting orbital angular momentum of photons through a multi-ring azimuthal-quadratic phase

Beams carrying orbital angular momentum (OAM) already play significant roles in many domains. Here we propose a practical design of an OAM beam splitter based on a single phase-only multi-ring azimuthal-quadratic diffraction optical element that can sort different OAM components into various spatial positions, and OAM state probing is also achieved. The performance is demonstrated through proof-of-principle experiments and shows favorable results. Furthermore, the intensity proportion of each OAM component, namely the OAM spectrum, is also diagnosed. This work offers high applicability and practicability for the recognition and separation of photon OAM, and thus paves the way for many advanced scenarios such as quantum communication, holographic encryption, and remote sensing.

Optical quantum super-resolution imaging and hypothesis testing

Estimating the angular separation between two incoherent thermal sources is a challenging task for direct imaging, especially at lengths within the diffraction limit. Moreover, detecting the presence of multiple sources of different brightness is an even more severe challenge. We experimentally demonstrate two tasks for super-resolution imaging based on hypothesis testing and quantum metrology techniques. We can significantly reduce the error probability for detecting a weak secondary source, even for small separations. We reduce the experimental complexity to a simple interferometer: we show (1) our set-up is optimal for the state discrimination task, and (2) if the two sources are equally bright, then this measurement can super-resolve their angular separation. Using a collection baseline of 5.3 mm, we resolve the angular separation of two sources placed 15 μm apart at a distance of 1.0 m with a 1.7% accuracy - an almost 3-orders-of-magnitude improvement over shot-noise limited direct imaging.

Spatial tomography of light resolved in time, spectrum, and polarisation

Measuring polarisation, spectrum, temporal dynamics, and spatial complex amplitude of optical beams is essential to studying phenomena in laser dynamics, telecommunications and nonlinear optics. Current characterisation techniques apply in limited contexts. Non-interferometric methods struggle to distinguish spatial phase, while phase-sensitive approaches necessitate either an auxiliary reference source or a self-reference, neither of which is universally available. Deciphering complex wavefronts of multiple co-propagating incoherent fields remains particularly challenging. We harness principles of spatial state tomography to circumvent these limitations and measure a complete description of an unknown beam as a set of spectrally, temporally, and polarisation resolved spatial state density matrices. Each density matrix slice resolves the spatial complex amplitude of multiple mutually incoherent fields, which over several slices reveals the spectral or temporal evolution of these fields even when fields spectrally or temporally overlap. We demonstrate these features by characterising the spatiotemporal and spatiospectral output of a vertical-cavity surface-emitting laser.

The work harnesses principles of spatial state tomography to fully characterise an optical beam in space, time, spectrum, and polarisation. Analysis of the output of a vertical-cavity surface-emitting laser illustrates the technique’s capabilities.

Demonstration of turbulence mitigation in a 200-Gbit/s orbital-angular-momentum multiplexed free-space optical link using simple power measurements for determining the modal crosstalk matrix

We experimentally demonstrate turbulence mitigation in a 200-Gbit/s quadrature phase-shift keying (QPSK) orbital-angular-momentum (OAM) mode-multiplexed system using simple power measurements for determining the modal coupling matrix. To probe and mitigate turbulence, we perform the following: (i) sequentially transmit multiple probe beams at 1550-nm wavelength each with a different combination of Laguerre-Gaussian (LG) modes; (ii) detect the power coupling of each probe beam to LG_0,0 for determining the complex modal coupling matrix; (iii) calculate the conjugate phase of turbulence-induced spatial phase distortion; (iv) apply this conjugate phase to a spatial light modulator (SLM) at the receiver to mitigate the turbulence distortion for the 1552-nm mode-multiplexed data-carrying beams. The probe wavelength is close enough to the data wavelength such that it experiences similar turbulence, but is far enough away such that the probe beams do not affect the data beams and can all operate simultaneously. Our experimental results show that with our turbulence mitigation approach the following occur: (a) the inter-channel crosstalk is reduced by ∼25 and ∼21 dB for OAM +1 and -2 channels, respectively; (b) the optical signal-to-noise ratio (OSNR) penalty is <1 dB for both OAM channels for a bit error rate (BER) at the 7% forward error correction (FEC) limit, compared with the no turbulence case.