Encoding amplitude information onto phase-only filters

Efficient Gradient-Based Metasurface Optimization toward the Limits of Wavelength-Polarization Multiplexing

Polarization and wavelength multiplexing are the two widely employed techniques to improve capacity in metasurfaces. While previous studies have pushed the channel numbers of each technique to its individual limits, achieving simultaneous limits of both techniques still presents challenges. Furthermore, current multiplexing methods often suffer from computational inefficiencies, hindering their applicability in computationally intensive tasks. In this work, we introduce and experimentally validate a gradient-based optimization algorithm using deep neural network (DNN) to achieve the limits of polarization and wavelength multiplexing with high computational efficiency. By leveraging the computational efficiency of the DNN-based method, we further implement nine multiplexed channels (three wavelengths × three polarizations) for large-scale image recognition tasks with a total of 36 classes in the single-layer metasurface. The classification accuracy reaches 96% in simulations and 91.5% in experiments. Our work sets a new benchmark for high-capacity multiplexing with gradient-based inverse design for advanced optical elements.

Shaped vector beams generated with a phase-only modulation-retarder optical configuration

This work presents a new configuration to generate vector beams, with shaped intensity and polarization distributions, based on two liquid-crystal spatial light modulators (SLM). The first device is used in a scalar mode to shape an input linearly polarized beam with a phase-only computer-generated hologram. Then, the Fourier transform is optically formed onto the second SLM, which operates as a pixelated retarder to spatially modify the state of polarization. The proposed optical architecture allows shaping the amplitude profile, while easily generating the cylindrically polarized vector beam pattern. Experimental results demonstrate the versatility of the approach.

Tailoring spatiotemporal wavepackets via two-dimensional space-time duality

Spatiotemporal (ST) beams-ultrafast optical wavepackets with customized spatial and temporal characteristics-present a significant contrast to conventional spatial-structured light and hold the potential to revolutionize our understanding and manipulation of light. However, progress in ST beam research has been constrained by the absence of a universal framework for its analysis and generation. Here, we introduce the concept of 'two-dimensional space-time duality', establishing a foundational duality between spatial-structured light and ST beams. We show that breaking the exact balance between paraxial diffraction and narrow-band dispersion is crucial for guiding the dynamics of ST wavepackets. Leveraging this insight, we pioneer a versatile complex-amplitude modulation strategy, enabling the precise crafting of ST beams with an exceptional fidelity exceeding 97%. Furthermore, we uncover a new range of ST wavepackets by harnessing the exact one-to-one relationship between scalar spatial-structured light and ST beams. Our results expand the toolkit for ST beam research and hold promise for applications across a diverse spectrum of wave-based physical systems.

Polarization-resolved transmission matrices of specialty optical fibers

Transmission matrix measurements of multimode fibers are now routinely performed in numerous laboratories, enabling control of the electric field at the distal end of the fiber and paving the way for the potential application to ultrathin medical endoscopes with high resolution. The same concepts are applicable to other areas, such as space division multiplexing, targeted power delivery, fiber laser performance, and the general study of the mode coupling properties of the fiber. However, the process of building an experimental setup and developing the supporting code to measure the fiber's transmission matrix remains challenging and time consuming, with full details on experimental design, data collection, and supporting algorithms spread over multiple papers or lacking in detail. Here, we outline a complete and self-contained description of the specific experiment we use to measure fully polarization-resolved transmission matrices, which enable full control of the electric field, in contrast to the more common scalar setups. Our exact implementation of the full polarization experiment is new and is easy to align while providing flexibility to switch between full-polarization and scalar measurements if desired. We utilize a spatial light modulator to measure the transmission matrix using linear phase gratings to generate the basis functions and measure the distal electric field using phase-shifting interferometry with an independent reference beam derived from the same laser. We introduce a new method to measure and account for the phase and amplitude drift during the measurement using a Levenberg-Marquardt nonlinear fitting algorithm. Finally, we describe creating distal images through the multimode fiber using phase-to-amplitude shaping techniques to construct the correct input electric field through a superposition of the basis functions with the phase-only spatial light modulator. We show that results are insensitive to the choice of phase-to-amplitude shaping technique as quantified by measuring the contrast of a razor blade at the distal end of the fiber, indicating that the simplest but most power efficient method may be the best choice for many applications. We also discuss some of the possible variations on the setup and techniques presented here and highlight the details that we have found key in achieving high fidelity distal control. Throughout the paper, we discuss applications of our setup and measurement process to a variety of specialty fibers, including fibers with harsh environment coatings, coreless fibers, rectangular core fibers, pedestal fibers, and a pump-signal combiner based on a tapered fiber bundle. This demonstrates the usefulness of these techniques across a variety of application areas and shows the flexibility of our setup in studying various fiber types.

All-Optical Trapping and Programmable Transport of Gold Nanorods with Simultaneous Orientation and Spinning Control

Gold nanorods (GNRs) are of special interest in nanotechnology and biomedical applications due to their biocompatibility, anisotropic shape, enhanced surface area, and tunable optical properties. The use of GNRs, for example, as sensors and mechanical actuators, relies on the ability to remotely control their orientation as well as their translational and rotational motion, whether individually or in groups. Achieving such particle control by using optical tools is challenging and exceeds the capabilities of conventional laser tweezers. We present a tool that addresses this complex manipulation problem by using a curve-shaped laser trap, enabling the optical capture and programmable transport of single and multiple GNRs along any trajectory. This type of laser trap combines confinement and propulsion optical forces with optical torque to transport the GNRs while simultaneously controlling their rotation (spinning) and orientation. The proposed system facilitates the light-driven control of GNRs and the quantitative characterization of their motion dynamics including transport speed, spinning frequency, orientation, and confinement strength. We experimentally demonstrate that remote control of the GNRs can be achieved both near a substrate surface (2D trapping) and deep within the sample (3D all-optical trapping). The motion dynamics of two sets of off-resonant GNRs, possessing similar aspect ratios but different resonance wavelengths, are analyzed to highlight the role played by their optical and mechanical properties in the optical manipulation process. The experimental results are supported by a theoretical model describing the observed motion dynamics of the GNRs. This optical manipulation tool can significantly facilitate applications of light-driven nanorods.

Spatiotemporal hologram

Spatiotemporal structured light has opened up new avenues for optics and photonics. Current spatiotemporal manipulation of light mostly relies on phase-only devices such as liquid crystal spatial light modulators to generate spatiotemporal optical fields with unique photonic properties. However, simultaneous manipulation of both amplitude and phase of the complex field for the spatiotemporal light is still lacking, limiting the diversity and richness of achievable photonic properties. In this work, a simple and versatile spatiotemporal holographic method that can arbitrarily sculpt the spatiotemporal light is presented. The capabilities of this simple yet powerful method are demonstrated through the generation of fundamental and higher-order spatiotemporal Bessel wavepackets, spatiotemporal crystal-like and quasi-crystal-like structures, and spatiotemporal flat-top wavepackets. Fully customizable spatiotemporal wavepackets will find broader application in investigating the dynamics of spatiotemporal fields and interactions between ultrafast spatiotemporal pulses and matters, unveiling previously hidden light-matter interactions and unlocking breakthroughs in photonics and beyond.

Resolving ambiguities in phase correction term for optical field encoding

This article addresses ambiguities regarding the existence and definition of a phase correction term in phase and amplitude optical field encoding techniques. We present a generalized mixed Fourier-Taylor series expansion that is valid for any phase-wrapping interval. Our theoretical analysis, along with numerical and experimental validations, confirm that maintaining consistency within a given phase-wrapping convention ensures equivalent results and reconciles previously conflicting interpretations.

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.

Twisted vortex Gaussian Schell-model beams, generalized ABCD systems, and multidimensional Hermite polynomials

We derive the cross-spectral density (CSD) function for a twisted vortex partially coherent beam at the output of a general ABCD system in terms of multidimensional Hermite polynomials (MDHPs). MDHPs offer notational and computational advantages over prior CSD function representations that use common (one-dimensional) Hermite polynomials. We explain how to compute MDHPs using the recurrence relation given in the literature and include MATLAB code to generate MDHPs of any order. Lastly, we validate our work experimentally by comparing the measured spectral density of a twisted vortex beam at the output of an asymmetric optical system to predictions from our theoretical CSD function.

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.

Selective excitation of high-order modes in two-dimensional cavity resonator integrated grating filters

The selective spatial mode excitation of a bi-dimensional grating-coupled micro-cavity called a cavity resonator integrated grating filter (CRIGF) is reported using an incident beam shaped to reproduce the theoretical emission profiles of the device in one and subsequently two dimensions. In both cases, the selective excitation of modes up to order 10 (per direction) is confirmed by responses exhibiting one (respectively two) spectrally narrowband resonance(s) with a good extinction of the other modes, the latter being shown to depend on the parity and order(s) of the involved modes. These results pave the way toward the demonstration of multi-wavelength spatially selective reflectors or fiber-to-waveguide couplers. Also, subject to an appropriate choice of the materials constituting the CRIGF, this work can be extended to obtain mode-selectable laser emission or nonlinear frequency conversion.

Non-orthogonal optical multiplexing empowered by deep learning

Orthogonality among channels is a canonical basis for optical multiplexing featured with division multiplexing, which substantially reduce the complexity of signal post-processing in demultiplexing. However, it inevitably imposes an upper limit of capacity for multiplexing. Herein, we report on non-orthogonal optical multiplexing over a multimode fiber (MMF) leveraged by a deep neural network, termed speckle light field retrieval network (SLRnet), where it can learn the complicated mapping relation between multiple non-orthogonal input light field encoded with information and their corresponding single intensity output. As a proof-of-principle experimental demonstration, it is shown that the SLRnet can effectively solve the ill-posed problem of non-orthogonal optical multiplexing over an MMF, where multiple non-orthogonal input signals mediated by the same polarization, wavelength and spatial position can be explicitly retrieved utilizing a single-shot speckle output with fidelity as high as ~ 98%. Our results resemble an important step for harnessing non-orthogonal channels for high capacity optical multiplexing.

Preparation of convex edges in fused silica by single pass perforation with a 2D Airy-Gaussian beam

Following ultrafast laser machining of fused silica, post-processing such as polishing and honing are typically required for edges. In this study, we employed a spatial light modulator (SLM) to generate the 2D Airy-Gaussian beam to prepare the convex edges in fused silica by using a single pass of a picosecond laser. It is found that, if the speed exceeds 5 mm/s, there would be plasma interference which is unfavorable for the separation process. A filament effect was observed when the internal laser peak power exceeds the damage threshold of fused silica. The shape of the convex edges was consistent with the propagation path of the 2D Airy-Gaussian beam inside the fused silica before separation. The inclination angle was 17° and 13°, respectively, on the upper and lower end of the edges. The results of this study provide a new, to our knowledge, method for the preparation of curved structures with different curvatures in transparent materials.

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.

Interdimensional radial discrete diffraction in Mathieu photonic lattices

We demonstrate transitional dimensionality of discrete diffraction in radial-elliptical photonic lattices. Varying the order, characteristic structure size, and ellipticity of the Mathieu beams used for the photonic lattices generation, we control the shape of discrete diffraction distribution over the combination of the radial direction with the circular, elliptic, or hyperbolic. We also investigate the transition from one-dimensional to two-dimensional discrete diffraction by varying the input probe beam position. The most pronounced discrete diffraction is observed along the crystal anisotropy direction.

Zero-order free holographic optical tweezers

Holographic optical tweezers (HOTs) use spatial light modulators (SLM) to modulate light beams, thereby enabling the dynamic control of optical trap arrays with complex intensity and phase distributions. This has provided exciting new opportunities for cell sorting, microstructure machining, and studying single molecules. However, the pixelated structure of the SLM will inevitably bring up the unmodulated zero-order diffraction possessing an unacceptably large fraction of the incident light beam power. This is harmful to optical trapping because of the bright, highly localized nature of the errant beam. In this paper and to address this issue, we construct a cost-effective, zero-order free HOTs apparatus, thanks to a homemade asymmetric triangle reflector and a digital lens. As there is no zero-order diffraction, the instrument performs excellently in generating complex light fields and manipulating particles.

Caustic networks with customized intensity statistics

Controlling random light is a key enabling technology that pioneered statistical imaging methods like speckle microscopy. Such low-intensity illumination is especially useful for bio-medical applications where photobleaching is crucial. Since the Rayleigh intensity statistics of speckles do not always meet the requirements of applications, considerable effort has been dedicated to tailoring their intensity statistics. A special random light distribution that naturally comes with radically different intensity structures to speckles are caustic networks. Their intensity statistics support low intensities while allowing sample illumination with rare rouge-wave-like intensity spikes. However, the control over such light structures is often very limited, resulting in patterns with inadequate ratios of bright and dark areas. Here, we show how to generate light fields with desired intensity statistics based on caustic networks. We develop an algorithm to calculate initial phase fronts for light fields so that they smoothly evolve into caustic networks with the desired intensity statistics during propagation. In an experimental demonstration, we exemplarily realize various networks with a constant, linearly decreasing and mono-exponential probability density function.

Transverse energy flow in an optical Skyrmionic Hopfion

The energy flow of light represents a natural way of investigating complex light fields with respect to their applicability. With the generation of a three-dimensional Skyrmionic Hopfion structure in light, which is a topological 3D field configuration with particle-like nature, we paved the way to employ optical, topological constructs. In this work, we present an analysis of the transverse energy flow in the optical Skyrmionic Hopfion, showing the transfer of the topological properties to the mechanical attributes such as the optical angular momentum (OAM). Our findings thus prepare topological structures to be applied in optical traps and data storage or communication.

Understanding the formation of surface relief gratings in azopolymers: A combined molecular dynamics and experimental study

The formation of surface relief gratings in thin azopolymeric films is investigated using atomistic molecular dynamics simulations and compared to experimental results for the specific case of poly-disperse-orange3-methyl-methacrylate. For this purpose, the film is illuminated with a light pattern of alternating bright and dark stripes in both cases. The simulations use a molecular mechanics switching potential to explicitly describe the photoisomerization dynamics between the E and Z isomers of the azo-units and take into account the orientation of the transition dipole moment with respect to the light polarization. Local heating and elevation of the illuminated regions with the subsequent movement of molecules into the neighboring dark regions are observed. This leads to the formation of valleys in the bright areas after re-cooling and is independent of the polarization direction. To verify these observations experimentally, the azopolymer film is illuminated with bright stripes of varying width using a spatial light modulator. Atomic force microscopy images confirm that the elevated areas correspond to the previously dark areas. In the experiment, the polarization of the incident light makes only a small difference since tiny grain-like structures form in the valleys only when the polarization is parallel to the stripes.

Generation of arbitrary complex fields with high efficiency and high fidelity by cascaded phase-only modulation method

Independent or joint control over the amplitude and phase of the complex field by phase-only modulation element is crucial in numerous applications. Existing modulation methods can realize high levels of accuracy but are accompanied by noticeable losses in light-usage efficiency. Here a cascaded modulation method is proposed for the generation of arbitrary complex fields with high efficiency and high fidelity. This approach is based on a gradient descent optimization algorithm that minimizes a customized cost function. The major advantage of our approach over existing modulation methods is that the efficiency is significantly enhanced while ensuring high modulation accuracy. For the generation of Laguerre-Gaussian mode (LG₀₁), with similar high accuracy, the efficiency by our approach can reach 79.5%, which is enhanced by 192% compared with the theoretical maximum efficiency of 41.5% [Opt. Express25, 11692 (2017)10.1364/OE.25.011692]. Furthermore, the efficiency of existing modulation methods deteriorates rapidly as the target field turns more intricate, whereas in our approach it maintains at a relatively high level. The field generation fidelity and energy efficiency of the proposed cascaded modulation method are compared with that of several different single-pass modulation methods in generating a series of typical Hermite-Gaussian and Laguerre-Gaussian modes and an amplitude-only "OSA" pattern. Our proposed method features both high efficiency and high accuracy in the simulation and experiment, which may be of growing interest to applications such as optical manipulation or quantum communication.

Dynamic Phase and Polarization Modulation Using Two-Beam Parallel Coding for Optical Storage in Transparent Materials

In this paper, we propose and experimentally demonstrate a parallel coding and two-beam combining approach for the simultaneous implementation of dynamically generating holographic patterns at their arbitrary linear polarization states. Two orthogonal input beams are parallelly and independently encoded with the same target image information but there is different amplitude information by using two-phase computer-generated holograms (CGH) on two Liquid-Crystal-on-Silicon-Spatial-Light Modulators (LCOS SLMs). Two modulated beams are then considered as two polarization components and are spatially superposed to form the target polarization state. The final linear vector beam is created by the spatial superposition of the two base beams, capable of controlling the vector angle through the phase depth of the phase-only CGHs. Meanwhile, the combined holographic patterns can be freely encoded by the holograms of two vector components. Thus, this allows us to tailor the optical fields endowed with arbitrary holographic patterns and the linear polarization states at the same time. This method provides a more promising approach for laser data writing generation systems in the next-generation optical data storage technology in transparent materials.

Creating stable trapping force and switchable optical torque with tunable phase of light

Light-induced rotation of microscopic objects is of general interest as the objects may serve as micromotors. Such rotation can be driven by the angular momentum of light or recoil forces arising from special light-matter interactions. However, in the absence of intensity gradient, simultaneously controlling the position and switching the rotation direction is challenging. Here, we report stable optical trapping and switchable optical rotation of nanoparticle (NP)-assembled micromotors with programmed phase of light. We imprint customized phase gradients into a circularly polarized flat-top (i.e., no intensity gradient) laser beam to trap and assemble metal NPs into reconfigurable clusters. Modulating the phase gradients allows direction-switchable and magnitude-tunable optical torque in the same cluster under fixed laser wavelength and handedness. This work provides a valuable method to achieve reversible optical torque in micro/nanomotors, and new insights for optical trapping and manipulation using the phase gradient of a spatially extended light field.

Steerable photonic jet for super-resolution microscopy

A promising technique in optical super-resolution microscopy is the illumination of the sample by a highly localized beam, a photonic jet (also called photonic nanojet). We propose a method of computation of incident field amplitude and phase profiles that produce photonic jets at desired locations in the near field after interaction with a fixed micro-scale dielectric lens. We also describe a practical way of obtaining the incident field profiles using spatial light modulators. We expect our photonic jet design method to work for a wide range of lens shapes, and we demonstrate its application numerically using two-dimensional micro-lenses of circular and square cross-sections. We furthermore offer a theoretical analysis of the resolution of photonic jet design, predicting among other that a larger lens can produce a narrower photonic jet. Finally, we give both theoretical and numerical evidence that the waist width of the achieved designed jets is increasing linearly and slowly over a large interval of radial distances. With uniform plane wave illumination, the circular two-dimensional micro-lens produces a similar-sized jet at a fixed radial distance, while the square lens does not form a jet at all. We expect our steerable optical photonic jet probe to enable highly localized adaptive real-time measurements and drive advances in super-resolution optical microscopy and scatterometry, as well as fluorescence and Raman microscopy. Our relatively weak peak jet intensity allows application in biology and health sciences, which require high resolution imaging without damaging the sample bio-molecules.

Experimental realization of modulated Hermite-Gaussian laser modes: a maximum number of highly intense lobes

Here, we present an experimental method that redistributes the optical energy among the lobes of high-order standard Hermite-Gaussian (SHG) laser modes in a controlled manner. We numerically designed diffractive optical elements, displayed over a spatial light modulator for redistribution of optical energy that converts low and moderate intense lobes into all highly intense lobes and vice versa at the Fourier plane. Such precise generation of modulated HG (MHG) laser modes offers a maximum number of highly intense lobes compared to SHG modes. Hence, we envisage that MHG beams may surpass SHG beams in many applications, such as particle manipulation and optical lithography, where highly intense lobes play a significant role.

Generation of combined half-integer Bessel-like beams using synthetic phase holograms

We discuss the generation of combined half-integer Bessel-like (CHB) beams using synthetic phase holograms (SPHs). We assess the efficiency and accuracy of the SPHs, in the task of generating CHB beams. The proposal is illustrated by the implementation of CHB beams, which are experimentally generated in a setup based on a phase spatial light modulator. Also, we analyze, numerically and experimentally, the propagation of the generated CHB beams. As the main result, the SPHs are able to generate several CHB beams with relatively high accuracy. Additionally, it is obtained that the efficiency values of the SPHs are close to the theoretical predictions.

Holographic Tailoring of Structured Light Field with Digital Device

Structured light fields have attracted much attention due to rich spatial degrees of freedom. The tailoring of an arbitrary structured light field on demand is the precondition for the application of structured light. Therefore, the computer holography method used to reconstruct a coherent light field wavefront has been naturally applied for generating structured light. In this work, we comprehensively demonstrate the principles and procedures of pure-phase computer-generated holography (PP-CGH) and binary-amplitude computer-generated holography (BA-CGH) methods for tailoring structured light, realized by two digitally programmable devices: liquid-crystal spatial light modulators (Lc-SLM) and digital micromirror devices (DMD), respectively. Moreover, we first compare the two approaches in detail and clarify the recipe to obtain a high tailoring accuracy and efficiency, which will help researchers to better understand and utilize the holographic tailoring of structured optical fields.

Optical computing of quantum revivals

Interference is the mechanism through which waves can be structured into the most fascinating patterns. While for sensing, imaging, trapping, or in fundamental investigations, structured waves play nowadays an important role and are becoming the subject of many interesting studies. Using a coherent optical field as a probe, we show how to structure light into distributions presenting collapse and revival structures in its wavefront. These distributions are obtained from the Fourier spectrum of an arrangement of aperiodic diffracting structures. Interestingly, the resulting interference may present quasiperiodic structures of diffraction peaks on a number of distance scales, even though the diffracting structure is not periodic. We establish an analogy with revival phenomena in the evolution of quantum mechanical systems and illustrate this computation numerically and experimentally, obtaining excellent agreement with the proposed theory.

Flexible trajectory control of Bessel beams with pure phase modulation

Spatial phase modulation has become an important method for the design of new self-accelerating light beams. Based on the transverse-longitudinal mapping of Bessel beam, we propose a method of pure phase modulation to directly convert a zero-order Bessel beam into a self-accelerating beam, of which the propagation trajectories can be flexibly predesigned. We experimentally demonstrate three typical types of curves that the modulated Bessel beam propagates along, and the parabolic, spiral, and teleporting self-accelarating beams are realized. The experimental results match the expected trajectory well. This method is simple to operate, and imposes fewer restrictions on the beam trajectory.

Dual projectile beams

Accelerating beams, of which the Airy beam is an important representative, are characterized by intensity maxima that propagate along curved trajectories. In this work we present a simple approach to directly generate accelerating beams with controllable trajectories by means of binary phase structures that consist of only a π phase step modulation in comparison to previous studies where two-dimensional cubic phase modulations for example are required, and which have practical limitations due to their challenging fabrication with phase plates or diffractive optical elements (DOEs), or the spatially extended system needed for their generation at the Fourier plane. In our approach, two intensity maxima are formed that propagate along root parabolic trajectories in contrast to Airy and higher order caustic beams that propagate along a parabolic curve, hence we call these beams Dual Projectile Beams (DPBs). By tailoring a step or slit phase patterns with additional Fresnel lenses, we either generate hollow-core or abruptly focusing beams and control their curvatures. Moreover, using DPBs as a simpler complement to complex structured light fields, we demonstrate their versatility at the example of their interaction with nonlinear matter, namely the formation of a spatial soliton in a photorefractive material. We show that the formed solitary state propagates almost unchanged for a distance of several Rayleigh lengths. This light matter interaction can be regarded as a light beam deceleration. The simplicity of this approach makes these beams suitable for integrated optics and high-power laser applications using DOEs or meta-surfaces.

High capacity topological coding based on nested vortex knots and links

Optical knots and links have attracted great attention because of their exotic topological characteristics. Recent investigations have shown that the information encoding based on optical knots could possess robust features against external perturbations. However, as a superior coding scheme, it is also necessary to achieve a high capacity, which is hard to be fulfilled by existing knot-carriers owing to the limit number of associated topological invariants. Thus, how to realize the knot-based information coding with a high capacity is a key problem to be solved. Here, we create a type of nested vortex knot, and show that it can be used to fulfill the robust information coding with a high capacity assisted by a large number of intrinsic topological invariants. In experiments, we design and fabricate metasurface holograms to generate light fields sustaining different kinds of nested vortex links. Furthermore, we verify the feasibility of the high-capacity coding scheme based on those topological optical knots. Our work opens another way to realize the robust and high-capacity optical coding, which may have useful impacts on the field of information transfer and storage.

Robust and high capacity optical coding will be at the base of future developments of information transfer and storage. Here the authors develop a topological all-optical coding scheme, which possesses good stability and a high capacity, using nested vortex knots and links.

Over 65% Sunlight Absorption in a 1 μm Si Slab with Hyperuniform Texture

Thin, flexible, and invisible solar cells will be a ubiquitous technology in the near future. Ultrathin crystalline silicon (c-Si) cells capitalize on the success of bulk silicon cells while being lightweight and mechanically flexible, but suffer from poor absorption and efficiency. Here we present a new family of surface texturing, based on correlated disordered hyperuniform patterns, capable of efficiently coupling the incident spectrum into the silicon slab optical modes. We experimentally demonstrate 66.5% solar light absorption in free-standing 1 μm c-Si layers by hyperuniform nanostructuring for the spectral range of 400 to 1050 nm. The absorption equivalent photocurrent derived from our measurements is 26.3 mA/cm², which is far above the highest found in literature for Si of similar thickness. Considering state-of-the-art Si PV technologies, we estimate that the enhanced light trapping can result in a cell efficiency above 15%. The light absorption can potentially be increased up to 33.8 mA/cm² by incorporating a back-reflector and improved antireflection, for which we estimate a photovoltaic efficiency above 21% for 1 μm thick Si cells.

Experimental observation and manipulation of optical tornado waves

We report experimental realization and manipulation of optical tornado waves (ToWs). By controlling the self-focusing length, total angular momentum, and foci deviation of ToWs, the propagation properties of optical ToWs, especially their angular velocity, can be manipulated. Controlling the accumulated rotation angle of the main intensity lobes of ToWs from 0° through 1100° is experimentally demonstrated, and their angular velocity is predicted to be the highest around the foci overlap situation. Our experimental results are in good agreement with numerical results.

Ultracompact meta-imagers for arbitrary all-optical convolution

Electronic digital convolutions could extract key features of objects for data processing and information identification in artificial intelligence, but they are time-cost and energy consumption due to the low response of electrons. Although massless photons enable high-speed and low-loss analog convolutions, two existing all-optical approaches including Fourier filtering and Green's function have either limited functionality or bulky volume, thus restricting their applications in smart systems. Here, we report all-optical convolutional computing with a metasurface-singlet or -doublet imager, considered as the third approach, where its point spread function is modified arbitrarily via a complex-amplitude meta-modulator that enables functionality-unlimited kernels. Beyond one- and two-dimensional spatial differentiation, we demonstrate real-time, parallel, and analog convolutional processing of optical and biological specimens with challenging pepper-salt denoising and edge enhancement, which significantly enrich the toolkit of all-optical computing. Such meta-imager approach bridges multi-functionality and high-integration in all-optical convolutions, meanwhile possessing good architecture compatibility with digital convolutional neural networks.

Light transport and localization in disordered aperiodic Mathieu lattices

Complex optical systems such as deterministic aperiodic Mathieu lattices are known to hinder light diffraction in a manner comparable to randomized optical systems. We systematically incorporate randomness in our complex optical system, measuring its relative contribution of randomness, to understand the relationship between randomness and complexity. We introduce an experimental method for the realization of disordered aperiodic Mathieu lattices with numerically controlled disorder degree. Added disorder always enhances light transport. For lower disorder degrees, we observe diffusive-like transport, and in the range of highest light transport, we detect Anderson localization. With further increase of disorder degree, light transport is slowly decreasing and localization length decreases indicating more pronounced Anderson localization. Numerical investigation at longer propagation distances indicates that the threshold of Anderson localization detection is shifted to lower disorder degrees.

Optimization for maximum modulation of a double-pass twisted nematic liquid crystal display

Spatial light modulators are widely used to perform modulations of different properties of the electromagnetic field. In this work, a simple optimization method for general double-pass setups was developed. It takes into account the involved polarizing elements and displays, and a numerical simulation based on an exhaustive search routine finds the optimal optical axis orientations of the polarizing elements for the desired modulation. By simultaneously considering both impingements, we are able to take full advantage of the modulation capabilities of the chosen spatial light modulators. In particular, different polarization modulations and complex amplitude modulations were studied for twisted nematic liquid crystal displays and passive linear optical elements. Examples of different optimization criteria are shown and compared with experimental results, supporting the feasibility of this approach. This method offers the possibility of independent modulation of two properties of the input light state, outperforming the use of a single screen.

Generation of periodic and quasi-periodic two-dimensional non-diffractive beams with inhomogeneous polarization

In this work, two-dimensional periodic and quasi-periodic non-diffractive spatial inhomogeneous polarization optical fields are generated, numerically and experimentally, by the superposition of multiple plane waves with different polarizations. For the experimental implementation of the fields, synthetic phase holograms are employed in conjunction with half-wave and quarter-wave retarder films as polarization modulators. The obtained spatially inhomogeneous polarization optical fields show good quality and are in good agreement with numerical results. The proposed method is highly efficient for the generation of these types of optical fields.

Generation of multi-focus abruptly autofocusing beams with adjustable focus characteristics

This work introduces and demonstrates a method for tailoring multi-focus abruptly autofocusing beams (MFAABs) in free space. Since MFAABs are formed by superposing the wavefronts of abruptly autofocusing beams (AABs), the number, positions, and relative intensity of foci are directly and independently adjusted during the pre-design of AABs. Also, we show that the size of the light field involves the characteristics of focus, such as peak intensity, focal size, and subsequent oscillations. We apply the double-phase hologram method to generate the required complex field with a phase-only spatial light modulator in experiments. With flexible control on foci characteristics, this work may broaden potential applications of autofocusing beams.

Particle-like topologies in light

Three-dimensional (3D) topological states resemble truly localised, particle-like objects in physical space. Among the richest such structures are 3D skyrmions and hopfions, that realise integer topological numbers in their configuration via homotopic mappings from real space to the hypersphere (sphere in 4D space) or the 2D sphere. They have received tremendous attention as exotic textures in particle physics, cosmology, superfluids, and many other systems. Here we experimentally create and measure a topological 3D skyrmionic hopfion in fully structured light. By simultaneously tailoring the polarisation and phase profile, our beam establishes the skyrmionic mapping by realising every possible optical state in the propagation volume. The resulting light field's Stokes parameters and phase are synthesised into a Hopf fibration texture. We perform volumetric full-field reconstruction of the [Formula: see text] mapping, measuring a quantised topological charge, or Skyrme number, of 0.945. Such topological state control opens avenues for 3D optical data encoding and metrology. The Hopf characterisation of the optical hypersphere endows a fresh perspective to topological optics, offering experimentally-accessible photonic analogues to the gamut of particle-like 3D topological textures, from condensed matter to high-energy physics.

Shaping light in 3d space by counter-propagation

We extend the established transverse customization of light, in particular, amplitude, phase, and polarization modulation of the light field, and its analysis by the third, longitudinal spatial dimension, enabling the visualization of longitudinal structures in sub-wavelength (nm) range. To achieve this high-precision and three-dimensional beam shaping and detection, we propose an approach based on precise variation of indices in the superposition of higher-order Laguerre-Gaussian beams and cylindrical vector beams in a counter-propagation scheme. The superposition is analyzed experimentally by digital, holographic counter-propagation leading to stable, reversible and precise scanning of the light volume. Our findings show tailored amplitude, phase and polarization structures, adaptable in 3D space by mode indices, including sub-wavelength structural changes upon propagation, which will be of interest for advanced material machining and optical trapping.

Compact vectorial optical field generator using a single phase-only spatial light modulator

In this study, we demonstrate a compact vectorial optical field generator for any coherent light, including femtosecond laser beams. The apparatus utilizes a single Köster prism for both beam splitting and recombining. A phase-only spatial light modulator is used as a diffractive optical element to encode the two complex fields that recombine after being converted to orthogonal polarizations, generating an arbitrary vectorial optical field. We apply this setup to shape focused femtosecond pulses in producing patterned structures.

Generation of vector beams using synthetic phase holograms

We discuss a class of synthetic phase holograms (SPHs) applied to the generation of vector fields. Each SPH encodes the transverse components of the vector field, modulated by different linear phase carriers. Such components, which are spatially separated by the carriers, are modulated by appropriate orthogonal polarizations. A final stage that makes the components collinear allows the generation of the vector field. We assess the efficiency and accuracy of the different SPHs, in the task of generating vector fields. The proposal is illustrated by the implementation of vector Bessel beams, which are experimentally generated in a setup based on a phase spatial light modulator.

Efficient direct mapping of the nonlinear optical response via modulated Airy beams

We report a scheme to achieve efficient direct mapping of the nonlinear optical response into a spatial beam profile. Compared with previous methods where a standard two-dimensional Airy beam was used as a probe, a modulated beam configuration allows for an improved mapping efficiency, stemming from the induced nonlinearity caused by the applied modulation. We find that the mapping efficiency along different orientations is highly related to the beam patterns and the type of nonlinearity. The improvement of the mapping quality and new, to the best of our knowledge, features found in simulations are further verified in experiments by testing a photorefractive nonlinearity. Our results represent a further step towards an effective tool for the direct measurement of the nonlinear optical response with low power consumption.

Uniform and efficient beam shaping for high-energy lasers

Phase-only beam shaping with liquid crystal on silicon spatial light modulators (SLM) allows modulating the wavefront dynamically and generating arbitrary intensity patterns with high efficiency. Since this method cannot take control of all degrees of freedom, a speckle pattern appears and drastically impairs the outcome. There are several methods to overcome this issue including algorithms which directly control phase and amplitude, but they suffer from low efficiency. Methods using two SLMs yield excellent results but they are usually limited in the applicable energy due to damage to the SLM's backplane. We present a method which makes use of two SLMs and simultaneously gives way for high-energy laser applications. The algorithm and setup are designed to keep the fluence on the SLMs low by distributing the light over a large area. This provides stability against misalignment and facilitates experimental feasibility while keeping high efficiency.

Rapid computational cell-rotation around arbitrary axes in 3D with multi-core fiber

Optical trapping is a vital tool in biology, allowing precise optical manipulation of nanoparticles, micro-robots, and cells. Due to the low risk of photodamage and high trap stiffness, fiber-based dual-beam traps are widely used for optical manipulation of large cells. Besides trapping, advanced applications like 3D refractive index tomography need a rotation of cells, which requires precise control of the forces, for example, the acting-point of the forces and the intensities in the region of interest (ROI). A precise rotation of large cells in 3D about arbitrary axes has not been reported yet in dual-beam traps. We introduce a novel dual-beam optical trap in which a multi-core fiber (MCF) is transformed to a phased array, using wavefront shaping and computationally programmable light. The light-field distribution in the trapping region is holographically controlled within 0.1 s, which determines the orientation and the rotation axis of the cell with small retardation. We demonstrate real-time controlled rotation of HL60 cells about all 3D axes with a very high degree of freedom by holographic controlled light through an MCF with a resolution close to the diffraction limit. For the first time, the orientation of the cell can be precisely controlled about all 3D axes in a dual-beam trap. MCFs provide much higher flexibility beyond the bulky optics, enabling lab-on-a-chip applications and can be easily integrated for applications like contactless cell surgery, refractive index tomography, cell-elasticity measurement, which require precise 3D manipulation of cells.

Reconfigurable generation of double-ring perfect vortex beam

Perfect vortex beam (PVB), whose ring radius is independent of its topological charge, play an important role in optical trapping and optical communication. Here, we experimentally demonstrate the reconfigurable double-ring PVB (DR-PVB) generation with independent manipulations of the amplitude, the radius, the width, and the topological charge for each ring. Based on complex amplitude modulation (CAM) with a phase-only spatial light modulator (SLM), we successfully verify the proposed DR-PVB generation scheme via the computer-generated hologram. Furthermore, we carry out a quantitative characterization for the generated DR-PVB, in terms of both the generation quality and the generation efficiency. The correlation coefficients of various reconfigurable DR-PVBs are above 0.8, together with the highest generation efficiency of 44%. We believe that, the proposed generation scheme of reconfigurable DR-PVB is desired for applications in both optical tweezers and orbital angular momentum (OAM) multiplexing.

Complex Wavefront Shaping through a Multi-Core Fiber

Wavefront shaping through a multi-core fiber (MCF) is turning into an attractive method for endoscopic imaging and optical cell-manipulation on a chip. However, the discrete distribution and the low number of cores induce pixelated phase modulation, becoming an obstacle for delivering complex light field distributions through MCFs. We demonstrate a novel phase retrieval algorithm named Core–Gerchberg–Saxton (Core-GS) employing the captured core distribution map to retrieve tailored modulation hologram for the targeted intensity distribution at the distal far-field. Complex light fields are reconstructed through MCFs with high fidelity up to 96.2%. Closed-loop control with experimental feedback denotes the capability of the Core-GS algorithm for precise intensity manipulation of the reconstructed light field. Core-GS provides a robust way for wavefront shaping through MCFs; it facilitates the MCF becoming a vital waveguide in endoscopic and lab-on-a-chip applications.

Optical grinder: sorting of trapped particles by orbital angular momentum

We customize a transversely structured, tunable light landscape on the basis of orbital angular momentum (OAM)-carrying beams for the purpose of advanced optical manipulation. Combining Laguerre-Gaussian (LG) modes with helical phase fronts of opposite OAM handedness, counter-rotating transfer of OAM is enabled in a concentric intensity structure, creating a dynamic "grinding" scenario on dielectric microparticles. We demonstrate the ability to trap and rotate silica spheres of various sizes and exploit the light fields' feature to spatially separate trapped objects by their size. We show the adaptability of the light field depending on the chosen LG mode indices, allowing on-demand tuning of the trapping potential and sorting criteria. The versatility of our approach for biomedical application is examined by spatial discriminating yeast cells and silica spheres of distinct diameter.

Coupling light to higher order transverse modes of a near-concentric optical cavity

Optical cavities in the near-concentric regime have near-degenerate transverse modes; the tight focusing transverse modes in this regime enable strong coupling with atoms. These features provide an interesting platform to explore multi-mode interaction between atoms and light. Here, we use a spatial light modulator (SLM) to shape the phase of an incoming light beam to match several Laguerre-Gaussian (LG) modes of a near-concentric optical cavity. We demonstrate coupling efficiency close to the theoretical prediction for single LG modes and well-defined combinations of them, limited mainly by imperfections in the cavity alignment.

Compensation-free high-dimensional free-space optical communication using turbulence-resilient vector beams

Free-space optical communication is a promising means to establish versatile, secure and high-bandwidth communication between mobile nodes for many critical applications. While the spatial modes of light offer a degree of freedom to increase the information capacity of an optical link, atmospheric turbulence can introduce severe distortion to the spatial modes and lead to data degradation. Here, we demonstrate experimentally a vector-beam-based, turbulence-resilient communication protocol, namely spatial polarization differential phase shift keying (SPDPSK), that can reliably transmit high-dimensional information through a turbulent channel without the need of any adaptive optics for beam compensation. In a proof-of-principle experiment with a controllable turbulence cell, we measure a channel capacity of 4.84 bits per pulse using 34 vector modes through a turbulent channel with a scintillation index of 1.09, and 4.02 bits per pulse using 18 vector modes through even stronger turbulence corresponding to a scintillation index of 1.54.

Resistance to turbulence is an ongoing challenge for point-to-point freespace communications. Here the authors present a protocol for encoding a large amount of information in vector beams that are transmittable through a moderately strong turbulent channel without adaptive beam compensation.

Self-healing property of focused circular Airy beams

We investigate the self-healing property of focused circular Airy beams (FCAB), and this property is associated with the transverse Poynting vector (energy flow) for a better interpretation. We both experimentally and numerically show the effect of the obstruction's position, size and shape on the self-healing property of FCAB. It is found that FCAB will heal if the obstruction is placed at the area between the two foci of FCAB, and it has the least influence on the FCAB when the obstruction is placed near the lens' rear focal plane, whereas FCAB cannot heal if the obstruction is out of the area between two foci. Our experimental results are in good agreement with numerical results.