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Computing metasurfaces are two-dimensional artificial nanostructures capable of performing mathematical operations on the input electromagnetic field, including its amplitude, phase, polarization, and frequency distributions. Rapid progress in the development of computing metasurfaces provide exceptional abilities for all-optical image processing, including the edge-enhanced imaging, which opens a broad range of novel and superior applications for real-time pattern recognition. In this paper, we review recent progress in the emerging field of computing metasurfaces for all-optical image processing, focusing on innovative and promising applications in optical analog operations, image processing, microscopy imaging, and quantum imaging.

As a revolutionary observation tool in life science, biomedical, and material science, optical microscopy allows imaging of samples with high spatial resolution and a wide field of view. However, conventional microscopy methods are limited to single imaging and cannot accomplish real-time image processing. The edge detection, image enhancement and phase visualization schemes have attracted great interest with the rapid development of optical analog computing. The two main physical mechanisms that enable optical analog computing originate from two geometric phases: the spin-redirection Rytov-Vlasimirskii-Berry (RVB) phase and the Pancharatnam-Berry (PB) phase. Here, we review the basic principles and recent research progress of the RVB phase and PB phase based optical differentiators. Then we focus on the innovative and emerging applications of optical analog computing in microscopic imaging. Optical analog computing is accelerating the transformation of information processing from classical imaging to quantum techniques. Its intersection with optical microscopy opens opportunities for the development of versatile and compact optical microscopy systems., Comment: 17 pages, 7 figures

Mathematically, any function can be expressed as the operation form of another function. Here, the idea is introduced into an optical system to generate structured light. In the optical system, a mathematical function is represented by an optical field distribution, and any structured light field can be generated by performing different optical analog computations for any input optical field. In particular, optical analog computing has a good broadband performance, as it can be achieved based on the Pancharatnam–Berry phase. Therefore, our scheme can provide a flexible way to generate broadband structured light, and this is theoretically and experimentally demonstrated. It is envisioned that our work may inspire potential applications in high-resolution microscopy and quantum computation.

By solving the Maxwell's equations in Fourier space, we find that the cross-polarized component of the dipole scattering field can be written as the second-order spatial differentiation of the copolarized component. This differential operation can be regarded as intrinsic which naturally arises as consequence of the transversality of electromagnetic fields. By introducing the intrinsic spatial differentiation into heralded single-photon microscopy imaging technique, it makes the structure of pure-phase object clearly visible at low photon level, avoiding any biophysical damages to living cells. Based on the polarization entanglement, the switch between dark-field imaging and bright-field imaging is remotely controlled in the heralding arm. This research enriches both fields of optical analog computing and quantum microscopy, opening a promising route toward a nondestructive imaging of living biological systems.

Several works on optical higher-order differential operations have recently attracted attention, particularly in image processing for edge detection. However, the inefficient differential operation leads to barriers to practical applications. Here, we report an anisotropic epsilon-near-zero slab to significantly enhance the transmission efficiency of second-order differentiators and discuss the Berry phase mechanism of this optical calculation process. Through a rigorous full-wave analysis of the process, we find that the conversion efficiency of differential operation depends on the spin-orbit interactions. Our scheme can strengthen the spin-orbit interaction by introducing anisotropy, which significantly enhances the transmission efficiency. We finally give transfer functions to reveal how to improve the efficiency and compare the quadratic coefficient among different systems. This highly efficient differentiation operation may develop significant applications in fast, compatible, and power-efficient ultrathin devices for data processing and biological imaging.

Imaging of transparent samples such as cells is important in the biomedicine field; however, insignificant absorption and weakly scattering limit the imaging contrast of phase objects. Here, we propose and demonstrate Brewster differential microscopy based on simple optical reflection at the glass interface. The combination of spin–orbit interaction of light and the Brewster effect can perform two-dimensional differentiation to the incident light distribution and, thus, achieves isotropic edge-enhanced imaging of pure phase objects, which overcomes the limitation of traditional one-dimensional imaging. Furthermore, by introducing bias retardation, we also reconstruct the original phase distribution. The proposed microscopic imaging mechanism does not involve any complex modulation devices and takes advantages of simple and low-cost structure. The results indicate that our research shows promising applications for nondestructive imaging of biological cells.

Cascaded operations play an important role in traditional electronic computing systems for the realization of advanced strategies. Here, we introduce the idea of cascaded operations into all-optical spatial analog computing. The single function of the firstorder operation is difficult to meet the requirements of practical applications in image recognition. The all-optical second-order spatial differentiators are implemented by cascading two first-order differential operation units, and the image edge detection of amplitude and phase objects are demonstrated. Our scheme provides a possible pathway towards the development of compact multifunctional differentiators and advanced optical analog computing networks., Comment: 11 pages, 4 figures

Optical analog computing operates on the amplitude, phase, polarization, and frequency distributions of the electromagnetic field through the interaction of light and matter. The differentiation operation is widely used in all-optical image processing technology, such as edge detection. Here, we propose a concise way to observe transparent particles, incorporating the optical differential operation that occurs on a single particle. The particle’s scattering and cross-polarization components combine into our differentiator. We achieve high-contrast optical images of transparent liquid crystal molecules. The visualization of aleurone grains (the structures that store protein particles in plant cells) in maize seed was experimentally demonstrated with a broadband incoherent light source. Avoiding the interference of stains, our designed method provides the possibility to observe protein particles directly in complex biological tissues.

In the previous works the spin Hall effect (SHE) of light was usually detected by the quantum weak measurement technique in which the complete information of the field was lost. In this work, we investigate the spatial evolution of the whole field in the SHE of light on reflection. First, we establish a model to describe the polarization state of reflected light and disclose its relationship with the SHE. Then, it is found that the reflected polarization generally becomes a vector field. The SHE due to the polarization gradient is manifested as a spin-dependent splitting. Further, it is found that both the incident angle and the incident polarization can affect the polarization of reflected light noticeably. Finally, the evolution of the energy flow is analyzed to disclose the underlying physical mechanism.

In this work, we report a general reflection model to describe the reflected behaviors of a Gaussian beam near photonic Dirac point at the optical interface. With spin polarized electromagnetic waves strikes near the single Dirac point on Dirac material interface, vortical phase distribution and spin inversion are demonstrated for reflected state, and we further develop a higher-order Poincar\'e sphere to describe the evolution of polarization states. It is possible to generate any desired Poincar\'e vortex beam on the sphere by modulating the incident polarization state of light. Moreover, we discuss the case of normal incidence around two adjacent Dirac points, reflection spectrum involves a couple of spin flip vortices corresponding to two points with the corresponding topological invariants, which are consistent with the Berry curvature and topological charge. These results can be extended to similar hyperbolic metamaterials with degenerate point, and inspire a different perspective for manipulating polarized vortex beam with photonic Dirac point.

We examine the noncommutation of Pancharatnam–Berry phase elements in the generation of vector beams. Any desirable vector beams on the two high-order Poincare spheres can be generated by incorporating the noncommutation and certain input polarization states. We show that the vector polarization states can be switched between two different high-order Poincare spheres by simply exchanging the order of two Pancharatnam–Berry phase elements. More importantly, the point-to-point conversion of vector beams makes our scheme highly flexible and easy to operate.

Significance Edge detection is a fundamental tool in image processing, computing, and machine vision. Compared with digital processes, optical analog approaches show enormous advantages owing to its intrinsic parallel nature for high-speed operation. Recently, optical metamaterials and metasurfaces have performed edge detection via analog spatial differentiation, which shows superior integration capability compared with the traditional bulky system. Unfortunately, experimental realization of optical-edge detection with metamaterials and metasurfaces remains challenging based on previous theoretical proposals. Here, we demonstrated a mechanism to realize an optical spatial differentiator consisting of a designed metasurface sandwiched by two orthogonally aligned linear polarizers. This approach relies on spin-orbit interaction of light and the metasurface, showing versatile edge-detection capability with exceptional quality., Optical edge detection is a useful method for characterizing boundaries, which is also in the forefront of image processing for object detection. As the field of metamaterials and metasurface is growing fast in an effort to miniaturize optical devices at unprecedented scales, experimental realization of optical edge detection with metamaterials remains a challenge and lags behind theoretical proposals. Here, we propose a mechanism of edge detection based on a Pancharatnam–Berry-phase metasurface. We experimentally demonstrated broadband edge detection using designed dielectric metasurfaces with high optical efficiency. The metasurfaces were fabricated by scanning a focused laser beam inside glass substrate and can be easily integrated with traditional optical components. The proposed edge-detection mechanism may find important applications in image processing, high-contrast microscopy, and real-time object detection on compact optical platforms such as mobile phones and smart cameras.

In recent decades, optical analog computing has attracted considerable interest in image processing and optical engineering. However, the optical analog computing system composed of traditional optical devices is bulky and difficult to integrate in practical applications. Here, we propose a method for inversely designing Pancharatnam–Berry phase metasurfaces based on specified optical computing. Derived from the evolution of the Pancharatnam–Berry phase on the Poincaré sphere, the special relationship between local optical axis structure and phase can be obtained. On this basis, we inversely design several metasurfaces and applied them into optical analog computing as well as all-optical image edge detection.

Photonic spin Hall effect (SHE) manifests itself as spin-dependent shift or splitting of a light beam, which is derived from spin–orbit interactions, and can be realized by breaking the rotation symmetry of light–matter interaction systems. Here, we demonstrate the observation of a photonic SHE by breaking the rotation symmetry of the optical field, while keeping the rotation symmetry of the inhomogeneous waveplate. The inhomogeneous waveplate constructed by dielectric nanostructures, introduces a spin-dependent Pancharatnam–Berry phase to the two spin components of the input beam, i.e., the left- and right-circular polarization components acquire exactly opposite vortex phases. During beam propagation, they experience opposite azimuthal rotations, and induce a four-lobe spin-dependent splitting in the azimuthal direction. In addition, the spin-dependent splitting becomes more evident upon beam propagation, and can be enhanced by increasing the topological orders of the nanostructures. For comparison, we also examine that no spin-dependent splitting can be observed when keeping the rotation symmetry of the incident optical field.

Since the construction of various topological photonic metamaterials, the Dirac degeneracy has been realized and provides a crucial opportunity to investigate the nonspecular effects [Goos-H\"anchen (GH) and Imbert-Fedorov (IF) shifts] of light at the unique optical interface. In this paper, we furnish a general and precise model to explore how photonic Dirac point affects nonspecular effects in Dirac metamaterial. Based on this model, the giant nonspecular effects are discovered when a Gaussian beam reflects in the vicinity of a photonic Dirac point. We confirm that the giant nonspecular effects are the consequence of degeneracy between Brewster angles and critical angle caused by the Dirac point. Furthermore, the ability to generate a vortex beam at the Dirac point has also been simply verified. We believe that our work is of underlying significance, and may be served as a reference for the measurement of Dirac point, even other degenerate points. Moreover, our precise model can also be used to describe the nonspecular effects in other analogous photonic systems.

Optical analog computing has attracted widespread attention in recent decades due to its advantages of lower consumption, higher efficiency, and real-time imaging in image processing. Here, we propose a two-dimensional optical analog computing scheme based on the Brewster effect. We experimentally demonstrate two-dimensional edge detection with high efficiency. By combining microscopy, our approach may develop some significant applications in cellular and molecular imaging.

Remotely switchable edge imaging is demonstrated on the basis of the metasurface illuminated by polarization-entangled photons., Metasurfaces consisting of engineered dielectric or metallic structures provide unique solutions to realize exotic phenomena including negative refraction, achromatic focusing, electromagnetic cloaking, and so on. The intersection of metasurface and quantum optics may lead to new opportunities but is much less explored. Here, we propose and experimentally demonstrate that a polarization-entangled photon source can be used to switch ON or OFF the optical edge detection mode in an imaging system based on a high-efficiency dielectric metasurface. This experiment enriches both fields of metasurface and quantum optics, representing a promising direction toward quantum edge detection and image processing with remarkable signal-to-noise ratio.

Bright-field imaging and edge imaging can extract different characteristics from objects, and therefore play important roles in image processing and pattern recognition. Here, we propose a fast, convenient, and electrically driven adjustable scheme to achieve tunable edge-enhanced images based on computing metasurfaces. The computing metasurface can perform spatial differential operation as optical waves propagate through it. This optical differential operation is polarization-dependent, thus any desirable contrast can be realized by the interplay between two orthogonal polarization components. By regulating the external voltages applied on the liquid-crystal phase plate, different phase retardances between two orthogonal polarization components are introduced; this allows us to quickly switch between the bright-field image and the edge image.

In modern optics, there are two general models to describe the behavior of light in graphene: the zero-thickness model and the slab model. The difference in physical phenomena predicted by the two models is very small, which is hardly distinguished by traditional measurement methods. Therefore, which model can describe the light–matter interaction in graphene more exactly is still a challenging issue. In this work, based on the sensitive optical phenomenon called the photonic spin Hall effect, the small difference can be magnified to a detectable level by the weak-value amplification. The experimental results show that the zero-thickness model can more accurately describe the interaction between light and monolayer or bilayer graphene, while the case of more than two layers, which can no longer be regarded as two-dimensional thickness, should be described by the slab model. Our results may provide information on light interacting with graphene for future investigation in photonics and optoelectronics.

Optical analog signal processing technology has been widely studied and applied in a variety of science and engineering fields, with the advantages of overcoming the low-speed and high-power consumption associated with its digital counterparts. Much attention has been given to emerging metasurface technology in the field of optical imaging and processing systems. Here, we demonstrate, for the first time, broadband two-dimensional spatial differentiation and high-contrast edge imaging based on a dielectric metasurface across the whole visible spectrum. This edge detection method works for both intensity and phase objects simply by inserting the metasurface into a commercial optical microscope. This highly efficient metasurface performing a basic optical differentiation operation opens up new opportunities in applications of fast, compactible and power-efficient ultrathin devices for data processing and biological imaging., High-contrast broadband two-dimensional edge detection is demonstrated for both the intensity and phase objects, which brings fast and power-efficient metasurfaces for optical information processing and imaging one step closer to the reality.

We theoretically propose the realization of a three-dimensional (3D) spin Hall effect (SHE) of light by tightly focusing a linearly polarized light. Owing to the spin-orbital interaction in focusing, the left and right circularly polarized components of light are partly converted into each other, acquiring opposite vortex phases. As the superposition of the vortex and the initial vortex-free light, the two polarized components exhibit spiral intensity patterns which rotate oppositely around the propagation axis. Consequently, the two spin components are distributed alternatively in both the azimuthal and the longitudinal directions, leading to a 3D array of split spin components, and the transverse intensity is also spit asynchronously. Moreover, that array is rotatable by the incident polarization, and the longitudinal spacing in the array can be controlled by the numerical aperture of the lens. The 3D SHE of light finds an additional degree of freedom available to control the spin state of the photon, which may be valuable in optical manipulation and quantum information.

How to measure the optical conductivity of atomically thin crystals is an important but challenging issue due to the weak light-matter interaction at the atomic scale. Photonic spin Hall effect, as a fundamental physical effect in light-matter interaction, is extremely sensitive to the optical conductivity of atomically thin crystals. Here, we report a precision measurement of the optical conductivity of graphene, where the photonic spin Hall effect acts as a measurement pointer. By incorporating with the weak-value amplification technique, the optical conductivity of monolayer graphene taken as a universal constant of $(0.993\pm0.005)\sigma_0$ is detected, and a high measuring resolution with $1.5\times10^{-8}\Omega^{-1}$ is obtained. For few-layer graphene without twist, we find that the conductivities increase linearly with layer number. Our idea could provide an important measurement technique for probing other parameters of atomically thin crystals, such as magneto-optical constant, circular dichroism, and optical nonlinear coefficient., Comment: 5 pages, 5 figures

The origin of spin-orbit interaction of light at a conventional optical interface lies in the transverse nature of the photon polarization: The polarizations associated with the plane-wave components experience slightly different rotations in order to satisfy the transversality after reflection or refraction. Recent advances in topological photonic materials provide crucial opportunities to reexamine the spin-orbit interaction of light at the unique optical interface. Here, we establish a general model to describe the spin-orbit interaction of light in the photonic Dirac metacrystal. We find a giant photonic spin Hall effect near the Dirac points when a Gaussian beam impinges at the interface of the photonic Dirac metacrystal. The giant photonic spin Hall effect is attribute to the strong spin-orbit interaction of light, which manifests itself as the large polarization rotations of different plane-wave components. We believe that these results may provide insight into the fundamental properties of the spin-orbit interaction of light in the topological photonic systems., 7 pages, 5 figures

Supplementary Material

Optical beam shifts, which mainly refer to the Goos–Hänchen shift and spin-Hall shift, widely exist in basic optical processes such as interface reflection and refraction. They are very sensitive to changes in the parameters of the materials that constitute the interface and therefore show great potential for applications in precision metrology and sensing. The interaction between light and two-dimensional (2D) atomic crystals is very weak, and beam shifts provide an alternative approach to explore and characterize 2D atomic crystals. In this paper, we first present a full-wave theory of beam shifts and introduce the experimental measurement of beam displacements with quantum weak measurement technology, and then review their applications in characterizing 2D atomic crystals, such as determining the layer number and measuring the optical conductivity of few-layer graphene. Finally, we discuss the beam displacements in twisted bilayer 2D atomic crystals and 2D atomic crystals under applied electric or magnetic fields.

Meta-lens represents a promising solution for optical communications and information processing owing to its miniaturization capability and desirable optical properties. Here, spin Hall meta-lens is demonstrated to manipulate photonic spin-dependent splitting induced by spin-orbital interaction in transverse and longitudinal directions simultaneously at visible wavelengths, with low dispersion and more than 90% diffraction efficiency. The broadband dielectric spin Hall meta-lens is achieved by integrating two geometric phase lenses with different functionalities into one single dynamic phase lens, which manifests the ultracompact, portable, and polarization-dependent features. The broadband spin Hall meta-lens may find important applications in imaging, sensing, and multifunctional spin photonics devices.

We reported an efficient ytterbium-doped vectorial fiber laser modulated by a low loss q-plate, which can manipulate the intra-cavity polarization evolution in a flexible and compact way. The vectorial fiber laser can deliver watt-level radially and azimuthally polarized laser around $1~\mu \text{m}$ from the same laser cavity with slope efficiency greater than 70.6%, and the polarization extinction ratio exceeding 97%. The polarization behavior of the radial and azimuthal polarization beams can be switched by simply controlling the intra-cavity polarization element.

A large cross-polarization (CP) rotation of light is found on the graphene surface experimentally and applied to measuring the layer number of graphene. First, a general propagation model for the polarization of light reflected on the graphene is established. By using this model, it is found that the CP effect rotates remarkably with the incident polarization near the pseudo-Brewster angle. More importantly, such a rotation differs noticeably for graphene surfaces with distinct layers, thereby providing a simple and efficient approach to detect the graphene layer number. Finally, the CP rotation is shown to be accompanied by the rotation of the spin Hall effect of light. Further experiments are performed to validate the theoretical results.

We report a graphene Q-switched ytterbium-doped fiber laser with switchable cylindrical vector beam output. The 6–8 layers CVD-grown graphene films were transferred to the target substrate by an ultrasonic processing method, and its saturation intensity and modulation depth are measured to be about 0.61 MW/cm2 and 13.2% at 1072 nm by the Z-scan technique. We used a nanograting spatially variant waveplate as an intracavity polarization controlling element to convert pulsed Gaussian beam to radially or azimuthally polarized beam in the fiber laser cavity. Stable Q-switching operation can be achieved with the output power up to 253 mW and pulse energy 7.73 μJ at the maximum incident pump power. The polarization extinction ratio of radially and azimuthally polarized beam is 97.4% and 96.9%, respectively. The experimental results suggest that the graphene can act as a potential nonlinear optical material to modulate pulsed fiber lasers with spatially inhomogeneous polarizations.

Optical spatial differentiation is important for applications in massively parallel computing and real-time image processing. This study makes use of the generalized spin Hall effect of light to perform optical spatial differentiation. Importantly, this scheme generally accompanies oblique light reflection and refraction at $a\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}y$ planar interface, regardless of material compositions or angles of incidence. Moreover, this spin-optical approach offers robust image processing to extract the boundaries of objects, where two distinct images can be stored in two different polarization states.