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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

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

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., Comment: 7 pages, 5 figures

Optical technology may provide important architectures for future computing, such as analog optical computing and image processing. Compared with traditional electric operation, optical operation has shown some unique advantages including faster operating speeds and lower power consumption. Here, we propose an optical full differentiator based on the spin-orbit interaction of light at a simple optical interface. The broadband optical operation is independent on the wavelength due to the nature of purely geometric. As an important application of the fully differential operation, the broadband image processing of edge detection is demonstrated. By adjusting the polarization of the incident beam, the one-dimension edge imaging at any desirable direction can be obtained. The broadband image processing of edge detection provides possible applications in autonomous driving, target recognition, microscopic imaging, and augmented reality., Comment: 20 pages, 7 figures

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

Optics naturally provides us with some powerful mathematical operations. Here we experimentally demonstrate that during reflection or refraction at a single optical planar interface, the optical computing of spatial differentiation can be realized by analyzing specific orthogonal polarization states of light. We show that the spatial differentiation is intrinsically due to the spin Hall effect of light and generally accompanies light reflection and refraction at any planar interface, regardless of material composition or incident angles. The proposed spin-optical method takes advantages of a simple and common structure to enable vectorial-field computation and perform edge detection for ultra-fast and energy-efficient image processing., Comment: 9 pages, 7 figures

The existence of Weyl nodes in the momentum space is a hallmark of a Weyl semimetal (WSM). A WSM can be confirmed by observing its Fermi arcs with separated Weyl nodes. In this paper, we study the spin- orbit interaction of light on the surface of WSM in the limit that the thickness is ultra-thin and the incident surface does not support Fermi arc. Our results show that the spin-dependent splitting induced by the spin-orbit interaction is related to the separation of Weyl nodes. By proposing an amplification technique called weak measurements, the distance of the nodes can be precisely determined. This system may have application in characterizing other parameters of WSM., Comment: 8 pages, 8 figures

We theoretically predict a giant quantized Goos-H\"{a}nchen (GH) effect on the surface of graphene in quantum Hall regime. The giant quantized GH effect manifests itself as an angular shift whose quantized step reaches the order of mrad for light beams impinging on a graphene-on-substrate system. The quantized GH effect can be attributed to quantized Hall conductivity, which corresponds to the discrete Landau levels in quantum Hall regime. We find that the quantized step can be greatly enhanced for incident angles near the Brewster angle. Moreover, the Brewster angle is sensitive to the Hall conductivity, and therefore the quantized GH effect can be modulated by the Fermi energy and the external magnetic field. The giant quantized GH effect offers a convenient way to determine the quantized Hall conductivity and the discrete Landau levels by a direct optical measurement., Comment: 6 pages, 6 figures

We examine the photonic spin Hall effect (SHE) in a graphene-substrate system with the presence of external magnetic field. In the quantum Hall regime, we demonstrate that the in-plane and transverse spin-dependent splittings in photonic SHE exhibit different quantized behaviors. The quantized SHE can be described as a consequence of a quantized geometric phase (Berry phase), which corresponds to the quantized spin-orbit interaction. Furthermore, an experimental scheme based on quantum weak value amplification is proposed to detect the quantized SHE in terahertz frequency regime. By incorporating the quantum weak measurement techniques, the quantized photonic SHE holds great promise for detecting quantized Hall conductivity and Berry phase. These results may bridge the gap between the electronic SHE and photonic SHE in graphene., Comment: 10 pages, 5 figures. Some improvements have been made

Perfect vortex beams are the orbital angular momentum (OAM)-carrying beams with fixed annular intensities, which provide a better source of OAM than traditional Laguerre- Gaussian beams. However, ordinary schemes to obtain the perfect vortex beams are usually bulky and unstable. We demonstrate here a novel generation scheme by designing planar Pancharatnam-Berry (PB) phase elements to replace all the elements required. Different from the conventional approaches based on reflective or refractive elements, PB phase elements can dramatically reduce the occupying volume of system. Moreover, the PB phase element scheme is easily developed to produce the perfect vector beams. Therefore, our scheme may provide prominent vortex and vector sources for integrated optical communication and micromanipulation systems., Comment: 14 pages, 5 figures, accepted for publication in Scientific Reports

The photonic spin Hall effect (SHE) can be regarded as a direct optical analogy of the SHE in electronic systems where a refractive index gradient plays the role of electric potential. However, it has been demonstrated that the effective refractive index fails to adequately explain the lightmatter interaction in atomically thin crystals. In this paper, we examine the spin-orbit interaction on the surface of the freestanding atomically thin crystals. We find that it is not necessary to involve the effective refractive index to describe the spin-orbit interaction and the photonic SHE in the atomically thin crystals. The strong spin-orbit interaction and giant photonic SHE have been predicted, which can be explained as the large polarization rotation of plane-wave components in order to satisfy the transversality of photon., Comment: 6 pages, 4 figures

We report the observation of the Goos-H\"anchen effect in graphene via a weak value amplification scheme. We demonstrate that the amplified Goos-H\"anchen shift in weak measurements is sensitive to the variation of graphene layers. Combining the Goos-H\"anchen effect with weak measurements may provide important applications in characterizing the parameters of graphene., Comment: 4 pages, 4 figures

Dielectric metasurfaces with spatially varying birefringence and high transmission efficiency can exhibit exceptional abilities for controlling the photonic spin states. We present here some of our works on spin photonics and spin-photonic devices with metasurfaces. We develop a hybrid-order Poincare sphere to describe the evolution of spin states of wave propagation in the metasurface. Both the Berry curvature and the Pancharatnam-Berry phase on the hybrid-order Poincare sphere are demonstrated to be proportional to the variation of total angular momentum. Based on the spin-dependent property of Pancharatnam-Berry phase, we find that the photonic spin Hall effect can be observed when breaking the rotational symmetry of metasurfaces. Moreover, we show that the dielectric metasurfaces can provide great flexibility in the design of novel spin-photonic devices such as spin filter and spin-dependent beam splitter., Comment: Invited contribution to the SPIE Optics+Photonics conference "Spintronics VIII", held in San Diego, August 9-13, 2015

Weak measurement is an important technique for detecting the tiny spin-dependent splitting in photonic spin Hall effect. The weak measurement is only valid when the probe wavefunction remains almost undisturbed during the procedure of measurements. However, it does not always satisfy such condition in some practical situations, such as in the strong-coupling regime or the preselected and postselected states are nearly orthogonal. In this paper, we develop a modified weak measurement for detecting photonic spin Hall effect when the probe wavefunction is distorted. We find that the measuring procedure with preselected and postselected ensembles is still effective. This scheme is important for us to detect the photonic spin Hall effect in the case where neither weak nor strong measurements can detect the spin-dependent splitting. The modified theory is valid not only in weak-coupling regime but also in the strong-coupling regime, and especially in the intermediate regime. The theoretical models of conventional weak measurements and modified weak measurements are established and compared. We show that the experimental results coincide well with the predictions of the modified theory., Comment: 9 pages, 8 figures, Accepted for publication in Physical Review A

We report the realization of spin-dependent splitting with arbitrary intensity patterns based on all-dielectric metasurface. Compared to the plasmonic metasurfaces, the all-dielectric metasurface exhibit more high transmission efficiency and conversion efficiency, which make it is possible to achieve the spin-dependent splitting with arbitrary intensity patterns. Our findings suggest a way for generation and manipulation of spin photons, and thereby offer the possibility of developing spin-based nanophotonic applications., Comment: 4 pages, 5 figures

In this work, we develop a hybrid-order Poincar\'{e} sphere to describe the evolution of polarization states of wave propagation in inhomogeneous anisotropic media. We extend the orbital Poincar\'{e} sphere and high-order Poincar\'{e} sphere to a more general form. Polarization evolution in inhomogeneous anisotropic media with special geometry can be conveniently described by state evolution along the longitude line on the hybrid-order Poincar\'{e} sphere. Similar to that in previously proposed Poincar\'{e} spheres, the Berry curvature can be regarded as an effective magnetic field with monopole centered at the origin of sphere and Berry connection can be interpreted as the vector potential. Both the Berry curvature and the Pancharatnam-Berry phase on the hybrid-order Poincar\'{e} sphere are demonstrated to be proportional to the total angular momentum. Our scheme provides a convenient method to describe the spin-orbit interaction in inhomogeneous anisotropic media., Comment: 6 pages, 3 figures

We report the realization of tunable spin-dependent splitting in intrinsic photonic spin Hall effect. By breaking the rotational symmetry of a cylindrical vector beam, the intrinsic vortex phases that the two spin components of the vector beam carries, which is similar to the geometric Pancharatnam-Berry phase, is no longer continuous in the azimuthal direction, and leads to observation of spin accumulation at the opposite edge of the beam. Due to the inherent nature of the phase and independency of light-matter interaction, the observed photonic spin Hall effect is intrinsic. Modulating the topological charge of the vector beam, the spin-dependent splitting can be enhanced and the direction of spin accumulation is switchable. Our findings may provide a possible route for generation and manipulation of spin-polarized photons, and enables spin-based photonics applications., Comment: 4 pages, 5 figures

Observation of photonic spin Hall effect (SHE) in dielectric-based metasurfaces with rotational symmetry breaking is presented. We find that the spin-dependent splitting is a unique angular splitting in the real position space, and is attributed to the space-variant Pancharatnam-Berry phase (PB). Breaking the rotational symmetry of the PB phase by misalignment of the central axes of the incident beam and the metasurface, the spin-dependent shift is observable. We show that the spin-dependent shift can be enhanced by increasing the rotation rate of the metasurface, so the metasurface provides a great flexibility in the manipulation of photonic SHE.

We present a simple and efficient method to generate any cylindrical vector vortex (CVV) beams based on two cascaded metasurfaces. The metasurface works as a space-variant Panchratnam-Berry phase element and can produce any desirable vortex phase and vector polarization. The first metasurface is used to switch the sign of topological charges associated with vortex, and the second metasurface is applied to manipulate the local polarization. This method allows us to simultaneously manipulate polarization and phase of the CVV beams., Comment: 9 pages, 5 figures

The photonic spin Hall effect (SHE) is generally believed to be a result of an effective spin-orbit coupling, which describes the mutual influence of the spin (polarization) and the trajectory of the light beam. The photonic SHE holds great potential for precision metrology owing to the fact that the spin-dependent splitting in photonic SHE are sensitive to the physical parameter variations of different systems. Remarkably, using the weak measurements, this tiny spin-dependent shifts can be detected with the desirable accuracy so that the corresponding physical parameters can be determined. Here, we will review some of our works on using photonic SHE for precision metrology, such as measuring the thickness of nanometal film, identifying the graphene layers, detecting the strength of axion coupling in topological insulators, and determining the magneto-optical constant of magnetic film., Comment: 10 pages, 6 figures. Invited contribution to the SPIE Optics+Photonics conference "Spintronics VII", held in San Diego, CA, August 17-21, 2014

We propose and experimentally demonstrate a novel interferometric approach to generate arbitrary cylindrical vector beams on the higher order Poincare sphere. Our scheme is implemented by collinear superposition of two orthogonal circular polarizations with opposite topological charges. By modifying the amplitude and phase factors of the two beams, respectively, any desired vector beams on the higher order Poincare sphere with high tunability can be acquired. Our research provides a convenient way to evolve the polarization states in any path on the high order Poincare sphere., Comment: 4 pages, 4 figures

We present a simple and convenient method to yield cylindrical vector (CV) beams and realize its polarization evolution on higher-order Poincare sphere based on inhomogeneous birefringent metasurface. By means of local polarization transformation of the metasurface, it is possible to convert a light beam with homogeneous elliptical polarization into a vector beam with any desired polarization distribution. The Stokes parameters of the output light are measured to verify our scheme, which show well agreement with the theoretical prediction. Our method may provide a convenient way to generate CV beams, which is expected to have potential applications in encoding information and quantum computation.

We develop a geometric photonic spin Hall effect (PSHE) which manifests as spin-dependent shift in momentum space. It originates from an effective space-variant Pancharatnam-Berry (PB) phase created by artificially engineering the polarization distribution of the incident light. Unlikely the previously reported PSHE involving the light-matter interaction, the resulting spin-dependent splitting in the geometric PSHE is purely geometrically depend upon the polarization distribution of light which can be tailored by assembling its circular polarization basis with suitably magnitude and phase. This metapolarization idea enables us to manipulate the geometric PSHE by suitably tailoring the polarization geometry of light. Our scheme provides great flexibility in the design of various polarization geometry and polarization-dependent application, and can be extrapolated to other physical system, such as electron beam or atom beam, with the similar spin-orbit coupling underlying., Comment: 11 pages, 4 figures

Photonic spin Hall effect (SHE) holds great potential applications in precision metrology. How to obtain a high measurement precision is an important issue to detect the photonic SHE. In this letter, we propose using optimal preselection and postselection in weak measurements to enhance the measurement precision. We find that the maximum weak value and pointer shift can be obtained with an optimal overlap of preselection and postselection states. These findings offer the possibility for improving the precision of weak measurements and thereby have possible applications for accurately characterizing the parameters of nanostructures., Comment: 4 pages, 4 figures

Recent developments in the field of photonic spin Hall effect (SHE) offer new opportunities for advantageous measurement of the optical parameters (refractive index, thickness, etc.) of nanostructures and enable spin-based photonics applications in the future. However, it remains a challenge to develop a tunable photonic SHE with any desired spin-dependent splitting for generation and manipulation of spin-polarized photons. Here, we demonstrate experimentally a scheme to realize the photonic SHE tunably by tailoring the space-variant Pancharatnam-Berry phase (PBP). It is shown that light beams whose polarization with a tunable spatial inhomogeneity can contribute to steering the space-variant PBP which creates a spin-dependent geometric phase gradient, thereby possibly realizing a tunable photonic SHE with any desired spin-dependent splitting. Our scheme provides a convenient method to manipulate the spin photon. The results can be extrapolated to other physical system with similar topological origins., Comment: 5 pages, 5 figures

In this paper we theoretically investigate the photonic spin Hall effect (SHE) of a Gaussian beam reflected from the interface between air and topological insulators (TIs). The photonic SHE is attributed to spin-orbit coupling and manifests itself as in-plane and transverse spin-dependent splitting. We reveal that the spin-orbit coupling effect in TIs can be routed by adjusting the axion angle variations. Unlike the transverse spin-dependent splitting, we find that the in-plane one is sensitive to the axion angle. It is shown that the polarization structure in magneto-optical Kerr effect is significantly altered due to the spin-dependent splitting in photonic SHE. We theoretically propose a weak measurement method to determine the strength of axion coupling by probing the in-plane splitting of photonic SHE.

An inhomogeneous anisotropic medium with specific structure geometry can apply the tunable spin-dependent geometrical phase to the light passing through the medium, and thus can be used to steer the spin-dependent splitting (SDS) of light. In this paper, we exemplify this inference by the q plate, an inhomogeneous anisotropic medium. It is demonstrated that when a linearly polarized light beam normally passes through a q plate, k-space SDS first occurs, and then the real-space SDS in the far-field focal plane of a converging lens is distinguishable. Interestingly, the SDS, described by the normalized Stokes parameter S3 shows a multilobe and rotatable splitting pattern with rotational symmetry. Further, by tailoring the structure geometry of the q plate and/or the incident polarization angle of light, the lobe number and the rotation angle both are tunable. Our result suggests that the q plate can serve as a potential device for manipulating the photon spin states and enable applications such as in nano-optics and quantum information., Comment: 5 pages, 5 figures

The spin Hall effect (SHE) of light is a useful metrological tool for characterizing the structure parameters variations of nanostructure. In this letter we propose using the SHE of light to identify the graphene layers. This technique is based on the mechanism that the transverse displacements in SHE of light are sensitive to the variations of graphene layer numbers., Comment: 4 pages, 4 figures

We reveal a large spin angular splitting of light beam on reflection at the Brewster angle both theoretically and experimentally. A simple weak measurements system manifesting itself for the built-in post-selection technique is proposed to explore this angular splitting. Remarkably, the directions of the spin accumulations can be switched by adjusting the initial handedness of polarization., Comment: 7 pages, 4 figures

In this paper, we present a systematic study of beam shifts and angular momenta of paraxial vortex beams at air-left-handed material (LHM) interfaces. It is shown that, compared to their counterparts at air-right-handed material (RHM) interfaces, the spatial Goos-H\"{a}nchen (GH) and Imbert-Fedorov (IF) shifts remains the same, while the angular GH and IF shifts are reversed, at air-LHM interfaces. The spatial and angular shifts of paraxial vortex beams have their respective origins in transverse angular momenta and transverse linear momenta. The spatial GH and IF shifts remain unreversed as a result of the both reversions of transverse angular momenta and z-component linear momentum, while the angular GH and IF shifts are reversed due to that the z-component linear momentum is reversed and the transverse linear momenta are unreversed, at air-LHM interfaces. In addition, we perform a quantitative analysis on spin-orbit angular momentum conversion and orbit-orbit angular momentum conversion, which further helps us understand the essence of vortex beam shifts at air-LHM interfaces and their fundamental distinctions with those at air-RHM interfaces., Comment: 11 pages, 6 figures, accepted for publication in Physical Review A

The optical path lengths travelled by rays across a wavefront essentially determine the resulting phase front irrespective of the shape of a medium according to the principle of equal optical path. Thereupon we propose a method for the transformation between two arbitrary wavefronts by a slab, i.e. the profile of the spatial separation between the two wavefronts is taken to be transformed to a plane surface. Interestingly, for the mutual conversion between planar and curved wavefronts, the method reduce to an inverse transformation method in which it is the reversed shape of the desired wavefront that is converted to a planar one. As an application, three kinds of phase transformation are realized and it is found that the transformation on phase is able to realize some important properties such as phase reversal or compensation, focusing, and expanding or compressing beams, which are further confirmed by numerical simulations. The slab can be applied to realizing compact electromagnetic devices for which the values of the refractive index or the permittivity and permeability can be high or low, positive or negative, or near zero, depending on the choice of coordinate transformations., Comment: 8 pages, 6 figures

We theorize the spin Hall effect of light (SHEL) on a nano-metal film and demonstrate it experimentally via weak measurements. A general propagation model to describe the relationship between the spin-orbit coupling and the thickness of the metal film is established. It is revealed that the spin-orbit coupling in the SHEL can be effectively modulated by adjusting the thickness of the metal film, and the transverse displacement is sensitive to the thickness of metal film in certain range for horizontal polarization light. Importantly, a large negative transverse shift can be observed as a consequence of the combined contribution of the ratio and the phase difference of Fresnel coefficients., Comment: 5 pages, 4 figures

We present a metamaterial-based random polarization control plate to produce incoherent laser irradiation by exploiting the ability of metamaterial in local polarization manipulation of beam upon transmission via tuning its local geometry. As a proof-of-principle, we exemplify this idea numerically in a simple optical system using a typical L-shaped plasmonic metamaterial with locally varying geometry, from which the desired polarization distribution can be obtained. The calculating results illustrate that this scheme can effectively suppress the speckle contrast and increase irradiation uniformity, which has potential to satisfy the increasing requirements for incoherent laser irradiation., Comment: 5 pages, 6 figures