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The refractive index (RI) of biological tissues is a fundamental material parameter that characterizes how light interacts with tissues, making accurate measurement of RI crucial for biomedical diagnostics and environmental monitoring. A Janus sensor (JBS) is designed in this paper, and the photonic spin Hall effect (PSHE) is used to detect subtle changes in RI in biological tissues. The asymmetric arrangement of the dielectric layers breaks spatial parity symmetry, resulting in significantly different PSHE displacements during the forward and backward propagation of electromagnetic waves, thereby realizing the Janus effect. The designed JBS can detect the RI range of 1.3~1.55 RIU when electromagnetic waves are incident along the + z -axis, with a sensitivity of 96.29°/refractive index unit (RIU). In the reverse direction, blood glucose concentrations are identified by the JBS, achieving a sensitivity of 18.30°/RIU. Detecting different RI range from forward and backward scales not only overcomes the limitation that single-scale sensors can only detect a single RI range, but also provides new insights and applications for optical biological detection through high-sensitivity, label-free and non-contact detection.

This study presents a novel method leveraging surface wave-assisted photonic spin Hall effect (PSHE) to construct physical unclonable functions (PUFs). PUFs exploit inherent physical variations to generate unique Challenge-Response pairs, which are critical for hardware security and arise from manufacturing discrepancies, device characteristics, or timing deviations. We explore PSHE generation-based PUF design, expanding existing design possibilities. With recent applications in precise sensing and computing, PSHE offers promising performance metrics for our proposed PUFs, including an inter-Hamming distance of 47.50% , an average proportion of unique responses of 62.5% , and a Pearson correlation coefficient of - 0.198. The PUF token demonstrates robustness to simulated noise. Additionally, we evaluate security using a machine learning-based attack model, employing a multi-layer perceptron (MLP) regression model with a randomized search method. The average accuracy of successful attack prediction is 9.70% for the selected dataset. Our novel PUF token exhibits high non-linearity due to the PSHE effect, resilience to MLP-based attacks, and sensitivity to process variation., (© 2024. The Author(s).)

Quantum spin Hall (QSH) insulators are two-dimensional electronic materials that have a bulk band gap similar to an ordinary insulator but have topologically protected pairs of edge modes of opposite chiralities 1-6 . So far, experimental studies have found only integer QSH insulators with counter-propagating up-spins and down-spins at each edge leading to a quantized conductance G 0  = e 2 /h (with e and h denoting the electron charge and Planck's constant, respectively) 7-14 . Here we report transport evidence of a fractional QSH insulator in 2.1° twisted bilayer MoTe 2 , which supports spin-S z conservation and flat spin-contrasting Chern bands 15,16 . At filling factor ν = 3 of the moiré valence bands, each edge contributes a conductance 3 2 G 0 with zero anomalous Hall conductivity. The state is probably a time-reversal pair of the even-denominator 3/2-fractional Chern insulators. Furthermore, at ν = 2, 4 and 6, we observe a single, double and triple QSH insulator with each edge contributing a conductance G 0 , 2G 0 and 3G 0 , respectively. Our results open up the possibility of realizing time-reversal symmetric non-abelian anyons and other unexpected topological phases in highly tunable moiré materials 17-19 ., (© 2024. The Author(s), under exclusive licence to Springer Nature Limited.)

To the best of our knowledge, a novel tunable photonic spin Hall effect is proposed based on a pair of liquid crystal Pancharatnam-Berry (PB) lenses. Owing to the spin-dependent geometric phases, a PB lens focus or defocus the incident light field according to its spin angular momentum. By cascading two PB lenses with a small gap, the focus and defocus effects can be suppressed, and the transmitted light fields with opposite spin will be deflected toward opposite directions when the two PB lenses have a relative lateral displacement. The deflection angles vary linearly with the displacements, thus double-lines two-dimensional continuous beam scanning is achieved with a scanning angle of 39 o  × 39° and a beam diverging angle of 0.028 o  × 0.028°. The scanning beam is used to write different patterns on a 200 nm thick gold film. We believe this beam scanning system can find wide applications ranging from laser processing, Lidar, particle manipulation, to free space optical communications.

Two linked gear wheels in a micromachine can be simultaneously rotated in opposite directions by using a laser beam that has in its section areas the spin angular momentum (SAM) of the opposite sign. However, for instance, a cylindrical vector beam has zero SAM in the focus. We alter a cylindrical vector beam so as to generate areas in its focus where the SAM is of opposite signs. The first alteration is adding to the cylindrical vector beam a linearly polarized beam. Thus, we study superposition of two rotationally symmetric beams: those with cylindrical and linear polarization. We obtain an expression for the SAM and prove two of its properties. The first property is that changing superposition coefficients does not change the shape of the SAM density distribution, whereas the intensity changes. The second property is that maximal SAM density is achieved when both beams in the superposition have the same energy. The second perturbation is adding a spatial carrier frequency. We study the SAM density of a cylindrical vector beam with a spatial carrier frequency. Due to periodic modulation, upon propagation in space, such a beam is split into two beams, having left and right elliptic polarization. Thus, in the beam transverse section, areas with the spin of different signs are separated in space, which is a manifestation of the spin Hall effect. We demonstrate that such light beams can be generated by metasurfaces, with the transmittance depending periodically on one coordinate.

Optical differential operation is the basic principle of optical image edge detection, which has the advantages of high efficiency, simple structure and markerless compared with the traditional digital image processing methods. In this paper, we propose an optical differential operation with high contrast based on the photonic spin Hall effect in a Weyl semimetal, which enables to switch between one- and two-dimensional edge detection. Due to the unique optical and electrical properties of the Weyl semimetal, a transport model for the differential operation is established, which is closely related to the beam shifts. By tuning the incidence conditions, we effectively manipulate the in-plane and transverse shifts to switch differential operations between one and two dimensions. The contrast of the differential operation is further regulated by changing the physical parameters of the Weyl semimetal, and can be improved by two orders of magnitude compared to the conventional differentiator. This study provides new possibilities in edge detection and image processing owing to the advantages of switchable dimension and high contrast.

It is widely recognized that light exhibits a wave-particle duality. However, the explanation for the photonic spin Hall effect (PSHE) primarily relies on the wave nature of light as dictated by Maxwell's Equations. There is a lack of exploration into the particle nature of light in this regard. In this context, we offer a fresh interpretation of the PSHE from the perspective of particle nature of light. For the out-of-plane PSHE, the spin shifts result from the macroscopic manifestation of the conservation of spin-orbital angular momentum of one photon. For the in-plane PSHE, the spin shifts arise from the spread of in-plane wavevector. Based on the wave nature of light, we also obtain the same spin shifts, confirming the consistency of the wave-particle duality of light. Furthermore, we find that the spin shifts of the PSHE are not the overall displacement of photons with the same handedness, but the outcome of coherent superposition among photons of the same handedness. These discoveries further enhance our comprehension of the fundamental nature of the PSHE.

The spin Hall effect (SHE) allows efficient generation of spin polarization or spin current through charge current and plays a crucial role in the development of spintronics. While SHE typically occurs in non-magnetic materials and is time-reversal even, exploring time-reversal-odd (T-odd) SHE, which couples SHE to magnetization in ferromagnetic materials, offers a new charge-spin conversion mechanism with new functionalities. Here, we report the observation of giant T-odd SHE in Fe 3 GeTe 2 /MoTe 2 van der Waals heterostructure, representing a previously unidentified interfacial magnetic spin Hall effect (interfacial-MSHE). Through rigorous symmetry analysis and theoretical calculations, we attribute the interfacial-MSHE to a symmetry-breaking induced spin current dipole at the vdW interface. Furthermore, we show that this linear effect can be used for implementing multiply-accumulate operations and binary convolutional neural networks with cascaded multi-terminal devices. Our findings uncover an interfacial T-odd charge-spin conversion mechanism with promising potential for energy-efficient in-memory computing., (© 2024. The Author(s).)

Studying the mechanisms of the spin Hall effect (SHE) is essential for the fundamental understanding of spintronic physics. By now, despite the intensive studies of SHE on heavy metal (HM)/metallic magnet heterostructures, the SHE on HM/ferrimagnetic insulator (FMI) heterostructures still remains elusive. Here, we study the mechanism of SHE in the Pt/Tm3Fe5O12 (TmIG) heterostructure. We first tune the crystallinity and resistivity of Pt by an annealing method, and then study the spin-orbit torque (SOT) in the tuned-Pt/TmIG devices. The SOT generation efficiency per unit electric field and spin Hall angle were obtained, which are insensitive to the annealing temperature. We further demonstrate that the intrinsic contribution in the moderately dirty regime is responsible for the SHE in our Pt/TmIG bilayer. Our study provides an important piece of information for the SHE in FMI-based spintronic physics.

In this paper, we propose a precision method to measure the chiroptical signal of Artemisinin solutions using the photonic spin Hall effect (PSHE) on the Ce:YIG-YIG-SiO 2 structure as a probe. The effects of transmission distance, incident angles, applied magnetic fields of different directions, and beam waist of light on the weak measurement system are analytically investigated through simulations. It is found that decreasing the beam waist of the incident spot, increasing the incident angle, increasing the transmission distance, and adding a longitudinal magnetic field is conducive to enhancing the amplification transverse shift of PSHE, thus the measurement sensitivity is greatly improved. Based on the optimal weak measurement scheme, the detection limit for concentration measurement of artemisinin based on optical rotatory (OR) was reduced to 0.05 mg/ml. The measurement precision of the OR angle has been improved to 10 -7 rad.

By inserting the monolayer graphene between the balanced gain and loss layers, the graphene-incorporated quasi-parity-time (PT) symmetric structure is established. In this contribution, the introduction of graphene provides a new degree of freedom to manipulate the optical performance as well as the photonic spin Hall effect (SHE). The coherent perfect absorption (CPA)-laser mode still remains in the graphene-incorporated quasi-PT symmetric system, and the spin shift of transmitted light can be significantly enhanced (i.e., up to its upper limitation) in the vicinity of CPA-laser mode, which is 18 times larger than the value of a simple PT symmetric structure. In addition, the excitation of the CPA-laser mode and the huge spin shift of transmitted light can be achieved with the thin gain/loss layers, which will be conducive to the miniaturization of nanophotonic devices based on the photonic SHE in the future.

The multi-focus metalens can couple the light into multiple channels in optical interconnections, which is beneficial to the development of planar, miniaturized, and integrated components. We propose broadband photonic spin Hall effect (PSHE) driven multi-focus metalenses, in which each nanobrick plays a positive role for all focal points. Three PSHE driven metalenses with four, six, and eight focal points have been designed and investigated, respectively. Under the incidences of left-/right-handed circularly polarized (LCP/RCP) light, these metalenses can generate regularly distributed two, three, and four RCP/LCP focal points, respectively. The uniformity of the focusing intensity has been investigated in detail by designing an additional four six-focus metalenses with different focus distributions. The uniqueness of these metalenses makes this design philosophy very attractive for applications in spin photonics, compact polarization detection, multi-imaging systems, and information processing systems.

In this study, we present a theoretical study of the quantum spin Hall effect in InN/InGaN coupled multiple quantum wells with the individual well widths equal to two atomic monolayers. We consider triple and quadruple quantum wells in which the In content in the interwell barriers is greater than or equal to the In content in the external barriers. To calculate the electronic subbands in these nanostructures, we use the eight-band k∙p Hamiltonian, assuming that the effective spin-orbit interaction in InN is negative, which represents the worst-case scenario for achieving a two-dimensional topological insulator. For triple quantum wells, we find that when the In contents of the external and interwell barriers are the same and the widths of the internal barriers are equal to two monolayers, a topological insulator with a bulk energy gap of 0.25 meV can appear. Increasing the In content in the interwell barriers leads to a significant increase in the bulk energy gap of the topological insulator, reaching about 0.8 meV. In these structures, the topological insulator can be achieved when the In content in the external barriers is about 0.64, causing relatively low strain in quantum wells and making the epitaxial growth of these structures within the range of current technology. Using the effective 2D Hamiltonian, we study the edge states in strip structures containing topological triple quantum wells. We demonstrate that the opening of the gap in the spectrum of the edge states caused by decreasing the width of the strip has an oscillatory character regardless of whether the pseudospin-mixing elements of the effective Hamiltonian are omitted or taken into account. The strength of the finite size effect in these structures is several times smaller than that in HgTe/HgCdTe and InAs/GaSb/AlSb topological insulators. Therefore, its influence on the quantum spin Hall effect is negligible in strips with a width larger than 150 nm, unless the temperature at which electron transport is measured is less than 1 mK. In the case of quadruple quantum wells, we find the topological insulator phase only when the In content in the interwell barriers is larger than in the external barriers. We show that in these structures, a topological insulator with a bulk energy gap of 0.038 meV can be achieved when the In content in the external barriers is about 0.75. Since this value of the bulk energy gap is very small, quadruple quantum wells are less useful for realizing a measurable quantum spin Hall system, but they are still attractive for achieving a topological phase transition and a nonlocal topological semimetal phase.

Elements of micromachines can be driven by light, including structured light with phase and/or polarization singularities. We investigate here a paraxial vector Gaussian beam with an infinite number of polarization singularities residing evenly on a straight line. The intensity distribution is derived analytically and the polarization singularities are shown to exist only in the initial plane and in the far field. The azimuthal angle of the polarization singularities is shown to increase in the far field by π/2. We obtain the longitudinal component of the spin angular momentum (SAM) density and show that it is independent of the azimuthal angle of the polarization singularities. Upon propagation in free space, an infinite number of C-points is generated, where polarization is circular. We show that the SAM density distribution has a shape of four spots, two with left and two with right elliptic polarization. The distance to the transverse plane with the maximal SAM density decreases with decreasing distance between the polarization singularities in the initial plane. Generating such alternating areas with positive and negative SAM density, despite linear polarization in the initial plane, manifests the optical spin Hall effect. Application areas of the obtained results include designing micromachines with optically driven elements.

In this paper, the sub-wavelength transverse displacement of photonic spin Hall effect (PSHE) is significantly enhanced by the surface exciton polariton (SEP) for application in gas sensing. The transverse displacement of 14.4 times the wavelength of incident light is achieved with the SEP enhanced PSHE, which is about 3 times that of surface plasmon resonance enhanced PSHE. A gas sensor based on SEP enhanced PSHE is proposed for the detection of SO 2 , and the refractive index sensitivity of 6320.4 µm/RIU is obtained in the refractive index range from 1.00027281 to 1.00095981. These results undoubtedly demonstrate SEP to be a promising mechanism for PSHE enhancement, and open up new opportunities for highly sensitive gas sensing, biosensing, and chemical sensing.

Multiple works suggest the possibility of classification of quantum spin Hall effect with magnetic flux tubes, which cause separation of spin and charge degrees of freedom and pumping of spin or Kramers-pair. However, the proof of principle demonstration of spin-charge separation is yet to be accomplished for realistic, ab initio band structures of spin-orbit-coupled materials, lacking spin-conservation law. In this work, we perform thought experiments with magnetic flux tubes on [Formula: see text]-bismuthene, and demonstrate spin-charge separation, and quantized pumping of spin for three insulating states, that can be accessed by tuning filling fractions. With a combined analysis of momentum-space topology and real-space response, we identify important role of bands supporting even integer invariants, which cannot be addressed with symmetry-based indicators. Our work sets a new standard for the computational diagnosis of two-dimensional, quantum spin-Hall materials by going beyond the [Formula: see text] paradigm and providing an avenue for precise determination of the bulk invariant through computation of quantized, real-space response., (© 2023. The Author(s).)

Metasurface-based research with phase-change materials has been a prominent and rapidly developing research field that has drawn considerable attention in recent years. In this paper, we proposed a kind of tunable metasurface based on the simplest metal-insulator-metal structure, which can be realized by the mutual transformation of insulating and metallic states of vanadium dioxide (VO 2 ) and can realize the functional switching of photonic spin Hall effect (PSHE), absorption and beam deflection at the same terahertz frequency. When VO 2 is insulating, combined with the geometric phase, the metasurface can realize PSHE. A normal incident linear polarized wave will be split into two spin-polarized reflection beams traveling in two off-normal directions. When VO 2 is in the metal state, the designed metasurface can be used as a wave absorber and a deflector, which will completely absorb LCP waves, while the reflected amplitude of RCP waves is 0.828 and deflects. Our design only consists of one layer of artificial structure with two materials and is easy to realize in the experiment compared with the metasurface of a multi-layer structure, which can provide new ideas for the research of tunable multifunctional metasurface.

As the in-plane spin splitting (IPSS) has a broad application for the precision measurement and sensing, it is extremely important to explore its enhancement mechanism via the photonic spin Hall effect (PSHE). However, for a multilayer structure, the thickness in most of previous works is generally set as a fixed value, lacking the deeply exploration of the influence of thickness on the IPSS. By contrast, here we demonstrate the comprehensive understanding of thickness-dependent IPSS in a three layered anisotropic structure. As thickness increases, near the Brewster angle, the enhanced in-plane shift exhibits a thickness-dependently periodical modulation, besides with much wider incident angle than that in an isotropic medium. While near the critical angle, it becomes thickness-dependently periodical or linear modulation under different dielectric tensors of the anisotropic medium, no longer keeps almost constant in an isotropic medium. In addition, as exploring the asymmetric in-plane shift with arbitrary linear polarization incidence, the anisotropic medium could bring more obvious and wider range of thickness-dependently periodical asymmetric splitting. Our results deepen the understanding of enhanced IPSS, which is expected to promise a pathway in an anisotropic medium for the spin control and integrated device based on PSHE.

Elements of micromachines can be driven by light, including structured light with phase and/or polarization singularities. We investigate a paraxial vectorial Gaussian beam with multiple polarization singularities residing on a circle. Such a beam is a superposition of a cylindrically polarized Laguerre-Gaussian beam with a linearly polarized Gaussian beam. We demonstrate that, despite linear polarization in the initial plane, on propagation in space, alternating areas are generated with a spin angular momentum (SAM) density of opposite sign, that manifest about the spin Hall effect. We derive that in each transverse plane, maximal SAM magnitude is on a certain-radius circle. We obtain an approximate expression for the distance to the transverse plane with the maximal SAM density. Besides, we define the singularities circle radius, for which the achievable SAM density is maximal. It turns out that in this case the energies of the Laguerre-Gaussian and of the Gaussian beams are equal. We obtain an expression for the orbital angular momentum density and find that it is equal to the SAM density, multiplied by - m /2 with m being the order of the Laguerre-Gaussian beam, equal to the number of the polarization singularities. We consider an analogy with plane waves and find that the spin Hall affect arises due to the different divergence between the linearly polarized Gaussian beam and cylindrically polarized Laguerre-Gaussian beam. Application areas of the obtained results are designing micromachines with optically driven elements.

We investigate the spin angular momentum (SAM) of double-index cylindrical vector beams in tight focus. Such a set of beams is a generalization of the conventional cylindrical vector beams since the polarization order is different for the different transverse field components. Based on the Richards-Wolf theory, we obtain an expression for the SAM distribution and show that if the polarization orders are of different parity, then the spin Hall effect occurs in the tight focus, which is there are alternating areas with positive and negative spin angular momentum, despite linear polarization of the initial field. We also analyze the orbital angular momentum spectrum of all the components of the focused light field and determine the overwhelming angular harmonics. Neglecting the weak harmonics, we predict the SAM distribution and demonstrate the ability to generate the focal distribution where the areas with the positive and negative spin angular momentum reside on a ring and are alternating in pairs, or separated in different semicircles. Application areas of the obtained results are designing micromachines with optically driven elements.

The spin Hall effect of light, referring to the spin-dependent and transverse splitting of light at an optical interface, is an interface-dependent phenomenon. In contrast to this commonly accepted statement, it has been recently reported that the spin Hall effect under circularly polarized light is interface-independent. Despite this interface-independence, however, the reflection of the spin Hall shifted beam is mostly suppressed under near-normal incidence, where the spin Hall shift is large because of the handedness reversal that occurs during the reflection. Here we present a single-layered dielectric metasurface to realize the interface-independent and strengthened spin Hall effect of light. Numerical simulation results confirmed that the anisotropic geometry of the metasurface induced phase-reversed reflection for one linear polarization and phase-preserved reflection for the other, thereby strongly strengthening the reflection of the spin-Hall-shifted beam. Our work will pave a route toward the precise displacement of the beam at the nanoscale without perturbing its polarization state.

Though numerous studies of spin-orbit interaction (SOI) of light beams propagating along the optic axis of uniaxial crystals have been carried out, in previous studies, the initial input beams have cylindrical symmetry. In this case, the total system preserves cylindrical symmetry so that the output light after passing through the uniaxial crystal doesn't exhibit spin dependent symmetry breaking. Therefore, no spin Hall effect (SHE) occurs. In this paper, we investigate the SOI of a kind of novel structured light beam, grafted vortex beam (GVB) in uniaxial crystal. The cylindrical symmetry of the system is broken by the spatial phase structure of the GVB. As a result, a SHE determined by the spatial phase structure emerges. It is found that the SHE and evolution of the local angular momentum are controllable both by changing the grafted topological charge of the GVB and by employing linear electro-optic effect of the uniaxial crystal. This can open a new perspective to investigate the SHE of light beams in uniaxial crystals via constructing and manipulating the spatial structure of the input beams artificially, hence offers novel regulation capabilities of spin photon.

The quantized photonic spin Hall effect (PSHE) in the strained graphene-substrate system is predicted under a sub-Tesla external magnetic field, which is two orders of magnitude smaller than required to produce the quantized effect in the conventional graphene-substrate system. It is found that in-plane and transverse spin-dependent splittings in the PSHE, exhibit different quantized behaviors and are closely related to the reflection coefficients. Unlike the quantized PSHE in the conventional graphene-substrate system formed by the splitting of real Landau levels, the quantized PSHE in the strained graphene-substrate system is attributed to the splitting of pseudo-Landau levels caused by the pseudo-magnetic field and the lifting of valley degeneracy of the n ≠ 0 pseudo-Landau levels induced by the sub-Tesla external magnetic field. At the same time, the pseudo-Brewster angles of the system are also quantized with the change of Fermi energy. The sub-Tesla external magnetic field and the PSHE appear as quantized peak values near these angles. The giant quantized PSHE is expected to be used for direct optical measurements of the quantized conductivities and pseudo-Landau levels in the monolayer strained graphene.

Optical image processing based on the photonic spin Hall effect (SHE) has been gaining significant attention as a convenient and an accurate way for image edge detection. However, the recent edge imaging techniques depending on optical differentiation is mainly achieved by modulation of one-dimensional photonic SHE. Here, we theoretically predict the two-dimensional photonic SHE in the anisotropic metamaterial, and find that its longitudinal and transverse displacements exhibit spin-dependent property at filling factors with increasing incidence angle. As the transverse and in-plane displacements induced by the photonic SHE can be controlled by the filling factor of the crystal structure, the optical axis angle, and the incident angle, this intrinsical effect can be used to realize a tunable edge imaging. Interestingly, by changing the optical axis of the anisotropic metamaterial, the in-plane displacements are equal to the transverse displacements for a certain filling factor and the corresponding incident angle. Therefore, we propose a two-dimensional image edge detection method based on the photonic SHE in anisotropic metamaterial. Further numerical results validate the theoretical proposal.

Topological superconductors (TSC) become a focus of research due to the accompanying Majorana fermions. However, the reported TSC are extremely rare. Recent experiments reported kagome TSC AV 3 Sb 5 (A = K, Rb, and Cs) exhibit unique superconductivity, topological surface states (TSS), and Majorana bound states. More recently, the first titanium-based kagome superconductor CsTi 3 Bi 5 with nontrivial topology was successfully synthesized as a perspective TSC. Given that Cs contributes little to electronic structures of CsTi 3 Bi 5 and binary compounds may be easier to be synthesized, here, by first-principle calculations, we predict five stable nonmagnetic kagome compounds Ti 6 X 4 (X = Bi, Sb, Pb, Tl, and In) which exhibit superconductivity with critical temperature Tc = 3.8 K - 5.1 K, nontrivial Z 2 band topology, and TSS close to the Fermi level. Additionally, large intrinsic spin Hall effect is obtained in Ti 6 X 4 , which is caused by gapped Dirac nodal lines due to a strong spin-orbit coupling. This work offers new platforms for TSC and spintronic devices., Competing Interests: The authors declare no competing interests., (© 2022 The Author(s).)

The realization of an optical cloak that can hide a target object is no longer fiction, yet distinguishing the optically cloaked surface from our illusion remains an open problem. Here, the detection of a one-dimensional optically cloaked surface is presented by leveraging the spin Hall effect of light, the microscopic and transverse splitting of linearly polarized light at an optical interface into two circular polarizations. We first derive an analytical formula for the spin Hall shift at a planar surface with a linear phase gradient and demonstrate that the spin Hall effect of light at the cloaked surface differs from that at its perceived image. The theoretical description and numerical computation are generalized for a curved surface with a nonlinear phase gradient. Two approaches for examining optically cloaked surfaces are presented, in which the unknown incident angle and phase gradient are successfully reproduced. This work suggests the potential of the spin Hall effect of light in various applications, including anti-counterfeiting and security.

While vector fields naturally offer additional degrees of freedom for emulating spin, acoustic pressure field is scalar in nature, and it requires engineering of synthetic degrees of freedom by material design. Here we experimentally demonstrate the control of sound waves by using two types of engineered acoustic systems, where synthetic pseudo-spin emerges either as a consequence of the evanescent nature of the field or due to lattice symmetry. First, we show that evanescent sound waves in perforated films possess transverse angular momentum locked to their propagation direction which enables their directional excitation. Second, we demonstrate that lattice symmetries of an acoustic kagome lattice also enable a synthetic transverse pseudo-spin locked to the linear momentum, enabling control of the propagation of modes both in the bulk and along the edges. Our results open a new degree of control of radiation and propagation of acoustic waves thus offering new design approaches for acoustic devices., (© 2022. The Author(s).)

We investigate theoretically the photonic spin Hall effect (PSHE) in bilayer borophene metasurfaces. Based on the combined effect of the Fabry-Perot resonance of the bilayer system and the resonant interaction of individual meta-atoms in borophene metasurface which lead to the topological transition, it is found that there exist giant PSHE shifts of the transmitted beams which can be flexibly regulated by adjusting the twist angle of metasurface bilayers, incident angle, spacer refractive index and spacer thickness. Near the topological transition of borophene metasurface the magnitude of PHSE shifts in bilayer borophene metasurfaces is generally on the order of tens of wavelengths and even on the order of hundreds of wavelengths near the epsilon-near-zero (ENZ) regions. The manipulation frequency range of the large PSHE shifts can reach hundreds of terahertz or even picohertz through adjusting the ribbon width of borophene metasurface or the electron density for borophene. It is found that in bilayer borophene metasurfaces there exist the ultrahigh sensitivity of the PSHE shifts to spacer refractive index, which can be applied to design the refractive index sensors with high performance.

Although the spin Hall effect provides a pathway for efficient and fast current-induced manipulation of magnetization, application of spin-orbit torque magnetic random access memory with low power dissipation is still limited to spin Hall materials with low spin Hall angles or very high resistivities. This work reports a group of spin Hall materials, Pt 1 -x (TiO 2 nanocomposites, that combines a giant spin Hall effect with a low resistivity. The spin Hall angle of Pt x nanocomposites, that combines a giant spin Hall effect with a low resistivity. The spin Hall angle of Pt 1 -x (TiO 2 ) x in an yttrium iron garnet/Pt 1 double-layer heterostructure is estimated from a combination of ferromagnetic resonance, spin pumping, and inverse spin Hall experiments. A giant spin Hall angle 1.607 ± 0.04 is obtained in a Pt -x (TiO 2 ) x nanocomposite film, which is an increase by an order of magnitude compared with 0.051 ± 0.002 in pure Pt thin film under the same conditions. The great enhancement of spin Hall angle is attributed to strong side-jump induced by TiO 0.94 impurities. These findings provide a new nanocomposite spin Hall material combining a giant spin Hall angle, low resistivity and excellent process compatibility with semiconductors for developing highly efficiency current-induced magnetization switching memory devices and logic devices.2 ) 0.06 nanocomposite film, which is an increase by an order of magnitude compared with 0.051 ± 0.002 in pure Pt thin film under the same conditions. The great enhancement of spin Hall angle is attributed to strong side-jump induced by TiO 2 impurities. These findings provide a new nanocomposite spin Hall material combining a giant spin Hall angle, low resistivity and excellent process compatibility with semiconductors for developing highly efficiency current-induced magnetization switching memory devices and logic devices., (© 2022 The Authors. Advanced Science published by Wiley-VCH GmbH.)

In this paper, a photonic spin Hall effect (PSHE) sensor for high-precision refractive index (RI) detection and graphene layer number detection is proposed. Numerical analysis is performed by the transfer matrix method. The graphene material is introduced into the layered topology to stimulate the generation of PSHE phenomenon, and both H polarization and V polarization displacements occur simultaneously. The effects of parameters such as chemical potential, relaxation time, and external temperature on the PSHE shift are also discussed. The displacement of H polarization can be used for RI detection, and the measurement range (MR), sensitivity (S), figure of merit (FOM), and detection limit (DL) are 1.1-1.5, 127.85 degrees/RIU, 2412, and 2.08×10 -5 , respectively. The superior sensing performance provides a theoretical possibility for the detection of solids, liquids, and gases. The shift characteristic of V polarization is appropriate for detecting the number of layers in graphene, with a MR and S of 1-9 layers and 4.54 degrees/layer. The impacts of dielectric loss on sensor performance are also considered. We hope that the proposed PSHE multifunctional sensor can improve a theoretical idea for novel sensor design.

Light carries spin angular momentum, which, in the free space, is aligned to the direction of propagation and leads to intriguing spin Hall phenomena at an interface. Recently, it was shown that a transverse-spin (T-spin) state could exist for surface waves at an interface or for bulk waves inside a judiciously engineered metamaterial, with the spin oriented perpendicular to the propagation direction. Here, we demonstrate the spin Hall effect for transversely spinning light-a T-spin-induced beam shift at the interface of a metamaterial. It is found that the beam shift takes place in the plane of incidence, in contrast to the well-known Imbert-Fedorov shifts. The observed T-spin-induced beam shift is of geometrodynamical nature, which can be rendered positive or negative controlled by the orientation of T-spin of the photons. The unconventional spin Hall effect of light found here provides a previously unexplored mechanism for manipulating light-matter interactions at interfaces.

Current induced spin-orbit torques driven by the conventional spin Hall effect are widely used to manipulate the magnetization. This approach, however, is nondeterministic and inefficient for the switching of magnets with perpendicular magnetic anisotropy that are demanded by the high-density magnetic storage and memory devices. Here, we demonstrate that this limitation can be overcome by exploiting a magnetic spin Hall effect in noncollinear antiferromagnets, such as Mn 3 Sn. The magnetic group symmetry of Mn 3 Sn allows generation of the out-of-plane spin current carrying spin polarization collinear to its direction induced by an in-plane charge current. This spin current drives an out-of-plane anti-damping torque providing the deterministic switching of the perpendicular magnetization of an adjacent Ni/Co multilayer. Due to being odd with respect to time reversal symmetry, the observed magnetic spin Hall effect and the resulting spin-orbit torque can be reversed with reversal of the antiferromagnetic order. Contrary to the conventional spin-orbit torque devices, the demonstrated magnetization switching does not need an external magnetic field and requires much lower current density which is useful for low-power spintronics., (© 2022. The Author(s).)

Pancharatnam-Berry (PB) phase has become an effective tool to realize the photonic spin Hall effect (PSHE) in recent years, due to its capacity of enhancing the spin-orbit interaction. Various forms of PSHEs have been proposed by tailoring the PB phase of light, however, the propagation trajectory control of the separated spin states has not been reported. In this paper, we realize the oscillated spin-dependent separation by using the well-designed PB phase optical elements based on the transverse-to-longitudinal mapping of Bessel beams. Two typical oscillated PSHEs, i.e., the spin states are circulated and reversed periodically, are experimentally demonstrated with two PB phase elements fabricated with liquid crystal. The displacements and periods of these oscillations can be controlled by changing the transverse vector of the input Bessel beam. The proposed method offers a new degree of freedom to manipulate the spin-dependent separation, and provides technical supports for the application in spin photonics., (© 2022. The Author(s).)

Ultrafast THz radiation generation from ferromagnetic/nonmagnetic (FM/NM) spintronic heterostructures generally exploits the spin-charge conversion within the nonmagnetic layer and its interface with the ferromagnetic layer. Various possible sub-contributions to the underlying mechanism need to be exploited not only for investigating the intricacies at the fundamental level in the material properties themselves but also for improving their performance for broadband and high-power THz emission. Here, we report ultrafast THz emission from (CoFeB,Fe)/(Ta,Pt) bilayers at varying sample temperatures to unravel the role of intrinsic and extrinsic spin-charge conversion processes through the extracted values of spin-Hall conductivities. An enhanced THz emission along with temperature-dependent THz signal polarity reversal is observed in the case of annealed CoFeB/Ta. These results demonstrate a large interfacial contribution to the overall spin-Hall angle arising from the modified interface in the annealed CoFeB/Ta., Competing Interests: The authors declare no competing interests., (© 2022 The Author(s).)

The photonic spin Hall effect (SHE), manifesting itself as spin-dependent splitting of light, holds potential applications in nano-photonic devices and precision metrology. However, the photonic SHE is generally weak, and therefore its enhancement is of great significance. In this paper, we propose a simple method for enhancing the photonic SHE of reflected light by taking advantage of the gradient-refractive-index (GRIN) material. The transverse shifts for a normal (homogeneous) layer and linear GRIN structure with three different types (singly increasing, singly decreasing, and doubly linear ones) are theoretically investigated. We found that the doubly linear GRIN materials exhibit the prominent photonic SHE of reflected light, which is mainly due to the Fabry-Perot resonance. By optimizing the thickness and the lower (higher) refractive index of the doubly linear GRIN layer, the transverse shift for a horizontally polarized incident beam can nearly reach its upper limitation (i.e., half of the beam waist). These findings provide us a potential method to enhance the photonic SHE, and therefore establish a strong foundation for developing spin-based photonic devices in the future.

In this paper, the magnetically tunable and enhanced photonic spin Hall effect (PSHE) of reflected light beam at terahertz frequencies is achieved by using a multilayer structure where anisotropic graphene is inserted. This enhanced PSHE phenomenon results from the excitation of surface plasmon polariton (SPP) at the interface between two dielectric materials. By considering the 4×4 transfer matrix method and the quantum response of graphene, the PSHE of the reflected light can be enhanced by harnessing the anisotropic conductivity of graphene. Besides, the PSHE can be tuned through the external magnetic field and structural parameters. This enhanced and tunable PSHE approach is promising for fabricating anisotropic graphene-based terahertz spin devices and other applications in nanophotonics.

With the nanoscale integration advantage of near field photonics, controllable manipulation and transportation of micro-objects have possessed plentiful applications in the fields of physics, biology and material sciences. However, multifunctional optical manipulation like controllable transportation and synchronous routing by nano-devices are limited and rarely reported. Here we propose a new type of Y-shaped waveguide optical conveyor belt, which can transport and route particles along the structured waveguide based on the plasmonic spin-hall effect. The routing of micro-particles in different branches is determined by the optical force components difference at the center of the Y junction along the two branches of the waveguide. The influence of light source and structural parameters on the optical forces and transportation capability are numerically studied. The results illustrate that the proposed structured waveguide optical conveyor belt can transport the microparticles controllably in different branches of the waveguide. Due to the selective transportation ability of microparticles by the 2D waveguide, our work shows great application potential in the region of on-chip optical manipulation.

Generally, when an arbitrary polarized light beam is reflected or refracted from an isotropic interface, the spin splitting in photonic spin Hall effect (SHE) shows asymmetry properties. In this paper, we theoretically propose a phase compensation scheme to achieve the transformation from asymmetric spin splitting to symmetric spin splitting in photonic SHE. We experimentally acquire the spin splitting after phase compensation in the case of a 45 degrees linear polarized Gaussian light beam totally internally reflected from a prism-air interface. Particularly, whether or not phase compensation, the transverse shift of total barycenter of reflected field [i.e., the Imbert-Fedorov (IF) shift] does not change. These findings can solve this problem that asymmetric spin splitting cannot be observed by weak measurements.

The photoinduced inverse spin Hall effect (PISHE) has been studied in three dimensional (3D) topological insulator (TI) Bi 2 Te 3 thin films with different thicknesses (3, 5, 12 and 20 quintuple layer (QL)). The sign of the PISHE current flips only once in the 3- and 20-QL Bi 2 Te 3 films, but it flips three times in the 5-, 7- and 12-QL samples. The three-times sign flip is due to the superposition of the PISHE current of the top and bottom surface states in Bi 2 Te 3 films. By analyzing the x-ray photoelectron spectroscopy (XPS) of the Bi 2 Te 3 films, we find that the top surface of the 3- and 20-QL Bi 2 Te 3 films are severely oxidized, leading to only one sign flip in the PISHE. The PISHE contributed by the top and bottom surface states in Bi 2 Te 3 films have been successfully separated by fitting a theoretical model to the PISHE current. The impact of the bulk states on PISHE current has been determined. The PISHE current is also measured at different light powers, and all the measurement results are in good agreement with the theoretical model. In addition, it is found that the PISHE current in Bi 2 Te 3 films grown on Si substrate is more than two orders larger than that grown on SrTiO 3 substrates, which can be attributed to the larger absorption coefficient for Bi 2 Te 3 /Si samples. It is revealed that the PISHE current in 3D TI Bi 2 Te 3 is as large as 140 nA/W in the 3-QL Bi 2 Te 3 film grown on Si substrate, which is more than one order larger than that reported in GaAs/AlGaAs heterojunction (about 2 nA/W) and GaN/AlGaN heterojunction (about 1.7 nA/W). The giant PISHE current demonstrates that the TIs with strong SOC may have good application prospects in spintronic devices with high spin-to-charge conversion efficiency.

In this paper, all-metallic reflective metasurfaces comprising S-shape streamline structures are proposed to achieve the photonic spin-Hall effect with average cross-polarization conversion efficiency exceeding ∼84% in the range of 8-14 µm. By comparing with all-metallic nanobricks, it is demonstrated that the electric field coupling could be enhanced by constructing a similar split ring resonator between adjacent unit elements to further improve its efficiency and bandwidth. As a proof of concept, the photonic spin Hall effect and spin-to-orbit angular momentum conversion could be observed by two metadevices with the maximum diffraction efficiency of ∼95.7%. Such an all-metallic configuration may provide a platform for various high-efficiency electromagnetic components, catenary optics, and practical applications.

The spin Hall effect of light refers to a spin-dependent transverse splitting of light at a planar interface. Previous demonstrations to enhance the splitting have suffered from exceedingly low efficiency. Achievements of the large splitting with high efficiency have been reported in the microwave, but those in the optical regime remain elusive. Here, an approach to attain the large splitting with high efficiency in the near-infrared is proposed and experimentally demonstrated at 800 nm by using a dielectric metasurface. Modulation of the complex transmission of the metasurface leads to the shifts that reach 10λ along with efficiencies over 70% under two linear polarizations. Our work extends the recent attempts to achieve the large and efficient spin Hall effect of light, which have been limited only to the microwave, to the optical regime., (© 2022. The Author(s).)

The photonic spin Hall effect (SHE) has great potential in precision metrology due to its unique spin modulation characteristics. To improve its potential, the effective enhancement of detection precision has become an important issue. In this work, we theoretically and experimentally demonstrate the optimal weak measurement (optimal overlap of pre-selected and post-selected states) with arbitrary linear polarization incidence for both amplified transverse and in-plane shift. Also, based on photonic SHE, a method for arbitrary linear polarization angle detection is then proposed experimentally with a detection accuracy of 0.04 degree. It can provide a guidance for the weak measurement and enlarge the potential application of photonic SHE in field of precision measurement.

Electrically generated spin accumulation due to the spin Hall effect of Pt/GaAs is detected by circular polarized photoconductivity (CPPC), which shows electron spins with different polarizations accumulated around opposite sample boundaries. An optical absorption model incorporating spin is used to explain these features. The detailed analysis of the observed degree of circular polarization of the photocurrent strongly suggests that Pt and GaAs have the same spin accumulation length in the Pt/GaAs heterostructure.

Spin-orbit torques (SOT) enable efficient electrical control of the magnetic state of ferromagnets, ferrimagnets and antiferromagnets. However, the conventional SOT has severe limitation that only in-plane spins accumulate near the surface, whether interpreted as a spin Hall effect (SHE) or as an Edelstein effect. Such a SOT is not suitable for controlling perpendicular magnetization, which would be more beneficial for realizing low-power-consumption memory devices. Here we report the observation of a giant magnetic-field-like SOT in a topological antiferromagnet Mn 3 Sn, whose direction and size can be tuned by changing the order parameter direction of the antiferromagnet. To understand the magnetic SHE (MSHE)- and the conventional SHE-induced SOTs on an equal footing, we formulate them as interface spin-electric-field responses and analyzed using a macroscopic symmetry analysis and a complementary microscopic quantum kinetic theory. In this framework, the large out-of-plane spin accumulation due to the MSHE has an inter-band origin and is likely to be caused by the large momentum-dependent spin splitting in Mn 3 Sn. Our work demonstrates the unique potential of antiferromagnetic Weyl semimetals in overcoming the limitations of conventional SOTs and in realizing low-power spintronics devices with new functionalities., (© 2021. The Author(s).)

In this paper, we show theoretically that the spin-dependent transverse shift of the transmitted photonic spin Hall effect (SHE) through layered structure cannot exceed half of the incident beam waist. Exact conditions for obtaining the upper limit of the transmitted SHE are clarified in detail. In addition, different from the popular view in many investigations, we find that there is no positive correlation between the spin-dependent transverse displacement and the ratio between the Fresnel transmission coefficients (t p , t s ). In contrast, the optimal transmission ratio is determined by the incident angle and the beam waist. Moreover, two conventional transmission structures are selected and studied in detail. The characteristics of the transverse displacements obtained are in very good agreement with our theoretical conclusions. These findings provide a deeper insight into the photonic spin Hall phenomena and offer a guide for future related research., (© 2021. The Author(s).)

In this work, based on the spin Hall effect of light (SHEL), by considering the surface plasmon resonance (SPR) effect, a multi-functional detecting and controllable refractive index (RI) sensing structure containing sodium is theoretically established. The results reveal that the sodium layer has great influence on transverse shift (TS) of SHEL, while the polymethyl methacrylate (PMMA) layer has a large impact on the resonance angle. In the symmetrical distribution of TS, sodium has obvious advantages over gold and silver in the TS and sensitivity. The quantitative relationship between the TS and the RI of the sensing medium is established. Fermi energy, thicknesses of PMMA and sodium can be adjusted to measure the RI of three different orders. Remarkably, the sensitivity can be controlled by changing the thickness of sodium. The structure can also be used to measure the resonance angle and Fermi energy. Therefore, besides the advantages of sodium, this work realizes controllable sensing of RI and the functions of resonance angle and Fermi energy detecting. These studies may open avenues for the application of optical RI sensors and the precision measurement of other physical quantities.

Topological corner state has attracted much research interests since it does not obey the conventional bulk-edge correspondence and enables tightly confined light within small volumes. In this work, we demonstrate an enhanced second harmonic generation (SHG) from a topological corner state and its directional emission. To this end, we design an all-dielectric topological photonic crystal based on optical quantum spin Hall effect. In this framework, pseudospin states of photons, topological phase, and topological corner state are subsequently constructed by engineering the structures. It is shown that a high Q-factor of 3.66×10 11 can be obtained at the corner state, showing strong confinement of light at the corner. Consequently, SHG is significantly boosted and manifests directional out-of-plane emission. More importantly, the enhanced SHG has robustness against a broad class of defects. These demonstrated properties offer practical advantages for integrated optical circuits.

The discovery of Photonic spin Hall effect (PSHE) on surface plasmon polaritons (SPPs) is an important progress in photonics. In this paper, a method of realizing multi-channel PSHE in two-dimensional metal-air-metal waveguide is proposed. By modulating the phase difference [Formula: see text] and polar angle [Formula: see text] of the dipole source, the SPP can propagate along a specific channel. We further prove that PSHE results from the component wave interference theory. We believe that our findings will rich the application of SPPs in optical devices.

Spin Hall effect (SHE) of Laguerre-Gaussian (LG) beams reflected and transmitted in parity-time (PT) symmetric metamaterials are investigated near the coherent-perfect-absorption (CPA)-laser point and exceptional points (EPs). The numerical results show that large transverse shifts occur at the CPA-laser point regardless of the incident direction. But at EPs, the SHE increases at one side and disappears at the other side, thus achieving the intense SHE of the reflected light beams at the specified side incidence. In addition, it is found that Bragg oscillation can be generated by increasing the period number of PT symmetric metamaterial layers, thus increasing the number of formants in transverse displacement. In particular, the transverse shift peaks of the transmitted beams merge into a positive peak when the incident angle is close to 90 ∘ and does not change basically with the increasing of Im(ɛ), which can also be considered as a strong tolerance to the variation of Im(ɛ). This feature is expected to realize a new type of optoelectronic devices with anti-interference performance. These results provide a feasible path for the modulation of spin Hall effect of light (SHEL) and provide the possibility for the development of new nanophotonic devices.

We investigated the optical spin Hall effect (OSHE) of the light field from a closed elliptical metallic curvilinear nanoslit instead of the usual truncated curvilinear nanoslit. By making use of the characteristic bright spots in the light field formed by the noncircular symmetry of the elliptical slit and by introducing a method to separate the incident spin component (ISC) and converted spin component (CSC) of the output field, the OSHE manifested in the spot shifts in the CSC was more clearly observable and easily measurable. The slope of the elliptical slit, which was inverse along the principal axes, provided a geometric phase gradient to yield the opposite shifts of the characteristic spots in centrosymmetry, with a double shift achieved between the spots. Regarding the mechanism of this phenomenon, the flip of the spin angular momentum (SAM) of CSC gave rise to an extrinsic orbital angular momentum corresponding to the shifts of the wavelet profiles of slit elements in the same rotational direction to satisfy the conservation law. The analytical calculation and simulation of finite-difference time domain were performed for both the slit element and the whole slit ellipse, and the evolutions of the spot shifts as well as the underlying OSHE with the parameters of the ellipse were achieved. Experimental demonstrations were conducted and had consistent results. This study could be of great significance for subjects related to the applications of the OSHE.