Spin Hall Shift Research Articles

Photonic spin Hall effect in twisted few-layer anisotropic two-dimensional atomic crystals

Motivated by the emergence of stacked two-dimensional materials with a twist angle, we examine the photonic spin Hall effect in twisted few-layer anisotropic two-dimensional atomic crystals. By developing a generalized model for arbitrary layers of anisotropic two-dimensional atomic crystals, the photonic spin Hall effect of twisted few-layer black phosphorus without interlayer interaction is demonstrated and discussed. We find that the twist between different layers results in the arise of the in-plane spin Hall shift, and the shift is very sensitive to the twist angle. While the in-plane spin Hall shifts are symmetric about the origin as a function versus the twist angle, the transverse spin Hall shifts are symmetric about the axis. And the photonic spin Hall shifts exhibit periodic changes versus the thickness of the interlayer due to the optical Fabry-P\'erot resonance. The results may provide different aspects for analysis and control of the optical properties of twisted multilayer two-dimensional materials.

Incident‐Polarization‐Independent Spin Hall Effect of Light Reaching Half Beam Waist

AbstractThe spin Hall effect of light (SHEL), a spin‐dependent transverse splitting of light at an optical interface, is intrinsically an incident‐polarization‐sensitive phenomenon. Recently, an approach to eliminate the polarization dependence by equalizing the reflection coefficients of two linear polarizations has been proposed, but is only valid when the beam waist is sufficiently larger than the wavelength. Here, it is demonstrated that an interface, at which the reflection coefficients of the two linear polarizations are the same and so are their derivatives with respect to the incident angle, supports the polarization‐independent spin Hall shift, even when the beam waist is comparable to the wavelength. In addition, an isotropic–anisotropic interface that exhibits the polarization‐independent spin Hall shift over the entire range of incident angles is presented. Monte‐Carlo simulations prove that spin Hall shifts are degenerate under any polarization and reach a half of beam waist under unpolarized incidence. An application of the beam‐waist‐scale SHEL as a tunable beam‐splitting device that is responsive to the incident polarization is suggested. The spin Hall shift that is independent of the incident polarization at any incident angle will facilitate a wide range of applications including practical spin‐dependent devices and active beam splitters.

High-Resolution Determination of Kinetic Parameters of Sucrose Hydrolysis Based on Weak Measurement

We propose a high-resolution scheme for determining the kinetic parameters of sucrose hydrolysis based on the weak measurement, and the parameters including rate constant, half-life, activation energy and pre-exponential factor are experimentally determined. In the scheme, the postselection state of weak measurement is modified by the optical rotation angle in the process of sucrose hydrolysis, and the amplified spin-Hall shift acts as a probe for determining the kinetic parameters. The rate constant and half-life are obtained based on the time variations of amplified spin-Hall shifts under different reaction conditions of temperatures and hydrochloric acid concentrations. The corresponding activation energy and pre-exponential factor are also evaluated for explaining the physical mechanism which influences the rate constant and analyzing how to adjust the reaction conditions to predict or control the rate. The high resolution for optical rotation angle is achieved in our scheme, which can reach <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\rm {4}}{\rm {.9}} \times {\rm {10}}^{\rm {-4}}$</tex-math></inline-formula> degree with one order of magnitude improvement over the polarimeter. These results can provide a possibility for the determination of chemical kinetic parameters with high-precision, real-time, label-free and convenient effects.

Generalized analytic formula for spin Hall effect of light: shift enhancement and interface independence

Abstract The spin Hall effect of light (SHEL) is the microscopic spin-dependent splitting of light at an optical interface. Whereas the spin Hall shift under linearly polarized light is well-formulated, studies on the SHEL under elliptically or circularly polarized light have primarily relied on numerical computation. In this work, an explicit analytic formula for the spin Hall shift is derived under arbitrarily polarized incidence. Furthermore, from this explicit expression, we demonstrate that the spin Hall shift can be enhanced at any incident angle by using polarization degree of freedom and is independent of the Fresnel coefficients of an interface under circularly polarized light. The analytic formula will help us understand the SHEL under general polarization intuitively and realize unprecedented modulation of the SHEL.

Large photonic spin Hall effect in two dimensional semi-Dirac materials

A strong photonic spin Hall effect (PSHE) in the absence of external magnetic field is important to control the spin states of photons and design next-generation photonic devices based on spinotpics. Herein, we theoretically study the PSHE on the surface of semi-Dirac materials. We established a general model, by changing various incident conditions, to describe the spin-orbit interaction of light in semi-Dirac materials. When we made these changes, we found that a large PSHE arises from the intrinsic anisotropy in the dispersion of semi-Dirac materials. The in-plane (transverse) spin Hall shift is dozens times of λ i , where λ i is the wavelength of the incident photon. Both of them can be effectively tuned by adjusting the optical axis angle and the photon energy. The maximum of the total in-plane and transverse spin Hall shift is 83.91λ i and 19.65λ i , respectively, which is larger than those in conventional anisotropic two-dimensional materials and isotropic Dirac materials. Our results shed light on the spin-orbit coupling of light in semi-Dirac materials and pave the way for designing spin-optical devices.

Probing topological quantum phase transitions via photonic spin Hall effects in spin-orbit coupled 2D quantum materials

Topological photonics is an emerging field in photonics in which various topological and geometrical ideas are used to manipulate and control the behavior of light photons. The interplay between topological matter and the spin degree of freedom of photons provides new opportunities for achieving spin-based photonics applications. In this paper, the photonic spin Hall effect (PSHE) of reflected light from the surface of the topological silicene quantum systems subjected to external electric and radiation fields in the terahertz regime is theoretically investigated. By tuning the external electric and the applied laser fields, we can drive the silicenic system through different topological quantum phase transitions. We demonstrate that the in-plane and transverse spatial spin dependent shifts exhibit extreme values near Brewster’s angles and away from the optical transition frequencies. We reveal that the photonic spin Hall shifts are sensitive to the spin and valley indices as well as to the number of closed gaps. We believe that the spin and valley-resolved PSHE will greatly impact the research in spinoptics, spintronics, and valleytronics.

Vortex mode decomposition of the topology-induced phase transitions in spin-orbit optics

The topology-induced phase transition (TPT) in spin-orbit optics refers to a process of topological transition from one kind of spin-orbit interaction (e.g., spin-controlled vortex generation) to another (e.g., photonic spin-Hall effect). However, it is not clear in the TPT how a light beam evolves from a vortex state with a topological charge of \ifmmode\pm\else\textpm\fi{}2 to nonvortex states with spin-Hall shifts. Here, we examine the orbital angular momentum content (vortex harmonics) of a typical TPT process, i.e., the spin-orbit interactions of a light beam transmitted through an optically thin slab, based on vortex mode decomposition. It is found that the two kinds of spin-orbit interactions and the intermediate states can be described in a unified framework by considering the superposition and competition of three vortex modes with topological charges of 2, 1, and 0 (or \ensuremath{-}2, \ensuremath{-}1, and 0). These findings provide an alternative perspective for understanding the two spin-orbit interactions of light in a unified form and can be extended to the TPT-like processes in other physical systems.

Revisiting the anomalous spin-Hall effect of light near the Brewster angle

Optical spin-Hall effect (SHE) exhibits many intriguing features as a linearly polarized (LP) light beam strikes an interface at incident angles around the Brewster angle, but the underlying physics remains obscure. Here, we elucidate the physics through reanalyzing this problem employing rigorous calculations and the Berry phase concept. As a circularly polarized (CP) light beam strikes an optical interface, the reflected light beam contains two components, a spin-flipped abnormal mode acquiring geometric phases (thus exhibiting a spin-Hall shift) and a spin-maintained normal mode without such phases. Strengths of these two modes are determined by the incident angle and the optical properties of the interface. Under the LP incidence, however, a spin component inside the reflected light beam must be the sum of normal and abnormal components of reflected light beams corresponding to CP incidences with different helicity, which thus sensitively depends on the incident angle. In particular, at incident angles near the Brewster one, reflection coefficients for two CP components exhibit opposite signs, leading to significant destructive interferences between normal and abnormal modes, finally generating highly deformed reflected light patterns with anomalously enhanced spin-Hall shifts. These findings can be extended to both reflected and transmitted cases with Brewster-like behaviors. Our analyses reinterpret previously discovered effects, providing an alternative understanding on the SHE of light.

Tunable spin Hall shift of light from graphene-wrapped spheres.

Graphene has taken impressive roles in light manipulation and optical engineering. The most attractive advantage of graphene is its tunable conductivity that could be dynamically modulated by various means. In this paper, we show that the spin Hall shift of light is dynamically tunable via changing the Fermi level of the graphene-wrapped spheres. Such tunability is prominent when different modes interfere with each other, such as at the interference of electric and magnetic dipolar modes or at the interference of electric dipolar and electric quadrupole modes. The circular polarization degree in the near field clearly demonstrates the strength of spin-orbit interaction, which is associated with spin Hall shift of light in the far-field. In addition, the spin Hall effect is shown in far-field detection plane and should be observed in experiment. Our results provide insights into how the spin Hall effect could be tuned and add new perspective in designing optical super-resolution imaging techniques.

Measurement of the optical constants of monolayer MoS2 via the photonic spin Hall effect

How to explore the physical effect and characterize physical parameters in atomic scale crystals is still a challenging issue in modern optics. We detect the photonic spin Hall effect in monolayer MoS2 to study the atomic light-matter interaction. Due to the sensitive dependence of the spin-Hall shifts on the optical constants of MoS2, we propose this fundamental effect as a metrological tool for the parameter characterization. Combined with the weak-value technique, the experimental results show that the complex refractive index can be extracted by treating the atomically thin MoS2 as a homogeneous slab with an effective thickness. However, modeling the thin crystal as a surface current can determine the optical conductivity with a high measurement resolution. We believe this fast and precise measurement of optical parameters can provide a reliable approach to investigate optical properties for transition metal dichalcogenides.

Study of electric field vector, angular momentum conservation and Poynting vector of nonparaxial beams

The angular momentum (AM) of light, comprising spin and orbital AMs, is conserved and produces a spin-Hall shift in this process for paraxial beams. For nonparaxial beams, the spin and orbital AMs are non-separable and produce many changes in the beams’ spatial profile contrary to paraxial beams. These changes can be manifested as polarization modulation in the transverse plane, and conversion to orbital angular momentum (OAM) structured beams in the transverse and longitudinal planes, which can be estimated by studying the electric field vector in detail. We have calculated theoretically and simulated numerically the electric field vector components in the focal plane, to study the polarization modulation and AM conservation for OAM and Gaussian light beams of circular and linear polarizations and compared the results. Further, we have calculated and simulated the Poynting vector components for the corresponding fields to study the energy flow. We have considered the focusing of light beams using a high Numerical Aperture objective lens to obtain the nonparaxial beam, and presented a detailed theoretical analysis therein. The interpretation studies presented here are new, which may have many applications in nanophotonics and help in understanding the spin–orbit interaction at the fundamental level.

Weak Measurements in Nano-optics

Background: Weak measurement involves weak coupling between the system and the measuring device (pointer) enables large amplification and high precision measurement of small physical parameters. The outcome of this special measurement procedure involving nearly mutually orthogonal pre- and post-selection of states in such weakly interacting systems leads to weak value that can become exceedingly large and lie outside the eigenvalue spectrum of the measured observable. This unprecedented ability of weak value amplification of small physical parameters has been successfully exploited for various metrological applications in the optical domain and beyond. Even though it is a quantum mechanical concept, it can be understood using the classical electromagnetic theory of light and thus can be realized in classical optics. Objective: Here, we briefly review the basic concepts of weak measurement and weak value amplification, provide illustrative examples of its implementation in various optical domains. The applications involve measuring ultra-sensitive beam deflections, high precision measurements of angular rotation, phase shift, temporal shift, frequency shift and so forth, and expand this extraordinary concept in the domain of nano-optics and plasmonics. Methods: In order to perform weak value amplification, we have used Gaussian beam and spectral response as the pointer subsequently. The polarization state associated with the pointer is used as pre and post-selection device. Results: We reveal the weak value amplification of sub-wavelength optical effects namely the Goos-Hänchen shift and the spin hall shift. Further, we demonstrate weak measurements using spectral line shape of resonance as a natural pointer, enabling weak value amplification beyond the conventional limit, demonstrating natural weak value amplification in plasmonic Fano resonances and so forth. The discussed concepts could have useful implications in various nano-optical systems to amplify tiny signals or effects. Conclusion: The emerging prospects of weak value amplification towards the development of novel optical weak measurement devices for metrological applications are extensively discussed.

Photonic Spin Hall Effect Modified by Ultrathin Au Films and Monolayer Transition Metal Dichalcogenides in One-Dimensional Photonic Crystal

When the metal film becomes far thinner than the electron mean free path (EMFP) in their bulk counterpart, many exotic optical properties accompanied with numbers of novel applications may emerge. Herein, the photonic spin Hall effect (PSHE) occurring on the surface of one-dimensional photonic crystal consisting of ultrathin Au films, monolayer transition metal dichalcogenides (TMDCs), and one defective layer is investigated. The Au film thickness ranges from 2.4 to 40 nm which covers the thickness range below the EMFP (37.7 nm) in bulk Au. Results show that ultrathin Au films are more competent to enhance the PSHE than bulk Au film. In particular, the maximum spin-dependent transverse displacement (37.94 times of the incident wavelength) at the Au film thickness of 4.4 nm is more than 12-fold higher than that at the bulk Au film with thickness of 40 nm. Besides it may be due to the coupling between the short-range surface plasmon polaritons and the B excitonic resonance in monolayer WS2, among four monolayer TMDCs (i.e., MoS2, MoSe2, WS2, WSe2), the photonic crystal with monolayer WS2 gives the strongest PSHE. Additionally, evolutions of photonic spin Hall shifts with the refractive index of defective layer, incident wavelength, and incident angle are also studied in detail. These findings shed light on the superiority of ultrathin metal films for light manipulation in spinoptics and may provide new routes to tailor the optical helicity in nanophotonic devices.

Topologically-tuned spin Hall shift around Fano resonance.

The topological magnetoelectric effect is associated with the photonic spin-orbit interaction. However, due to the proportionate fine structure constant of the topological term, the topological magnetoelectric effect is usually weak. In this paper, we demonstrate that the axion term enables manipulation of the spin Hall shift of light around Fano resonance. And, the excited surface plasmon near the nanoparticle's interface could enhance the topological magnetoelectric effect for several orders. Numerical simulation of near field and far-field scattering confirms our theoretical results. Our work may pave the way to exploit the topological magnetoelectric effect in practical applications, such as optical sensing and nanoprobing.

Photonic spin Hall effect on the surfaces of type-I and type-II Weyl semimetals

Abstract Topological optics is an emerging research area in which various topological and geometrical ideas are being proposed to design and manipulate the behaviors of photons. Here, the photonic spin Hall effect on the surfaces of topological Weyl semimetal (WSM) films was studied. Our results show that the spin-dependent splitting (i.e. photonic spin Hall shifts) induced by the spin-orbit interaction is little sensitive to the tilt αt of Weyl nodes and the chemical potential μ in type-I WSM film. In contrast, photonic spin Hall shifts in both the in-plane and transverse directions present versatile dependent behaviors on the αt and μ in type-II WSM film. In particular, the largest in-plane and transverse spin Hall shifts appear at the tilts between −2 and −3, which are ~40 and ~10 times of the incident wavelength, respectively. Nevertheless, the largest spin Hall shifts for type-II WSM film with positive αt are only several times of incident wavelength. Moreover, the photonic spin Hall shifts also exhibit different variation trends with decreasing the chemical potential for different signs of αt in type-II WSM films. This dependence of photonic spin Hall shifts on tilt orientation in type-II WSM films has been explained by time-reversal-symmetry-breaking Hall conductivities in WSMs.

Ultrasensitive and real-time detection of chemical reaction rate based on the photonic spin Hall effect

A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. However, the precise and real-time detection of the reaction rate remains challenging due to its fast and dynamical process. In this paper, the photonic spin Hall effect is proposed to realize the ultrasensitive and real-time detection of the reaction rate of sucrose hydrolysis. By incorporating with quantum weak measurement, the photonic spin-Hall shift acts as the measurement pointer, and the optical rotation in the process of sucrose hydrolysis acts as the postselection state. The high measurement resolution with 1.25 × 10−4 degree is achieved due to the weak-value amplification in quantum weak measurement which outperforms the standard polarimeter. In our scheme, the amplified measurement pointer is real-time monitoring the chemical reaction process. It does not involve any mechanical adjustment of optical elements once the experimental setup is established and thereby realizes a real-time detection of the dynamic chemical reaction.

Ultrasensitive detection of ion concentration based on photonic spin Hall effect

We propose a unique application of the photonic spin Hall effect for ultrasensitive detection of the ion concentration in solution. By incorporating the quantum weak measurement, the photonic spin-Hall shift acts as the measurement pointer and the optical rotation of solution in the magnetic field acts as the postselection state. The optical rotation is related to the Faraday effect, which is sensitive to the ion concentration of the solution. The high measurement resolution with 1.4×10−4 degree for the optical rotation angle is achieved, which outperforms the standard polarimeter. Furthermore, the high resolution with 2×10−5mol/ml for the ion concentration is obtained due to the weak-value amplification in the quantum weak measurement. In our scheme, the ion concentration is real-time detected by the amplified spin-Hall shift and thereby provides possible applications in biochemical sensing and water-quality monitoring.

Landau quantisation of photonic spin Hall effect in monolayer black phosphorus

Abstract The photonic spin Hall effect (PSHE) is a promising candidate for controlling the spin states of photons and exploiting next-generation photonic devices based on spinoptics. Herein, the influences of a perpendicular magnetic field on the PSHE appearing on the surface of monolayer black phosphorus (BP) are investigated. Results reveal that both the in-plane and transverse spin-dependent shifts are quantised and show an oscillating pattern due to the splitting of Landau levels (LLs) induced by the external magnetic field B. And the oscillation period of spin Hall shifts gradually increases with strengthening B because of the increase of LL spacings. By contrast, for a fixed magnetic field, as the LL spacings become smaller and smaller with increasing the LL index, the oscillation period of spin Hall shifts gradually decreases as the photonic energy increases. Moreover, it is possibly due to the synergistic role of intrinsic anisotropy, high crystallinity, and quantisation-incurred localised decreases in beating-like complex conductivities of the BP film, giant spin Hall shifts, hundreds of times of the incident wavelength, are obtained in both transverse and in-plane directions. These unambiguously confirm the strong impact of the external magnetic field on the PSHE and shed important insights into understanding the rich magneto-optical transport properties in anisotropic two-dimensional atomic crystals.

Spin-Hall effect of light at a tilted polarizer.

We describe the spin-Hall effect of light (as well as the angular Goos-Hänchen effect) at a tilted linear-dichroic plate, such as a usual linear polarizer. Although the spin-Hall effect at a tilted polarizer was previously associated with the geometric spin-Hall effect of light (which was contrasted to the regular spin-Hall effect) [Phys. Rev. Lett.112, 113902 (2014) PRLTAO0031-900710.1103/PhysRevLett.112.113902], we show that the effect is actually an example of the regular spin-Hall effect that occurs at tilted anisotropic plates [Optica3, 1039 (2016) OPTIC82334-253610.1364/OPTICA.3.001039]. Moreover, our approach reveals the angular spin-Hall shift, which is absent in the "geometric" approach. We verify our theory experimentally using the method of quantum weak measurements.

Observation of diffractive-correction and spin-orbit interaction induced effects around the Brewster angle

We report the observation of splitting, rotation and spiraling behavior in the polarization components of the Laguerre–Gaussian beam, reflected around the Brewster angle for a TM-polarized input beam. The measurements carried out using Stokes parameters in addition show that the strength and behavior of the above-mentioned effects depend on the order of the Laguerre–Gaussian beam. These polarization effects appear to be a manifestation of the collaborative behavior of the diffraction-corrective longitudinal Goos–Hänchen and spin-orbit interaction induced transverse spin-Hall shifts, wherein the coupling between these shifts play a critical role. Except for the polarization splitting, other observed effects are absent for a TE polarized input beam. These studies are useful to understand the topological aspect of complex light field in various applications, including optical manipulation, wherein the source optical angular momentum has been point of discussion. Additionally, they can be used as a promising tool in the identification of the thickness of thin layer and optical sensing.