Optical Spin Hall Effect Research Articles

Spin-Hall conductivity and optical characteristics of noncentrosymmetric quantum spin Hall insulators: the case of PbBiI

Quantum spin Hall insulators have attracted significant attention in recent years. Understanding the optical properties and spin Hall effect in these materials is crucial for technological advancements. In this study, we present theoretical analyses to explore the optical properties, Berry curvature and spin Hall conductivity of pristine and perturbed PbBiI using the linear combination of atomic orbitals and the Kubo formula. The system is not centrosymmetric and it is hosting at the same time Rashba spin-splitting and quantized spin Hall conductivity. Our calculations reveal that the electronic structure can be modified using staggered exchange fields and electric fields, leading to changes in the optical properties. Additionally, the spin Berry curvature and spin Hall conductivity are investigated as a function of the energy and temperature. The results indicate that due to the small dynamical spin Hall conductivity, generating an ac spin current in the PbBiI requires the use of external magnetic fields or magnetic materials.

Coherent optical spin Hall transport for polaritonics at room temperature.

Spin or valley degrees of freedom hold promise for next-generation spintronics. Nonetheless, the macroscopic coherent spin current formations are still hindered by rapid dephasing due to electron scattering, specifically at room temperature. Exciton polaritons offer excellent platforms for spin-optronic devices via the optical spin Hall effect. However, this effect could neither be unequivocally observed at room temperature nor be exploited for practical spintronic devices due to the presence of strong thermal fluctuations or large linear spin splitting. Here we report the observation of room-temperature optical spin Hall effect of exciton polaritons, with the spin current flow over 60 μm in a formamidinium lead bromide perovskite microcavity. We provide direct evidence of long-range coherence in the flow of polaritons and the spin current carried by them. Leveraging the spin Hall transport of polaritons, we further demonstrate two polaritonic devices, namely, a NOT gate and a spin-polarized beamsplitter, advancing the frontier of room-temperature polaritonics in perovskite microcavities.

Design of a beam splitter based on an adjustable beam-splitting ratio of a hexagonal star-like topological photonic crystal

We propose a new, to the best of our knowledge, mechanism to realize topological phase transition, that is, in a hexagonal star-like honeycomb lattice photonic crystal (PC), the optical quantum spin Hall effect (QSHE) can be realized by changing the materials of the outer or inner ring dielectric rods in the cells. We calculated the energy band and analyzed the topological phase transition law of a hexagonal star-like honeycomb PC. By changing the permittivity of the PC, the disturbance is introduced to the edge state. It is found that with the decrease of the permittivity of the PC, the gap decreases, the lower boundary state gradually redshifts, and the maximum transmittance in the straight waveguide can reach 98.8%. On this basis, a topological beam splitter was designed and analyzed. Results show that the beam splitting ratio obtained by the system is in the wide range of 0.2–3.5. Our research enriches the implementation of topological photonics, provides potential applications for topological boundary states in terahertz technology, and offers a new avenue for the design of current optical integrated devices.

Quasicrystal metasurface for dual functionality of holography and diffraction generation

Quasicrystal has attracted lots of attention since its discovery because of the mathematically non-periodic arrangement and physically unique diffraction patterns. By combining the quasi-periodic features of quasicrystal and the special rotational symmetry with metasurface, many novel phenomena and applications are proposed such as optical spin-Hall effect, non-linear far-field radiation control, and broadband polarization conversion. However, the additional functions and effects brought by phase and amplitude modulation on quasicrystal arrangement still lack research. Here, we design and fabricate a dielectric quasicrystal metasurface which can simultaneously reconstruct holographic images and exhibit diffraction patterns by assembling the nanostructures in a quasi-periodic array. Most importantly, we combine the global arrangement of metasurfaces with the local responses (phase and amplitude) of meta-atoms for achieving the dual functionality. Furthermore, we also suppress the zero diffraction order in the far-field based on the quasi-momentum matching rule. The proposed method has great mathematical importance and explores new possibilities for multifunctional meta-devices for holographic display, optical switching and anti-counterfeiting.

Optical spin hall effect in exciton-polariton condensates in lead halide perovskite microcavities.

An exciton-polariton condensate is a hybrid light-matter state in the quantum fluid phase. The photonic component endows it with characters of spin, as represented by circular polarization. Spin-polarization can form stochastically for quasi-equilibrium exciton-polariton condensates at parallel momentum vector k|| ∼ 0 from bifurcation or deterministically for propagating condensates at k|| > 0 from the optical spin-Hall effect (OSHE). Here, we report deterministic spin-polarization in exciton-polariton condensates at k|| ∼ 0 in microcavities containing methylammonium lead bromide perovskite (CH3NH3PbBr3) single crystals under non-resonant and linearly polarized excitation. We observe two energetically split condensates with opposite circular polarizations and attribute this observation to the presence of strong birefringence, which introduces a large OSHE at k|| ∼ 0 and pins the condensates in a particular spin state. Such spin-polarized exciton-polariton condensates may serve not only as circularly polarized laser sources but also as effective alternatives to ultracold atom Bose-Einstein condensates in quantum simulators of many-body spin-orbit coupling processes.

Focusing of linearly polarized optical vortex and a Hall effect

Polarization of a higher-order cylindrical vector beam (CVB) is known to be locally linear. The higher the beam order, the larger number of full circles the local linear polarization vector makes around the optical axis. It is also known that the CVB with radially symmetric amplitude has zero spin angular momentum (SAM) and zero orbital angular momentum (OAM) both in the initial plane and in the focal plane (because in both Cartesian components of the vector field, the angular derivative of phase is zero). We show here that near the focal plane of the CVB (i.e. before and beyond the focus), an even number of local subwavelength areas with rotating polarization vectors are generated. In addition, in the neighboring areas, the polarization vectors are rotating in the opposite directions. Thus, the longitudinal components of the SAM vector in such neighboring areas are of different sign. After passing through the focal plane, the rotation direction of the polarization vector at each point of the beam cross-section changes to the opposite one. Such a spatial separation of the left and right rotation of the polarization vectors is a manifestation of the optical spin Hall effect.

Focusing a cylindrical vector beam and the Hall effect

Polarization of a higher-order cylindrical vector beam (CVB) is known to be locally linear. The higher the beam order, the larger number of full circles the local linear polarization vector makes around the optical axis. It is also known that the CVB with radially symmetric amplitude has zero spin angular momentum (SAM) and zero orbital angular momentum (OAM) both in the initial plane and in the focal plane (because in both Cartesian components of the vector field, the angular derivative of phase is zero). We show here that near the focal plane of the CVB (i.e. before and beyond the focus), an even number of local subwavelength areas with rotating polarization vectors are generated. In addition, in the neighboring areas, the polarization vectors are rotating in the opposite directions. Thus, the longitudinal components of the SAM vector in such neighboring areas are of different sign. After passing through the focal plane, the rotation direction of the polarization vector at each point of the beam cross-section changes to the opposite one. Such a spatial separation of the left and right rotation of the polarization vectors is a manifestation of the optical spin Hall effect.

Visualization of the optical spin Hall effect in out-of-plane refraction

The traditional law of refraction defines the incidence plane as the plane including the incident beam wavevector and the surface normal vector at the interface of two different optical media. The optical spin Hall effect (OSHE) refers to the spin-dependent transverse shift of the refracted beam perpendicular to the incidence plane. In this Letter, we demonstrate that OSHE in out-of-plane refraction can be detected and visualized in the far-field, even at small and normal incidence angles. The extent of spin-dependent photon spatial separation induced by anomalous refraction can be customized by manipulating the 2D additive momentum from the metasurface. Experimental visualization of the OSHE confirms the existence of a new, to the best of our knowledge, plane to describe the OSHE of the refracted beam outside the incidence plane.

Analogue of Charge Conjugation in the Optical Spin Hall Effect

Analogue of Charge Conjugation in the Optical Spin Hall Effect

Spin angular momentum and angular harmonics spectrum of two-order polarization vortices at the tight focus

We investigate the spin angular momentum (SAM) of two-order cylindrical vector beams at the tight focus. Such beams are a generalization of the conventional cylindrical vector beams since the transverse field components on the Cartesian axes have different polarization orders. Using the Richards-Wolf approximation, we derive an expression for the longitudinal component of the SAM density distribution. We show that if the polarization indices are of different parity then, an optical spin Hall effect arises at the tight focus, meaning that alternating areas with positive and negative SAM are originated although the initial light field is linearly polarized. We study the angular harmonics spectrum of all the components of the focused light field and determine the predominant angular harmonics. Then, neglecting the insignificant harmonics, we define the shape of the longitudinal component of the SAM density distribution and demonstrate the possibility of generating a focal SAM distribution where the areas with positive and negative SAM reside on a circle as alternating pairs or separated into different half-circles.

Spin Hall Effect in Paraxial Vectorial Light Beams with an Infinite Number of Polarization Singularities.

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.

Spin angular momentum at the tight focus of a cylindrical vector beam with an imbedded optical vortex

We discuss sharp focusing of a light field that possess a double (phase + polarization) singularity. An exact analytical expression for the longitudinal projection of the spin angular momentum (SAM) vector at the focus is deduced based on a Richards-Wolf approach. The expression deduced suggests that at the focus, 4(n-1) subwavelength regions are generated (n denotes the cylindrical beam order), which are arranged on a circle centered on the optical axis. In the adjacent regions, the SAM is revealed to change sign, meaning that the light has alternating left- and right-handed elliptic polarization (an optical spin Hall effect) in these regions. At the near-axis focus center, the light is shown to have right-handed elliptical polarization at m> 0 or left-handed elliptic polarization at m< 0, where m denotes the topological charge of the optical vortex. The total longitudinal spin, i.e. the cross-section-averaged longitudinal SAM component, is shown to be zero and conserve upon focusing. Thanks to the presence of an optical vortex with topological charge m, the near-focus transverse energy flow is found to rotate on a spiral path, rotating on a circle at the focus. In the optical axis vicinity, the rotation occurs anticlockwise at m> 0 or clockwise at m< 0.

Convolution Operation on Pancharatnam-Berry Coding Metasurfaces in Visible Band

Coding metasurfaces bring photonic design into a new era for their convenience in manipulating electromagnetic waves in a programmable way. Different coding patterns can be further convoluted to give rise to nontrivial effects such as multiple beam steering, simultaneous control of surface and space waves, and the integration of multiple functionalities. However, previous experimental works have been limited to low frequencies. Extending convoluted coding metasurfaces to optical frequency can significantly reduce the size of structures, and therefore facilitate their applications in optical circuits. Here, we experimentally demonstrate a Pancharatnam-Berry metasurface designed by convoluting two distinct coding patterns. Such a metasurface exhibits integrated functionalities: the optical spin Hall effect and spin to orbital angular momentum conversion, which are robust over a broad visible band and a wide range of incident angles. Our work represents an important step towards multifunctional coding metasurfaces at optical frequency based on convolution operation.

Resonant spin Hall effect of light in random photonic arrays

It has been recently shown that the coherent component of light propagating in transversally disordered media, the so-called coherent mode, exhibits an optical spin Hall effect (SHE). In non-resonant materials, however, this phenomenon shows up at a spatial scale much larger than the mean free path, making its observation challenging due to the exponential attenuation of the coherent mode. Here, we show that in disordered photonic arrays exhibiting Mie resonances, the SHE on the contrary appears at a scale smaller than the mean free path if one operates in the close vicinity of the lowest transverse-magnetic resonance of the array. In combination with a weak measurement, this gives rise to a giant SHE that should be observable in optically-thin media. Furthermore, we show that by additionally exploiting the cooperative emission of a flash of light following the abrupt extinction of the incoming beam, one can achieve a time-dependent SHE, observable at large optical thickness as well.

Time-Varying Optical Spin-Orbit Interactions in Tight Focusing of Self-Torqued Beams

Self-torque has recently been observed as a novel property of light that features time-varying orbital angular momentum (OAM) along a light pulse. This property offers an additional degree of freedom for manipulating light fields and light-matter interactions on ultrafast time scales. In this work, we theoretically study the self-torque's role in modulating tightly focused fields and reveal spin-orbit interactions (SOIs) in the focused fields using time-dependent vectorial diffraction theory. It is found that time-varying SOIs occur between the spin angular momentum (SAM), intrinsic OAM and extrinsic OAM. Specifically, the spin-to-orbit conversion, orbit-to-local-spin conversion, and optical spin-Hall effect are observed in the focused self-torqued beams. In particular, when the incident beams are circularly polarized, the time-dependent transverse SAM distributions will appear in the focal plane. Moreover, the self-torque of the focused light fields can be controlled via spin-to-orbit conversion. These observations could benefit potential applications in ultrafast light field modulation, microscopy, and optical manipulation.

Magneto-Optical Spin Hall Effect Regulation at Terahertz Frequencies Based on Graphene–Gold Heterojunction

In this paper, we theoretically consider the magneto-optical spin Hall effect of light (MOSHEL) in a graphene–gold heterojunction structure at terahertz frequencies, and determine the maximum value of the transverse shift of the spin Hall effect of light (SHEL) in the designed structure by varying the terahertz frequency, the thickness of the metal layer, the Fermi energy level of the graphene, and the magnetic induction density. When the terahertz frequency was 1.2 THz, the metal layer thickness 50 nm, the Fermi level 0.2 eV, and the magnetic induction density B was 10 T, the SHEL shifts of left-handed circularly polarized (LHCP) and right-handed circularly polarized (RHCP) components was greatest at the critical angle (58°), with as value of 498μm, 1000 times larger than the visible light. At this point, graphene exhibited a significant magneto-optical effect, dramatically enhancing the splitting extrema of LHCP and RHCP. This structure will provide possibilities for enhancement of the transverse shift and efficient regulation of the optical spin Hall effect within the terahertz range.

Spin Hall Effect before and after the Focus of a High-Order Cylindrical Vector Beam

It is known that in the cross-section of a high-order cylindrical vector beam (CVB), polarization is locally linear. The higher the beam order, the higher the number of full rotations of the vector of local linear polarization when passing along a contour around the optical axis. It is also known that both in the input and in the focal planes, the CVB has neither the spin angular momentum (SAM), nor the orbital angular momentum (OAM). We demonstrate here that near the focal plane of the CVB (before and after the focus), an even number of local subwavelength areas is generated, where the polarization vector in each point is rotating. In addition, in the neighboring areas, polarization vectors are rotating in different directions, so that the longitudinal component of SAM vectors in these neighboring areas is of the opposite sign. In addition, after the beam passes the focus, the rotation direction of the polarization vector in each point of the beam cross-section is changed to the opposite one. Such spatial separation of the left and right rotation of the polarization vectors manifests so that the optical spin Hall effect takes place.

Direct Observation of Spin-Orbit Interaction of Light via Chiroptical Responses.

The spin-orbit interaction of light is a fundamental manifestation of controlling its angular momenta with numerous applications in photonic spin Hall effects and chiral quantum optics. However, observation of an optical spin Hall effect, which is normally very weak with subwavelength displacements, needs quantum weak measurements or sophisticated metasurfaces. Here, we theoretically and experimentally demonstrate the spin-orbit interaction of light in the form of strong chiroptical responses by breaking the in-plane inversion symmetry of a dielectric substrate. The chiroptical signal is observed at the boundary of a microdisk illuminated by circularly polarized vortex beams at normal incidence. The generated chiroptical spectra are tunable for different photonic orbital angular momenta and microdisk diameters. Our findings, correlating photonic spin-orbit interaction with chiroptical responses, may provide a route for exploiting optical information processing, enantioselective sensing, and chiral metrology.

Topological boundary states of two-dimensional restricted isosceles triangular photonic crystals.

We propose an all-media photonic crystal (PC) composed of isosceles triangle dielectric cylinders that realizes the topological phase transition by simply rotating the isosceles triangular dielectric cylinders. Additionally, the topological phase transition is closely linked with the size parameters and rotation angle of the isosceles triangle. The topological boundary states with lossless transmission are constructed on the interface of two different topological structures, and the optical quantum spin Hall effect is simulated. Further, we verified that the boundary state is unidirectional and immune to disorder, cavity, and sharp bend defects. By rotating the angle of the triangle to control the transmission path of the pseudo-spin state, we realize diverse transport pathways of light, such as the "straight line" shape, "Z" shape, "U" shape, and "Y" shape. This topological system shows a higher degree of freedom, which can promote the research on topological boundary states and the development of topological insulators in practical applications.

Multiplexed multi-focal and multi-dimensional SHE (spin Hall effect) metalens

Metalenses are two-dimensional ultrathin metalenses composed of subwavelength artificial microstructures. In this paper, various multi-focal spin Hall effect (SHE)-based metalenses are designed to provide spin-dependent splitting in transverse and longitudinal directions, which possess spin-dependent two focal points under left-circularly polarized (LCP) or right-circularly polarized (RCP) incidence, and all four focal points can be observed under the linearly polarized (LP) incidence. A spin-independent bifocal metalens was investigated, which possesses the same bifocal focusing phenomena for LCP and RCP incidences. Our method is significant for designing high-efficiency multifunctional optics devices based on optical SHE.