We examine the spin-orbit coupling effects that appear when a wave carrying intrinsic angular momentum interacts with a medium. The Berry phase is shown to be a manifestation of the Coriolis effect in a non-inertial reference frame attached to the wave. In the most general case, when both the direction of propagation and the state of the wave are varied, the phase is given by a simple expression that unifies the spin redirection Berry phase and the Pancharatnam--Berry phase. The theory is supported by the experiment demonstrating the spin-orbit coupling of electromagnetic waves via a surface plasmon nano-structure. The measurements verify the unified geometric phase, demonstrated by the observed polarization-dependent shift (spin-Hall effect) of the waves.
We review the geometrical-optics evolution of an electromagnetic wave propagating along a curved ray trajectory in a gradient-index dielectric medium. A Coriolis-type term appears in Maxwell equations under transition to the rotating coordinate system accompanying the ray. This term describes the spin-orbit coupling of light which consists of (i) the Berry phase responsible for a trajectory-dependent polarization variations and (ii) the spin Hall effect representing polarization-dependent trajectory perturbations. These mutual phenomena are described within universal geometrical structures und…
We consider propagation of a paraxial beam carrying the spin angular momentum (polarization) and intrinsic orbital angular momentum (IOAM) in a smoothly inhomogeneous isotropic medium. It is shown that the presence of IOAM can dramatically enhance and rearrange the topological phenomena that previously were considered solely in connection to the polarization of transverse waves. In particular, the appearance of a new-type Berry phase that describes the parallel transport of the beam structure along a curved ray is predicted. We derive the ray equations demonstrating the splitting of beams with…
We consider an optically thick spherical agglomerate of magneto-optical scatterers with a central isotropic, unpolarized light source, placed in a homogeneous magnetic field. The Photon Hall Effect induces a rotating Poynting vector, both inside and outside the medium. We show that electromagnetic (orbital) angular momentum leaks out and induces a torque proportional to the injection power of the source and the photon Hall angle. This effect represents a novel class of optical phenomena, generating angular momentum from diffusive magneto-transport.
We examine the evolution of paraxial beams carrying intrinsic spin and orbital angular momenta (AM) in gradient-index media. A parabolic-type equation is derived which describes the beam diffraction in curvilinear coordinates accompanying the central ray. The center of gravity of the beam experiences transverse AM-dependent deflections -- the spin and orbital Hall effects. The spin Hall effect generates a transverse translation of the beam as a whole, in precise agreement with recent geometrical optics predictions. At the same time, the orbital Hall effect is significantly affected by the diff…
The effect of a tunable, externally coupled Fabry-Pérot cavity to resonantly enhance the optical Hall effect signatures at terahertz frequencies produced by a traditional Drude-like two-dimensional electron gas is shown and discussed in this communication. As a result, the detection of optical Hall effect signatures at conveniently obtainable magnetic fields, for example by neodymium permanent magnets, is demonstrated. An AlInN/GaN-based high electron mobility transistor structure grown on a sapphire substrate is used for the experiment. The optical Hall effect signatures and their dispersions…
We report the relative frequency stabilization of an intracavity frequency doubled singly resonant optical parametric oscillator on a Fabry-Perotétalon. The red/orange radiation produced by the frequency doubling of the intracavity resonant idler is stabilized using the Pound-Drever-Hall locking technique. The relative frequency noise of this orange light, when integrated from 1 Hz to 50 kHz, corresponds to a standard deviation of 700 Hz. The frequency noise of the pump laser is shown experimentally to be transferred to the non resonant signal beam.
Hyperbolic metamaterials, horizontally stacked metal and dielectric multilayer, have recently been studied as a platform to observe optical spin Hall effect. However, the large optical spin Hall effect in the horizontal hyperbolic metamaterials accompanies extremely low transmission, which obstructs its practical applications. Reducing the sample thickness to augment the transmission causes diminishment of the shift. In this letter, we demonstrate that a vertical hyperbolic metamaterial can enhance the shift by several orders of magnitude in comparison to the shift of its horizontal counterpar…
Dynamic dipolar toroidal response is demonstrated by an optical plasmonic metamaterial composed of double disks. This response with a hotspot of localized E-field concentration is a well-behaved toroidal cavity mode that exhibits a large Purcell factor due to its deep-subwavelength mode volume. All-optical Hall effect (photovoltaic) due to this optical toroidal moment is demonstrated numerically, in mimicking the magnetoelectric effect in multiferroic systems. The result shows a promising avenue to explore various optical phenomena associated with this intriguing dynamic toroidal moment.
We study the spin-orbit coupling induced by the splitting between TE and TM optical modes in a photonic honeycomb lattice. Using a tight-binding approach, we calculate analytically the band structure. Close to the Dirac point,we derive an effective Hamiltonian. We find that the local reduced symmetry ($\mathrm{D_{3h}}$) transforms the TE-TM effective magnetic field into an emergent field with a Dresselhaus symmetry. As a result, particles become massive, but no gap opens. The emergent field symmetry is revealed by the optical spin Hall effect.
The robust spin and momentum valley locking of electrons in two-dimensional semiconductors make the valley degree of freedom of great utility for functional optoelectronic devices. Owing to the difference in optical selection rules for the different valleys, these valley electrons can be addressed optically. The electrons and excitons in these materials exhibit valley Hall effect, where the carriers from specific valleys are directed to different directions under electrical or thermal bias. Here we report the optical valley Hall effect where the light emission from the valley polarized exciton…
The spin orbit interaction (SOI) of light has been in the focus in recent times because of fundamental consequences and potential applications in diverse systems ranging from inhomogeneous anisotropic media to engineered plasmonics and metamaterial strutures. Here we demonstrate perhaps one of the simplest means to realize SOI and the Spin Hall Shift (SHS) using a standard Gaussian TEM$_{00}$ beam in an optical trap. Our system exploits the versatility and interference generated in a stratified medium to control and manipulate SOI and transfer the resulting angular momentum to optically trappe…
How to measure the optical conductivity of atomically thin crystals is an important but challenging issue due to the weak light-matter interaction at the atomic scale. Photonic spin Hall effect, as a fundamental physical effect in light-matter interaction, is extremely sensitive to the optical conductivity of atomically thin crystals. Here, we report a precision measurement of the optical conductivity of graphene, where the photonic spin Hall effect acts as a measurement pointer. By incorporating with the weak-value amplification technique, the optical conductivity of monolayer graphene taken …
Geometrical optics is extended so as to provide a model for spinning light rays via the coadjoint orbits of the Euclidean group characterized by color and spin. This leads to a theory of ``geometrical spinoptics'' in refractive media. Symplectic scattering yields generalized Snell-Descartes laws that include the recently discovered optical Hall effect.
Scattering immune propagation of light in topological photonic systems may revolutionarize the design of integrated photonic circuits for information processing and communications. In optics, various photonic topological circuits have been developed, which were based on classical emulation of either quantum spin Hall effect or quantum valley Hall effect. On the other hand, the combination of both the valley and spin degrees of freedom can lead to a new kind of topological transport phenomenon, dubbed quantum spin valley Hall effect (QSVH), which can further expand the number of topologically p…
Presented here is the development and demonstration of a tunable cavity-enhanced terahertz frequency-domain optical Hall effect technique. The cavity consists of at least one fixed and one tunable Fabry-Pérot resonator. The approach is suitable for enhancement of the optical signatures produced by the optical Hall effect in semi-transparent conductive layer structures with plane parallel interfaces. The physical principle is the constructive interference of electric field components that undergo multiple optical Hall effect induced polarization rotations upon multiple light passages through th…
Light possesses both spin and orbital angular momentum (AM). While spin AM is determined by helicity of circular-polarization, orbital AM is characterized by topological charge of vortex beam. Interaction of AM with optical beam orbit leads to optical spin Hall or orbital Hall effect, exhibited as spin-dependent or topological charge-dependent transverse shift of optical beam. Conservation of AM enables spin-to-orbital AM conversion, where circular-polarized Gaussian beam is converted to opposite-helicity circular-polarized vortex beam with topological charge $\pm 2$, an example of controlling…
Optical spin Hall (OSH) shift has been observed by weak measurement amplification in a refraction beam passing through air-glass interface, the refractive index gradient $\vec{\nabla} n$ being normal to the interface. Phase-discontinuity metasurface (PMS) possesses $\vec{\nabla} n$ tangential to the metasurface, and depending on the incidence angle either positive or negative refraction takes place satisfying the generalized Snell's law. Rapid phase-change over subwavelength distance at PMS leads to a large $\vec{\nabla} n$, enabling a direct observation of OSH shift. Here, we identify that th…
Nonlinear optical responses to external electromagnetic field, characterized by second and higher order susceptibilities, play crucial roles in nonlinear optical devices and novel optoelectronics. Herein we present a quantum nonlinear ferroic optical Hall effect (QNFOHE) in multiferroics - a Hall-like direct photocurrent originated from the second order current response to intense electromagnetic field whose direction can be controlled by both internal ferroic orders and external light polarization. QNFOHE consists of two types of nonlinear photocurrent responses - shift current and circular p…
We propose a set of three simple photonic platforms capable of emulating quantum topologically insulating phases corresponding to Hall, spin-Hall, and valley-Hall effects. It is shown that an interface between any two of these heterogeneous photonic topological insulators supports scattering-free surface states. Spin and valley degrees of freedom characterizing such topologically protected surface waves determine their unique pathways through complex photonic circuits comprised of multiple heterogeneous interfaces.
Optics naturally provides us with some powerful mathematical operations. Here we experimentally demonstrate that during reflection or refraction at a single optical planar interface, the optical computing of spatial differentiation can be realized by analyzing specific orthogonal polarization states of light. We show that the spatial differentiation is intrinsically due to the spin Hall effect of light and generally accompanies light reflection and refraction at any planar interface, regardless of material composition or incident angles. The proposed spin-optical method takes advantages of a s…
The effective electron mass parameter in Si-doped Al$_{0.72}$Ga$_{0.28}$N is determined to be $m^\ast=(0.336\pm0.020)\,m_0$ from mid-infrared optical Hall effect measurements. No significant anisotropy of the effective electron mass parameter is found supporting theoretical predictions. Assuming a linear change of the effective electron mass with the Al content in AlGaN alloys and $m^\ast=0.232\,m_0$ for GaN, an average effective electron mass of $m^\ast=0.376\,m_0$ can be extrapolated for AlN. The analysis of mid-infrared spectroscopic ellipsometry measurements further confirms the two phonon…
The optical spin Hall effect (OSHE) is a transport phenomenon of exciton polaritons in semiconductor microcavities, caused by the polaritonic spin-orbit interaction, that leads to the formation of spin textures. In the semiconductor cavity, the physical basis of the spin orbit coupling is an effective magnetic field caused by the splitting of transverse-electric and transverse-magnetic (TE-TM) modes. The spin textures can be observed in the near field (local spin distribution of polaritons), and as light polarization patterns in the more readily observable far field. For future applications in…
We propose an optical counterpart of the quantum spin Hall (QSH) effect in a two-dimensional photonic crystal composed of a gyrotropic medium exhibiting both gyroelectric and gyromagnetic properties simultaneously. Such QSH effect shows unidirectional polarization-dependent transportation of photonic topological edged states, which is robust against certain disorders and impurities. More importantly, we find that such unique property is not protected by conventional time-reversal symmetry of photons obeying the Bosonic statistics but rather by the same symmetry, as electron's time-reversal sym…
The study of spin-orbit coupling of photons has attracted much attention in recent years, and leads to many potential applications in optics. In the recently discovered metamaterial -- photonic crystals with Weyl points, the pseudospin-orbit coupling of photons bears a resemblance to the spin-orbit coupling. We study the pseudospin Hall effect of light in such metamaterials and find that during total reflection, the light beam experiences a transverse shift that is proportional to the pseudospin (or the monopole charge) of the Weyl point. As the spin Hall effect has inspired many works to expl…
Spin-orbit interactions (SOI) are a set of sub-wavelength optical phenomenon in which spin and spatial degrees of freedom of light are intrinsically coupled. One of the unique example of SOI, spin-Hall effect of light (SHEL) has been an area of extensive research with potential applications in spin controlled photonic devices as well as emerging fields of spinoptics and spintronics. Here, we report our experimental study on SHEL due to forward scattering of focused linearly polarized Gaussian and Hermite-Gaussian ($\textrm{HG}_{10}$) beams from a silver nanowire (AgNW). Spin dependent anti-sym…
We have proposed a unified framework towards the dynamics of optical and electron vortex beams from the perspective of geometric phase and the associated Hall effects. The unification is attributed to the notion that the spin degrees of freedom of a relativistic particle, either massive or massless, is associated with a vortex line. %The formulation in cylindrical coordinates leads to a local vortex structure related to orbital angular momentum(OAM). Based on cylindrical corodinate formulation, which leads to a local vortex structure related to orbital angular momentum (OAM), it can be shown t…
