Spin-orbit coupling and the optical spin Hall effect in photonic graphene

Engineering effective optical gauge fields in anisotropic Fabry-Pérot cavities

Gauge fields, fundamental to the study of classical electromagnetism and the standard model of particle physics, have recently found significant applications in optics and photonics. Here, we investigate the emergence of effective optical gauge fields in anisotropic Fabry-Pérot cavities, resulting from the coupling between cavity modes with different polarization. As an example, the intrinsic biaxial anisotropy of the intracavity material induces an effective optical gauge field, manifesting as a transition from the optical spin Hall effect to Zitterbewegung of light at different frequencies. The simulation results confirm that the wave packet dynamics, along with the evolution of pseudo-spins driven by anisotropy, can be comprehensively understood using effective optical gauge field theory around unique band crossings. A kind of metamaterial embedded in the Fabry-Pérot cavity is proposed and implemented to realize biaxial anisotropy using effective medium theory, as verified by simulation results and experimental measurements. The emergent effective optical gauge field in a biaxial anisotropic cavity may offer what we believe to be new insights into manipulating light trajectories and designing advanced polarization-sensitive optical devices.

Optical Spin Hall Effect Pattern Switching in Polariton Condensates in Organic Single-Crystal Microbelts

Topological polaritons, combining the robustness of the topologically protected edge states against defects and disorder with the strong nonlinear properties of polariton bosons, represent an excellent platform to investigate novel photonic topological phases. We demonstrate the optical spin Hall effect (OSHE) and its symmetry switching in the exciton-polariton regime of pure DPAVBi crystals. Benefiting from the photonic Rashba-Dresselhaus spin-orbit coupling, we observe the separation of left- and right-circularly polarized emission in momentum space and real space, a signature of the OSHE. Above the lasing threshold, the OSHE pattern changes due to transverse quantization in the microbelt. This simple device has great potential applications in topological polaritons, such as information transmission, photonic integrated chips, and quantum information.

Prediction and observation of topological modes in fractal nonlinear optics

This item from the News and Views (N&V) category aims to provide a summary of theoretical and experimental results recently published in ref. 24, which demonstrates the creation of corner modes in nonlinear optical waveguides of the higher-order topological insulator (HOTI) type. Actually, these are second-order HOTIs, in which the transverse dimension of the topologically protected edge modes is smaller than the bulk dimension (it is 2, in the case of optical waveguide) by 2, implying zero dimension of the protected modes, which are actually realized as corner or defect ones. Work24 reports the prediction and creation of various forms of the corner modes in a HOTI with a fractal transverse structure, represented by the Sierpiński gasket (SG). The self-focusing nonlinearity of the waveguide's material transforms the corner modes into corner solitons, almost all of which are stable. The solitons may be attached to external or internal corners created by the underlying SG. This N&V item offers an overview of these new findings reported in ref. 24 and other recent works, and a brief discussion of directions for further work on this topic.

Topological Moiré Polaritons

The combination of an in-plane honeycomb potential and of a photonic spin-orbit coupling (SOC) emulates a photonic or polaritonic analog of bilayer graphene. We show that modulating the SOC magnitude allows us to change the overall lattice periodicity, emulating any type of moiré-arranged bilayer graphene with unique all-optical access to the moiré band topology. We show that breaking the time-reversal symmetry by an effective exciton-polariton Zeeman splitting opens a large topological gap in the array of moiré flat bands. This gap contains one-way topological edge states whose constant group velocity makes an increasingly sharp contrast with the flattening moiré bands.

Improved performance of temperature sensors based on the one-dimensional topological photonic crystals comprising hyperbolic metamaterials

This paper seeks to progress the field of topological photonic crystals (TPC) as a promising tool in face of construction flaws. In particular, the structure can be used as a novel temperature sensor. In this regard, the considered TPC structure comprising two different PC designs named PC1 and PC2. PC1 is designed from a stack of multilayers containing Silicon (Si) and Silicon dioxide (SiO2), while layers of SiO2 and composite layer named hyperbolic metamaterial (HMM) are considered in designing PC2. The HMM layer is engineered using subwavelength layers of Si and Bismuth Germinate, or BGO (Bi 4 Ge 3 O 12 ). The mainstay of our suggested temperature sensor is mainly based on the emergence of some resonant modes inside the transmittance spectrum that provide the stability in the presence of the geometrical changes. Meanwhile, our theoretical framework has been introduced in the vicinity of transfer matrix method (TMM), effective medium theory (EMT) and the thermo-optic characteristics of the considered materials. The numerical findings have extensively introduced the role of some topological parameters such as layers' thicknesses, filling ratio through HMM layers and the periodicity of HMM on the stability or the topological features of the introduced sensor. Meanwhile, the numerical results reveal that the considered design provides some topological edge states (TESs) of a promising robustness and stability against certain disturbances or geometrical changes in the constituent materials. In addition, our sensing tool offers a relatively high sensitivity of 0.27 nm/°C.

Non-Abelian physics in light and sound

Non-Abelian phenomena arise when the sequence of operations on physical systems influences their behaviors. By possessing internal degrees of freedom such as polarization, light and sound can be subjected to various manipulations, including constituent materials, structured environments, and tailored source conditions. These manipulations enable the creation of a great variety of Hamiltonians, through which rich non-Abelian phenomena can be explored and observed. Recent developments have constituted a versatile testbed for exploring non-Abelian physics at the intersection of atomic, molecular, and optical physics; condensed matter physics; and mathematical physics. These fundamental endeavors could enable photonic and acoustic devices with multiplexing functionalities. Our review aims to provide a timely and comprehensive account of this emerging topic. Starting from the foundation of matrix-valued geometric phases, we address non-Abelian topological charges, non-Abelian gauge fields, non-Abelian braiding, non-Hermitian non-Abelian phenomena, and their realizations with photonics and acoustics and conclude with future prospects.

Theory of nonlinear corner states in photonic fractal lattices

We study linear and nonlinear higher-order topological insulators (HOTIs) based on waveguide arrays arranged into Sierpiński gasket and Sierpiński carpet structures, both of which have non-integer effective Hausdorff dimensionality. Such fractal structures possess different discrete rotational symmetries, but both lack transverse periodicity. Their characteristic feature is the existence of multiple internal edges and corners in their optical potential landscape, and the formal absence of an insulating bulk. Nevertheless, we show that a systematic geometric shift of the waveguides in the first generation of such fractal arrays, which affects the coupling strengths between sites of this building block as well as in subsequent structure generations, enables the formation of corner states of topological origin at the outer corners of the array. We find that, in contrast to HOTIs based on periodic arrays, Sierpiński gasket arrays always support topological corner states, irrespective of the direction of the shift of the waveguides, while in Sierpiński carpet structures, corner states emerge only for one direction of the waveguide shift. We also find families of corner solitons bifurcating from linear corner states of fractal structures that remain stable practically in the entire gap in which they form. These corner states can be efficiently excited by injecting Gaussian beams into the outer corner sites of the fractal arrays. Our results pave the way toward the investigation of nonlinear effects in topological insulators with non-integer dimensionality and enrich the variety of higher-order topological states.

Observation of Zitterbewegung in photonic microcavities

We present and experimentally study the effects of the photonic spin-orbit coupling on the real space propagation of polariton wavepackets in planar semiconductor microcavities and polaritonic analogues of graphene. In particular, we demonstrate the appearance of an analogue Zitterbewegung effect, a term which translates as 'trembling motion' in English, which was originally proposed for relativistic Dirac electrons and consisted of the oscillations of the centre of mass of a wavepacket in the direction perpendicular to its propagation. For a planar microcavity, we observe regular Zitterbewegung oscillations whose amplitude and period depend on the wavevector of the polaritons. We then extend these results to a honeycomb lattice of coupled microcavity resonators. Compared to the planar cavity, such lattices are inherently more tuneable and versatile, allowing simulation of the Hamiltonians of a wide range of important physical systems. We observe an oscillation pattern related to the presence of the spin-split Dirac cones in the dispersion. In both cases, the experimentally observed oscillations are in good agreement with theoretical modelling and independently measured bandstructure parameters, providing strong evidence for the observation of Zitterbewegung.

Controllable oscillated spin Hall effect of Bessel beam realized by liquid crystal Pancharatnam-Berry phase elements

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.

Nontrivial band geometry in an optically active system

Optical activity, also called circular birefringence, is known for two hundred years, but its applications for topological photonics remain unexplored. Unlike the Faraday effect, the optical activity provokes rotation of the linear polarization of light without magnetic effects, thus preserving the time-reversal symmetry. In this work, we report a direct measurement of the Berry curvature and quantum metric of the photonic modes of a planar cavity, containing a birefringent organic microcrystal (perylene) and exhibiting emergent optical activity. This experiment, performed at room temperature and at visible wavelength, establishes the potential of organic materials for implementing non-magnetic and low-cost topological photonic devices.

PT-Symmetric Topological Edge-Gain Effect

We demonstrate a non-Hermitian topological effect that is characterized by having complex eigenvalues only in the edge states of a topological material, despite the fact that the material is completely uniform. Such an effect can be constructed in any topological structure formed by two gapped subsystems, e.g., a quantum spin-Hall system, with a suitable non-Hermitian coupling between the spins. The resulting complex-eigenvalued edge state is robust against defects due to the topological protection. In photonics, such an effect can be used for the implementation of topological lasers, in which a uniform pumping provides gain only in the edge lasing state. Furthermore, such a topological lasing model is reciprocal and is thus compatible with standard photonic platforms.

Multi-orbital tight binding model for cavity-polariton lattices

In this work we present a tight-binding model that allows to describe with a minimal amount of parameters the band structure of exciton-polariton lattices. This model based on s and p non-orthogonal photonic orbitals faithfully reproduces experimental results reported for polariton graphene ribbons. We analyze in particular the influence of the non-orthogonality, the inter-orbitals interaction and the photonic spin-orbit coupling on the polarization and dispersion of bulk bands and edge states.

Topological photonic crystals: a review

The field of topological photonic crystals has attracted growing interest since the inception of optical analog of quantum Hall effect proposed in 2008. Photonic band structures embraced topological phases of matter, have spawned a novel platform for studying topological phase transitions and designing topological optical devices. Here, we present a brief review of topological photonic crystals based on different material platforms, including all-dielectric systems, metallic materials, optical resonators, coupled waveguide systems, and other platforms. Furthermore, this review summarizes recent progress on topological photonic crystals, such as higherorder topological photonic crystals, non-Hermitian photonic crystals, and nonlinear photonic crystals. These studies indicate that topological photonic crystals as versatile platforms have enormous potential applications in maneuvering the flow of light.

Topological phase transition with p orbitals in the exciton-polariton honeycomb lattice

We study the topological phase transition with the TE-TM splitting in the p-orbital exciton-polariton honeycomb lattice. We find that some Dirac points survive at the high-symmetry points with space-inversion symmetry breaking, which reflects the characteristic of p orbitals. A phase diagram is obtained by the gap Chern number, from which the topological phase transition takes place in the intermediate gap. There is no topological phase transition in the bottom or top gap, and its edge state has the potential application for transporting signals in optoelectronic devices. When taking into account the non-degenerate p orbitals, we find that the bottom gap arises owing to the competition between the Zeeman energy and rotating angular velocity, and topological phase transition also appears in the complete gaps. These results can facilitate the experimental investigations of the topological properties of p-orbital exciton-polariton lattice structure.

Photonic Hall effect and helical Zitterbewegung in a synthetic Weyl system

Systems supporting Weyl points have gained increasing attention in condensed physics, photonics and acoustics due to their rich physics, such as Fermi arcs and chiral anomalies. Acting as sources or drains of Berry curvature, Weyl points exhibit a singularity of the Berry curvature at their core. It is, therefore, expected that the induced effect of the Berry curvature can be dramatically enhanced in systems supporting Weyl points. In this work, we construct synthetic Weyl points in a photonic crystal that consists of a honeycomb array of coupled rods with slowly varying radii along the direction of propagation. The system possesses photonic Weyl points in the synthetic space of two momenta plus an additional physical parameter with an enhanced Hall effect resulting from the large Berry curvature in the vicinity of the Weyl point. Interestingly, a helical Zitterbewegung (ZB) is observed when the wave packet traverses very close to a Weyl point, which is attributed to the contribution of the non-Abelian Berry connection arising from the near degenerate eigenstates.

Polariton Anomalous Hall Effect in Transition-Metal Dichalcogenides

We analyze the properties of strongly coupled excitons and photons in systems made of semiconducting two-dimensional transition-metal dichalcogenides embedded in optical cavities. Through a detailed microscopic analysis of the coupling, we unveil novel, highly tunable features of the spectrum that result in polariton splitting and a breaking of light-matter selection rules. The dynamics of the composite polaritons is influenced by the Berry phase arising both from their constituents and from the confinement-enhanced coupling. We find that light-matter coupling emerges as a mechanism that enhances the Berry phase of polaritons well beyond that of its elementary constituents, paving the way to achieve a polariton anomalous Hall effect.

Exciton Polaritons in a Two-Dimensional Lieb Lattice with Spin-Orbit Coupling

We study exciton polaritons in a two-dimensional Lieb lattice of micropillars. The energy spectrum of the system features two flat bands formed from S and P_{x,y} photonic orbitals, into which we trigger bosonic condensation under high power excitation. The symmetry of the orbital wave functions combined with photonic spin-orbit coupling gives rise to emission patterns with pseudospin texture in the flat band condensates. Our Letter shows the potential of polariton lattices for emulating flat band Hamiltonians with spin-orbit coupling, orbital degrees of freedom, and interactions.

Photonic-crystal exciton-polaritons in monolayer semiconductors

Semiconductor microcavity polaritons, formed via strong exciton-photon coupling, provide a quantum many-body system on a chip, featuring rich physics phenomena for better photonic technology. However, conventional polariton cavities are bulky, difficult to integrate, and inflexible for mode control, especially for room-temperature materials. Here we demonstrate sub-wavelength-thick, one-dimensional photonic crystals as a designable, compact, and practical platform for strong coupling with atomically thin van der Waals crystals. Polariton dispersions and mode anti-crossings are measured up to room temperature. Non-radiative decay to dark excitons is suppressed due to polariton enhancement of the radiative decay. Unusual features, including highly anisotropic dispersions and adjustable Fano resonances in reflectance, may facilitate high temperature polariton condensation in variable dimensions. Combining slab photonic crystals and van der Waals crystals in the strong coupling regime allows unprecedented engineering flexibility for exploring novel polariton phenomena and device concepts.

Semiconductor microcavities can host polaritons formed by strong exciton-photon coupling, yet they may be plagued by scalability issues. Here, the authors demonstrate a sub-wavelength-thick, one-dimensional photonic crystal platform for strong coupling with atomically thin van der Waals crystals.

Exploring nonlinear topological states of matter with exciton-polaritons: Edge solitons in kagome lattice

Matter in nontrivial topological phase possesses unique properties, such as support of unidirectional edge modes on its interface. It is the existence of such modes which is responsible for the wonderful properties of a topological insulator - material which is insulating in the bulk but conducting on its surface, along with many of its recently proposed photonic and polaritonic analogues. We show that exciton-polariton fluid in a nontrivial topological phase in kagome lattice, supports nonlinear excitations in the form of solitons built up from wavepackets of topological edge modes - topological edge solitons. Our theoretical and numerical results indicate the appearance of bright, dark and grey solitons dwelling in the vicinity of the boundary of a lattice strip. In a parabolic region of the dispersion the solitons can be described by envelope functions satisfying the nonlinear Schrödinger equation. Upon collision, multiple topological edge solitons emerge undistorted, which proves them to be true solitons as opposed to solitary waves for which such requirement is waived. Importantly, kagome lattice supports topological edge mode with zero group velocity unlike other types of truncated lattices. This gives a finer control over soliton velocity which can take both positive and negative values depending on the choice of forming it topological edge modes.

Acoustic Type-II Weyl Nodes from Stacking Dimerized Chains

Lorentz-violating type-II Weyl fermions, which were missed in Weyl's prediction of nowadays classified type-I Weyl fermions in quantum field theory, have recently been proposed in condensed matter systems. The semimetals hosting type-II Weyl fermions offer a rare platform for realizing many exotic physical phenomena that are different from type-I Weyl systems. Here we construct the acoustic version of a type-II Weyl Hamiltonian by stacking one-dimensional dimerized chains of acoustic resonators. This acoustic type-II Weyl system exhibits distinct features in a finite density of states and unique transport properties of Fermi-arc-like surface states. In a certain momentum space direction, the velocity of these surface states is determined by the tilting direction of the type-II Weyl nodes rather than the chirality dictated by the Chern number. Our study also provides an approach of constructing acoustic topological phases at different dimensions with the same building blocks.

The effects of dissipation on topological mechanical systems

We theoretically study the effects of isotropic dissipation in a topological mechanical system which is an analogue of Chern insulator in mechanical vibrational lattice. The global gauge invariance is still conserved in this system albeit it is destroyed by the dissipation in the quantum counterpart. The chiral edge states in this system are therefore robust against strong dissipation. The dissipation also causes a dispersion of damping for the eigenstates. It will modify the equation of motion of a wave packet by an extra effective force. After taking into account the Berry curvature in the wave vector space, the trace of a free wave packet in the real space should be curved, feinting to break the Newton’s first law.

Pseudospin-induced chirality with staggered optical graphene

Pseudospin has an important role in understanding many interesting physical phenomena that are associated with two-dimensional materials such as graphene. Pseudospin has been proposed to be directly related to angular momentum, and orbital angular momentum was recently experimentally demonstrated to be an intrinsic property of pseudospin in a photonic honeycomb lattice. However, in photonics, the interaction between spin and pseudospin for light has not been investigated. In this letter, we propose that in an optical analog of staggered graphene (that is, a photonic honeycomb lattice waveguide with in-plane inversion symmetry breaking), the pseudospin mode can strongly couple to the spin of an optical beam that is incident in certain directions. The spin-pseudospin coupling that is caused by the spin-orbit conversion in the scattering process induces a strong optical chiral effect for the transmitted optical beam. Spin-pseudospin coupling of light opens the door to the design of pseudospin-mediated spin or valley-selective photonic devices.

Ultrafast exciton-polariton scattering towards the Dirac points

Using the Feynman-Dyson diagram technique, we study nonlinear polariton-polariton scattering in a two-dimensional micropillar-based optical superlattice with hexagonal symmetry. We demonstrate that both the emerging polariton chirality and the loop Feynman diagrams up to infinite order should be strictly accounted for in the evaluation of the self-energy of the system. Further, we explicitly show that in such a design the time of polariton scattering towards the Dirac points can be drastically decreased which can be used, for instance, in engineering novel classes of polariton lasers with substantially reduced thresholds.

Longitudinal spin separation of light and its performance in three-dimensionally controllable spin-dependent focal shift

Spin Hall effect of light, which is normally explored as a transverse spin-dependent separation of a light beam, has attracted enormous research interests. However, it seems there is no indication for the existence of the longitudinal spin separation of light. In this paper, we propose and experimentally realize the spin separation along the propagation direction by modulating the Pancharatnam-Berry (PB) phase. Due to the spin-dependent divergence and convergence determined by the PB phase, a focused Gaussian beam could split into two opposite spin states, and focuses at different distances, representing the longitudinal spin separation. By combining this longitudinal spin separation with the transverse one, we experimentally achieve the controllable spin-dependent focal shift in three dimensional space. This work provides new insight on steering the spin photons, and is expected to explore novel applications of optical trapping, manipulating, and micromachining with higher degree of freedom.

Kibble-Zurek Mechanism in Topologically Nontrivial Zigzag Chains of Polariton Micropillars

We consider a zigzag chain of coupled micropillar cavities, taking into account the polarization of polariton states. We show that the TE-TM splitting of photonic cavity modes yields topologically protected polariton edge states. During the strongly nonadiabatic process of polariton condensation, the Kibble-Zurek mechanism leads to a random choice of polarization, equivalent to the dimerization of polymer chains. We show that dark-bright solitons appear as domain walls between polarization domains, analogous to the Su-Schrieffer-Heeger solitons in polymers. The soliton density scales as a power law with respect to the quenching parameter.

Extremely strong bipolar optical interactions in paired graphene nanoribbons

Extremely strong bipolar optical forces are demonstrated in a pair of coupled graphene nanoribbons, due to the remarkable confinement and enhancement of optical fields, and analytical formulae are derived.

Magnetic ordering induced giant optical property change in tetragonal BiFeO3

Magnetic ordering could have significant influence on band structures, spin-dependent transport, and other important properties of materials. Its measurement, especially for the case of antiferromagnetic (AFM) ordering, however, is generally difficult to be achieved. Here we demonstrate the feasibility of magnetic ordering detection using a noncontact and nondestructive optical method. Taking the tetragonal BiFeO3 (BFO) as an example and combining density functional theory calculations with tight-binding models, we find that when BFO changes from C1-type to G-type AFM phase, the top of valance band shifts from the Z point to Γ point, which makes the original direct band gap become indirect. This can be explained by Slater-Koster parameters using the Harrison approach. The impact of magnetic ordering on band dispersion dramatically changes the optical properties. For the linear ones, the energy shift of the optical band gap could be as large as 0.4 eV. As for the nonlinear ones, the change is even larger. The second-harmonic generation coefficient d33 of G-AFM becomes more than 13 times smaller than that of C1-AFM case. Finally, we propose a practical way to distinguish the two AFM phases of BFO using the optical method, which is of great importance in next-generation information storage technologies.

Polariton Z topological insulator

We demonstrate that honeycomb arrays of microcavity pillars behave as an optical-frequency two-dimensional photonic topological insulator. We show that the interplay between the photonic spin-orbit coupling natively present in this system and the Zeeman splitting of exciton polaritons in external magnetic fields leads to the opening of a nontrivial gap characterized by a C=±2 set of band Chern numbers and to the formation of topologically protected one-way edge states.