We propose a method to detect the geometric phase produced by the Dirac-type band structure of a triangular-lattice photonic crystal. The spectrum is known to have a conical singularity (= Dirac point) with a pair of nearly degenerate modes near that singularity described by a spin-1/2 degree of freedom (= pseudospin). The geometric Berry phase acquired upon rotation of the pseudospin is in general obscured by a large and unspecified dynamical phase. We use the analogy with graphene to show how complementary media can eliminate the dynamical phase. A transmission minimum results as a direct consequence of the geometric phase shift of pi acquired by rotation of the pseudospin over 360 degrees around a perpendicular axis. We support our analytical theory based on the Dirac equation by a numerical solution of the full Maxwell equations.
Light manipulations such as spin-direction locking propagation, robust transport, quantum teleportation and reconfigurable electromagnetic pathways have been investigated at the boundaries of photonic systems. Recently by breaking Dirac cones in time-reversal invariant photonic crystals, valley-pseudospin coupled edge states have been employed to realize selective propagation of light. Here, without photonic boundaries, we realize the propagation of pseudospin states in three-dimensional bulk metacrystal waveguides by employing the ubiquitous valley degree of freedom. Valley-dependent pseudosp…
Pseudospin plays a very important role in understanding various interesting physical phenomena associated with 2D materials such as graphene. It has been proposed that pseudospin is directly related to angular momentum, and it was recently experimentally demonstrated that orbit angular momentum is an intrinsic property of pseudospin in a photonic honeycomb lattice. However, in photonics, the interaction between spin and pseudospin for light has never been investigated. In this Letter, we propose that, in an optical analogue of staggered graphene, i.e. a photonic honeycomb lattice waveguide wit…
Electromagnetic topological insulators have been explored extensively due to the robust edge states they support. In this work, we propose a topological electromagnetic system based on a line defect in topologically nontrivial photonic crystals (PCs). With a finite-difference supercell approach, modal analysis of the PCs structure is investigated in detail. The topological line-defect states are pseudospin polarized and their energy flow directions are determined by the corresponding pseudospin helicities. These states can be excited by using two spatially-symmetric line-source arrays carrying…
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…
We uncover a superscattering behavior of pseudospin-1 wave from weak scatterers in the subwavelength regime where the scatterer size is much smaller than wavelength. The phenomenon manifests itself as unusually strong scattering characterized by extraordinarily large values of the cross section even for arbitrarily weak scatterer strength. We establish analytically and numerically that the physical origin of superscattering is revival resonances, for which the conventional Born theory breaks down. The phenomenon can be experimentally tested using synthetic photonic systems.
We demonstrate the coexistence of pseudospin- and valley-Hall-like edge states in a photonic crystal with $C_{3v}$ symmetry, which is composed of three interlacing triangular sublattices with the same lattice constants. By tuning the geometry of the sublattices, three complete photonic band gaps with nontrivial topology can be created, one of which is due to the band inversion associated with the pseudospin degree of freedom at the $Γ$ point and the other two due to the gapping out of Dirac cones associated with the valley degree of freedom at the $K, K'$ points. The system can support tri-ban…
Valley-Hall phases, first proposed in two-dimensional (2D) materials, originate from nontrivial topologies around valleys which denote local extrema in momentum space. Since they are extended into classical systems, their designs draw inspirations from existing quantum counterparts, and their transports show similar topological protections. In contrast, it is recently established in acoustics that layer pseudospins in valley-Hall phases can give rise to special valley-Hall edge states with fundamentally different transport behaviors at the interfaces compared with various 2D materials. Their r…
Pseudo-spin and valley degrees of freedom (DOFs) engineered in photonic analogues of topological insulators (TI) provide potential approaches to optical encoding and robust signal transport. Here we observe a ballistic edge state whose spin-valley indices are locked to the direction of propagation along the interface between a valley photonic crystal and a metacrystal emulating the quantum spin Hall effect. We demonstrate the inhibition of inter-valley scattering at a Y-junction formed at the interfaces between photonic TIs carrying different spin-valley Chern numbers. These results open up th…
Photonic pseudospin-1/2 systems, which exhibit Dirac cone dispersion at Brillouin zone corners in analogy to graphene, have been extensively studied in recent years. However, it is known that a linear band crossing of two bands cannot emerge at the center of Brillouin zone in a two-dimensional photonic system respecting time reversal symmetry. Using a square lattice of elliptical magneto-optical cylinders, we constructed an unpaired Dirac point at the Brillouin zone center as the intersection of the second and third bands corresponding to the monopole and dipole excitations. Effective medium t…
Pseudospin plays a central role in many novel physical properties of graphene and other artificial systems which have pseudospins of 1/2. Here we show that in certain photonic crystals (PCs) exhibiting conical dispersions at k = 0, the eigenmodes near the "Dirac-like point" can be described by an effective spin-orbit Hamiltonian with a pseudospin of 1, treating wave propagations in the upper cone, the lower cone and a flat band (corresponding to zero refractive index) within a unified framework. The 3-component spinor gives rise to boundary conditions distinct from those of pseudospin-1/2, lea…
Southeast University（东南大学）；Southern University of Science and Technology（南方科技大学）；Beijing Institute of Technology（北京理工大学）；Dongguan University of Technology（东莞理工学院）；Aerospace Information Research Institute, Chinese Academy of Sciences（中国科学院空天信息创新研究院）
The recent realization of photonic topological insulators has brought the discovery of fundamentally new states of light and revolutionary applications such as non-reciprocal devices for photonic diodes and robust waveguides for light routing. The spatially distinguished layer pseudospin has attracted attention in two-dimensional electronic materials. Here we report layered photonic topological insulators based on all-dielectric bilayer photonic crystal slabs. The introduction of layer pseudospin offers more dispersion engineering capability, leading to the layer-polarized and layer-mixed phot…
Topological edge states are the core of topological photonics. Here we introduce the antihelical edge states of time-reversal symmetric topological metals and propose a photonic realization in an anisotropic square lattice of coupled ring resonators, where the clockwise and counterclockwise modes play the role of pseudospins. The antihelical edge states robustly propagate across the corners toward the diagonal of the square lattice: The same (opposite) pseudospins copropagate in the same (opposite) direction on the parallel lattice boundaries; the different pseudospins separate and converge at…
The presence of topological edge modes at the interface of two perturbed honeycomb photonic crystals with $C_6$ symmetry is often attributed to the different signs of Berry curvature at the K and K$'$ valleys. In contrast to the electronic counterpart, the Chern number defined in photonic valley Hall effect is not a quantized quantity but can be tuned to finite values including zero simply by changing geometrical perturbations. Here, we argue that the edge modes in photonic valley Hall effect can exist even when Berry curvature vanishes. We numerically demonstrate the presence of the zero-Berr…
Recent developments in the field of photonic spin Hall effect (SHE) offer new opportunities for advantageous measurement of the optical parameters (refractive index, thickness, etc.) of nanostructures and enable spin-based photonics applications in the future. However, it remains a challenge to develop a tunable photonic SHE with any desired spin-dependent splitting for generation and manipulation of spin-polarized photons. Here, we demonstrate experimentally a scheme to realize the photonic SHE tunably by tailoring the space-variant Pancharatnam-Berry phase (PBP). It is shown that light beams…
We investigate a photonic device consisting of two coupled optical cavities possessing Rashba-Dresselhaus spin-orbit coupling, TE-TM splitting, and linear polarisation splitting that opens a tuneable energy gap at the diabolic points of the photon dispersion; giving rise to an actively addressable local Berry curvature. The proposed architecture stems from recent advancements in the design of artificial photonic gauge fields in liquid crystal cavities [K. Rechcińska et al., Science 366, 727 (2019)]. Our study opens new perspectives for topological photonics, room-temperature spinoptronics, and…
We study the emergence of a parity breaking coherent photonic state of a photon mode coupled to finite array of two-level systems, represented by pseudospins 1/2. The pseudospin-photon interaction is realised via a shift of the photonic oscillator equilibrium position by an amount linear in Cartesian component of the total pseudospin. We demonstrate analytically, that the instability is manifested in an upturn from concave to convex of the ground state energy dependence on the total pseudospin component coupled to the photons. The perturbation, sufficient for parity breaking, tends to zero in …
Realising photonic analogues of the robust, unidirectional edge states of electronic topological insulators would improve our control of light on the nanoscale and revolutionise the performance of photonic devices. Here we show that new symmetry protected topological phases can be detected by reformulating energy eigenproblems as Berry curvature eigenproblems. The "Berry bands" span the same eigenspace as the original valence energy bands, but separate into pseudo-spinful and pseudo-spinless subspaces in $\mathrm{C}_2\mathcal{T}$-symmetric crystals. We demonstrate the method on the well-known …
Dielectric metasurfaces with spatially varying birefringence and high transmission efficiency can exhibit exceptional abilities for controlling the photonic spin states. We present here some of our works on spin photonics and spin-photonic devices with metasurfaces. We develop a hybrid-order Poincare sphere to describe the evolution of spin states of wave propagation in the metasurface. Both the Berry curvature and the Pancharatnam-Berry phase on the hybrid-order Poincare sphere are demonstrated to be proportional to the variation of total angular momentum. Based on the spin-dependent property…
Valley pseudospin, a new degree of freedom in photonic lattices, provides an intriguing way to manipulate photons and enhance the robustness of optical networks. Here we experimentally demonstrated topological waveguiding, refracting, resonating, and routing of valley-polarized photons in integrated circuits. Specifically, we show that at the domain wall between photonic crystals of different topological valley phases, there exists a topologically protected valley kink state that is backscattering-free at sharp bends and terminals. We further harnessed these valley kink states for constructing…
In periodic systems, nodal lines are loops in the three-dimensional momentum space where two bands are degenerate with each other. Nodal lines exhibit rich topological features as they can take various configurations such as rings, links, chains and knots. These line nodes are usually protected by mirror or PT symmetry. Here we propose and demonstrate a novel type of photonic straight nodal lines in a D2d meta-crystal which are protected by roto-inversion time (roto-PT) symmetry. The nodal lines are located at the central axis and hinges of the Brillouin zone. They appear as quadrupole sources…
We discuss the propagation of an electromagnetic field in an inhomogeneously anisotropic material where the optic axis is rotated in the transverse plane but is invariant along the propagation direction. In such a configuration, the evolution of an electromagnetic wavepacket is governed by the Pancharatnam-Berry phase (PBP), responsible for the appearance of an effective photonic potential. In a recent paper [A. Alberucci et al., "Electromagnetic confinement via spin-orbit interaction in anisotropic dielectrics", ACS Photonics \textbf{3}, 2249 (2016)] we demonstrated that the effective potenti…
Chiral edge-state signatures of Berry monopole merging and splitting in a bilayer photonic crystal slab with synthetic momentum
Donostia International Physics Center（多诺斯蒂亚国际物理中心）；Institute of Physics, Vietnam Academy of Science and Technology（越南科学技术院物理研究所）；Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules（里尔大学、法国国家科学研究中心、激光与原子分子物理联合研究实验室）；Advanced Polymers and Materials: Physics, Chemistry and Technology, Chemistry Faculty (UPV/EHU)（巴斯克国立自治大学/圣塞巴斯蒂安大学化学学院先进聚合物与材料物理、化学与技术系）；Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS)（韩国基础科学研究院复杂系统理论物理中心）；Institute for Interdisciplinary Research in Science and Education, ICISE（越南归仁市科学与教育跨学科研究所）；Ecole Centrale de Lyon, CNRS, INSA Lyon, Université Claude Bernard Lyon 1, CPE Lyon, CNRS, INL, UMR5270（里昂中央理工学院、法国国家科学研究中心、里昂国立应用科学学院、里昂第一大学、里昂化工学院、法国国家科学研究中心里昂纳米技术研究所）；CNRS-International-NTU-Thales Research Alliance (CINTRA), IRL 3288（法国国家科学研究中心-国际南洋理工大学-泰雷兹研究联盟）；Institut Universitaire de France (IUF)（法兰西学院）；IKERBASQUE, Basque Foundation for Science（伊克尔巴斯科奎，巴斯克科学基金会）
The properties that quantify photonic topological insulators (PTIs), Berry phase, Berry connection, and Chern number, are typically obtained by making analogies between classical Maxwell's equations and the quantum mechanical Schrödinger equation, writing both in Hamiltonian form. However, the aforementioned quantities are not necessarily quantum in nature, and for photonic systems they can be explained using only classical concepts. Here we provide a derivation and description of PTI quantities using classical Maxwell's equations, we demonstrate how an electromagnetic mode can acquire Berry p…
We measure the local near-field spin in topological edge state waveguides that emulate the quantum spin Hall effect. We reveal a highly structured spin density distribution that is not linked to a unique pseudospin value. From experimental near-field real-space maps and numerical calculations, we confirm that this local structure is essential in understanding the properties of optical edge states and light-matter interactions. The global spin is reduced by a factor of 30 in the near field and, for certain frequencies, flipped compared to the pseudospin measured in the far-field. We experimenta…
Core concepts in singular optics, especially the polarization singularity, have rapidly penetrated the surging fields of topological and nonhermitian photonics. For open photonic structures with degeneracies in particular, the polarization singularity would inevitably encounter another sweeping concept of Berry phase. Several investigations have discussed, in an inexplicit way, the connections between both concepts, hinting at that nonzero topological charges for far-field polarizations on a loop is inextricably linked to its nontrivial Berry phase when degeneracies are enclosed. In this work,…
Three-dimensional (3D) artificial metacrystals host rich topological phases, such as Weyl points, nodal rings and 3D photonic topological insulators. These topological states enable a wide range of applications, including 3D robust waveguide, one-way fiber and negative refraction of surface wave. However, these carefully designed metacrystals are usually very complex, hindering their extension to nanoscale photonic systems. Here, we theoretically proposed and experimentally realized an ideal nodal ring in visible region using a simple 1D photonic crystal. The pi Berry phase around the ring is …
We examine the photonic spin Hall effect (SHE) in a graphene-substrate system with the presence of external magnetic field. In the quantum Hall regime, we demonstrate that the in-plane and transverse spin-dependent splittings in photonic SHE exhibit different quantized behaviors. The quantized SHE can be described as a consequence of a quantized geometric phase (Berry phase), which corresponds to the quantized spin-orbit interaction. Furthermore, an experimental scheme based on quantum weak value amplification is proposed to detect the quantized SHE in terahertz frequency regime. By incorporat…
The topological phases of matter are characterized using the Berry phase, a geometrical phase, associated with the energy-momentum band structure. The quantization of the Berry phase, and the associated wavefunction polarization, manifest themselves as remarkably robust physical observables, such as quantized Hall conductivity and disorder-insensitive photonic transport. Recently, a novel class of topological phases, called higher-order topological phases, were proposed by generalizing the fundamental relationship between the Berry phase and the quantized polarization, from dipole to multipole…
We report on transport properties of the super-honeycomb lattice, the band structure of which possesses a flat band and Dirac cones, according to the tight-binding approximation. This super-honeycomb model combines the honeycomb lattice and the Lieb lattice and displays the properties of both. The super-honeycomb lattice also represents a hybrid fermionic and bosonic system, which is rarely seen in nature. By choosing the phases of input beams properly, the flat-band mode of the super-honeycomb will be excited and the input beams will exhibit strong localization during propagation. On the othe…
The introduction of topology unravels a new chapter of physics. Topological systems provide unique edge/interfacial quantum states which are expected to contribute to the development of novel spintronics and open the door to robust quantum computation. Optical systems can also benefit from topology. Engineering locally in real space a honeycomb photonic crystal with double Dirac cone in its photonic dispersion, topology transition in photonic band structure is induced and a pseudospin unidirectional optical channel is created and demonstrated by the backscattering immune electromagnetic transp…
Circularly polarized photons have the Berry curvature in the semiclassical regime. Based on the kinetic equation for such chiral photons, we derive the (non)equilibrium expression of the photon current in the direction of the vorticity. We briefly discuss the relevance of this "photonic chiral vortical effect" in pulsars and rotating massive stars and its possible realization in semiconductors.
Photonic crystal topological insulators host protected states at their edges. In the band structure these edge states appear as continuous bands crossing the photonic band gap. They allow light to propagate unidirectionally and without scattering. In practice it is essential to make devices relying on these effects as miniature as possible. Here we study all-dielectric photonic topological insulator particles (finite crystals) which do not require a magnetic field. In such particles the edge states' frequencies are discrete. Nevertheless, the discrete states support pseudospin-dependent unidir…
Topological protection in photonics offers new prospects for guiding and manipulating classical and quantum information. The mechanism of spin-orbit coupling promises the emergence of edge states that are helical; exhibiting unidirectional propagation that is topologically protected against back-scattering. We directly observe the topological states of a photonic analogue of electronic materials exhibiting the quantum Spin Hall effect, living at the interface between two silicon photonic crystals with different topological order. Through the far-field radiation that is inherent to the states' …
Topological physics and in particular its connection with artificial gauge fields is a forefront topic in different physical systems, ranging from cold atoms to photonics and more recently semiconductor dressed exciton-photon states, called polaritons. Engineering the energy dispersion of polaritons in microcavities through nanofabrication or exploiting the intrinsic material and cavity anisotropies has demonstrated many intriguing effects related to topology and emergent gauge fields. Here, we show that we can control the Berry curvature distribution of polariton bands in a strongly coupled o…
Photonic crystals with a two-dimensional triangular lattice have a conical singularity in the spectrum. Close to this so-called Dirac point, Maxwell's equations reduce to the Dirac equation for an ultrarelativistic spin-1/2 particle. Here we show that the half-integer spin and the associated Berry phase remain observable in the presence of disorder in the crystal. While constructive interference of a scalar (spin-zero) wave produces a coherent backscattering peak, consisting of a doubling of the disorder-averaged reflected photon flux, the destructive interference caused by the Berry phase sup…
We report on the experimental realization of flat mirrors enabling the broadband generation of optical vortices upon reflection. The effect is based on the geometric Berry phase associated with the circular Bragg reflection phenomenon from chiral uniaxial media. We show the reflective optical vortex generation from both diffractive and nondiffractive paraxial light beams using spatially patterned chiral liquid crystal films. The intrinsic spectrally broadband character of spin-orbit generation of optical phase singularities is demonstrated over the full visible domain. Our results do not rely …
The Moebius strip, as a fascinating loop structure with one-sided topology, provides a rich playground for manipulating the non-trivial topological behavior of spinning particles, such as electrons, polaritons, and photons in both real and parameter spaces. For photons resonating in a Moebius-strip cavity, the occurrence of an extra phase, known as Berry phase, with purely topological origin is expected due to its non-trivial evolution in the parameter space. However, despite numerous theoretical investigations, characterizing optical Berry phase in a Moebius-strip cavity has remained elusive.…
The discovery of photonic topological insulators (PTIs) has opened the door to fundamentally new topological states of light.Current time-reversal-invariant PTIs emulate either the quantum spin Hall (QSH) effect or the quantum valley Hall (QVH) effect in condensed-matter systems, in order to achieve topological transport of photons whose propagation is predetermined by either 'photonic pseudospin' (abbreviated as 'spin') or valley. Here we demonstrate a new class of PTIs, whose topological phase is not determined solely by spin or valley, but is controlled by the competition between their indu…
Control and manipulation of electromagnetic waves has reached a new level with the recent understanding of topological states of matter. These metamaterials have the potential to revolutionize many areas in traditional electromagnetic design, from highly robust cavities to small footprint waveguides. Much of the past literature has been on the cutting edge of condensed matter physics, but there is now ample opportunity to explore their usage for practical microwave and optical devices. To assist the beginner, in this Tutorial we give a basic introduction to the essential concepts of topologica…
Weyl points in three-dimensional photonic crystals behave as monopoles of Berry flux in momentum space. Here, based on general symmetry analysis, we show that a minimal number of four symmetry-related (consequently equifrequency) Weyl points can be realized in time-reversal invariant photonic crystals. We further propose an experimentally-feasible way to modify double-gyroid photonic crystals to realize four equifrequency Weyl points, which is explicitly confirmed by our first-principle photonic band-structure calculations. Remarkably, photonic crystals with equifrequency Weyl points are quali…
The Chern topological numbers of a material platform are usually written in terms of the Berry curvature, which depends on the normal modes of the system. Here, we use a gauge invariant Green's function method to determine from first principles the topological invariants of photonic crystals. The proposed formalism does not require the calculation of the photonic band-structure, and can be easily implemented using the operators obtained with a standard plane-wave expansion. Furthermore, it is shown that the theory can be readily applied to the classification of topological phases of non-Hermit…
To a significant extent, the rich physical properties of photonic crystals are determined by the underlying geometry, in which the composed symmetry operators and their combinations contribute to the unique topological invariant to characterize the topological phases. Particularly, the inter- and intra-coupling modulation in the two-dimensional (2D) Su-Schrieffer-Heeger model yields the topological phase transition, and exhibit first-order edge localized states and second-order corner localized corner states. In this work, we use the geometric anisotropy into the 2D square lattice composed of …
The geometric phase and topological property for one-dimensional hybrid plasmonic-photonic crystals consisting of a simple lattice of graphene sheets are investigated systematically. For transverse magnetic waves, both plasmonic and photonic modes exist in the momentum space. The accidental degeneracy point of these two kinds of modes is identified to be a diabolic point accompanied with a topological phase transition. For a closed loop around this degeneracy point, the Berry phase is Pi as a consequence of the discontinuous jump of the geometric Zak phase. The wave impedance is calculated ana…
Second order nonlinearities in whispering gallery mode resonators are highly investigated for their many applications such as wavelength converters, entangled photon sources and generation of frequency combs. In such systems, depending on the material under scrutiny, the derivation of quasi-phase matching equations can lead to the appearance of additional quanta in the selection rule on the azimuthal confinement order. Here, we demonstrate that these additional quanta show up due to the Berry phase experienced by the transverse spin angular momentum components of the whispering gallery modes d…
In the research of topological phases of matter, valley pseudospins have been introduced into photonic systems. Here, we construct a split-ring photonic crystal (SPC) in which the spilt rings are distributed according to the Kagome model. By rotating three split rings as a whole under the condition of ensuring the existence of C3v symmetry, we obtain a traditional two-band-inversion valley topology (2IVT) driven by opening twofold Dirac degeneracy point. When three split rings are rotated as a whole without ensuring the existence of C3v symmetry, a valley-like topology driven by opening twofol…
