Topological edge and corner states of valley photonic crystals with zipper-like boundary conditions

We present a stable valley photonic crystal(VPC)unit cell with C_(3v)symmetric quasi-ring-shaped dielectric columns and realize its topological phase transition by breaking mirror symmetry.Based on this unit cell structure,topological edge states(TESs)and topological corner states(TCSs)are realized.We obtain a new type of wave transmission mode based on photonic crystal zipper-like boundaries and apply it to a beam splitter assembled from rectangular photonic crystals(PCs).The constructed beam splitter structure is compact and possesses frequency separation functions.In addition,we construct a box-shaped triangular PC structures with zipper-like boundaries and discover phenomena of TCSs in the corners,comparing its corner states with those formed by other boundaries.Based on this,we explore the regularities of the electric field patterns of TESs and TCSs,explain the connection between the characteristic frequencies and locality of TCSs,which helps better control photons and ensures low power consumption of the system.

High-performance chiral all-optical OR logic gate based on topological edge states of valley photonic crystal

For all-optical communication and information processing,it is necessary to develop all-optical logic gates based on photonic structures that can directly perform logic operations.All-optical logic gates have been demonstrated based on conventional waveguides and interferometry,as well as photonic crystal structures.Nonetheless,any defects in those structures will introduce high scattering loss,which compromises the fidelity and contrast ratio of the information process.Based on the spin-valley locking effect that can achieve defect-immune unidirectional transmission of topological edge states in valley photonic crystals(VPCs),we propose a high-performance all-optical logic OR gate based on a VPC structure.By tuning the working bandwidth of the two input channels,we prevent interference between the two channels to achieve a stable and high-fidelity output.The transmittance of both channels is higher than 0.8,and a high contrast ratio of 28.8 dB is achieved.Moreover,the chirality of the logic gate originated from the spin-valley locking effect allows using different circularly polarized light as inputs,representing“1”or“0”,which is highly desired in quantum computing.The device’s footprint is 18μm×12μm,allowing high-density on-chip integration.In addition,this design can be experimentally fabricated using current nanofabrication techniques and will have potential applications in optical communication,information processing,and quantum computing.

Topological resonators based on hexagonal-star valley photonic crystals

In valley photonic crystals, topological edge states can be gained by breaking the spatial inversion symmetry without breaking time-reversal symmetry or creating pseudo-spin structures, making highly unidirectional light transmission easy to achieve. This paper presents a novel physical model of a hexagonal-star valley photonic crystal. Simulations based on the finite element method(FEM) are performed to investigate the propagation of TM polarized mode and its application to ring resonators. The results show that such a topologically triangular ring resonator exhibits an optimum quality factor Q of about 1.25×104, and Q has a maximum value for both frequency and the cavity length L. Our findings are expected to have significant implications for developing topological lasers and wavelength division multiplexers.

Nonlinear topological valley Hall edge states arising from type-Ⅱ Dirac cones

A Dirac point is a linear band crossing point originally used to describe unusual transport properties of materials like graphene.In recent years,there has been a surge of exploration of type-II Dirac/Weyl points using various engineered platforms including photonic crystals,waveguide arrays,metasurfaces,magnetized plasma and polariton micropillars,aiming toward relativistic quantum emulation and understanding of exotic topological phenomena.Such endeavors,however,have focused mainly on linear topological states in real or synthetic Dirac/Weyl materials.We propose and demonstrate nonlinear valley Hall edge(VHE)states in laserwritten anisotropic photonic lattices hosting innately the type-Ⅱ Dirac points.These self-trapped VHE states,manifested as topological gap quasi-solitons that can move along a domain wall unidirectionally without changing their profiles,are independent of external magnetic fields or complex longitudinal modulations,and thus are superior in comparison with previously reported topological edge solitons.Our finding may provide a route for understanding nonlinear phenomena in systems with type-Ⅱ Dirac points that violate the Lorentz invariance and may bring about possibilities for subsequent technological development in light field manipulation and photonic devices.

Tailoring edge and interface states in topological metastructures exhibiting the acoustic valley Hall effect

In this study, we investigate the acoustic topological insulator or topological metastructure, where an acoustic wave can exist only in an edge or interface state instead of propagating in bulk. Breaking the structural symmetry enables the opening of the Dirac cone in the band structure and the generation of a new band gap, wherein a topological edge or interface state emerges.Further, we systematically analyze two types of topological states that stem from the acoustic valley Hall effect mechanism;one type is confined to the boundary, whereas the other type can be observed at the interface between two topologically different structures. Results denote that the selection of different boundaries along with appropriately designed interfaces provides the acoustic waves in the band gap range with abilities of one-way propagation, dual-channel propagation, immunity from backscattering at sharp corners, and/or transition between propagation at interfaces and boundaries. Furthermore, we show that the acoustic wave propagation paths can be tailored in diverse and arbitrary ways by combing the two aforementioned types of topological states.

Valley-Chiral Edge States of Antisymmetric Plate Wave in Phononic Crystals with Linear Defect

In this work,two typical interfaces are established for the antisymmetric plate wave by introducing linear defect in between phononic crystals with opposite valley Hall phases.The evolution of projected curves is demonstrated as the defect width increases,which magnifies the occurrence of multiple edge states on both interfaces.The mapping of transmission coefficient is obtained upon the incidence of transversely symmetric and antisymmetric sources,respectively.It is shown that the first edge state contains only symmetric or antisymmetric component regardless the defect width modulation,while other edge states contain both components.When void cavity occurs on the interfaces,the mapping of transmission coefficient shows that the first edge state is topologically protected and its transverse symmetry or antisymmetry is almost unperturbed by the void cavity,while other edge states do not perform the same way.Our work provides useful guidance for the design of topological edge states,and bridges the topological edge states and linear defect modes on the same interface.

Vector valley Hall edge solitons in the photonic lattice with type-Ⅱ Dirac cones

Topological edge solitons represent a significant research topic in the nonlinear topological photonics.They maintain their profiles during propagation,due to the joint action of lattice potential and nonlinearity,and at the same time are immune to defects or disorders,thanks to the topological protection.In the past few years topological edge solitons were reported in systems composed of helical waveguide arrays,in which the time-reversal symmetry is effectively broken.Very recently,topological valley Hall edge solitons have been demonstrated in straight waveguide arrays with the time-reversal symmetry preserved.However,these were scalar solitary structures.Here,for the first time,we report vector valley Hall edge solitons in straight waveguide arrays arranged according to the photonic lattice with innate type-II Dirac cones,which is different from the traditional photonic lattices with type-I Dirac cones such as honeycomb lattice.This comes about because the valley Hall edge state can possess both negative and positive dispersions,which allows the mixing of two different edge states into a vector soliton.Our results not only provide a novel avenue for manipulating topological edge states in the nonlinear regime,but also enlighten relevant research based on the lattices with type-II Dirac cones.

Nonlinear harmonic generation of terahertz waves in a topological valley polaritonic microcavity

Compact terahertz(THz)devices,especially for nonlinear THz components,have received more and more attention due to their potential applications in THz nonlinearity-based sensing,communications,and computing devices.However,effective means to enhance,control,and confine the nonlinear harmonics of THz waves remain a great challenge for micro-scale THz nonlinear devices.In this work,we have established a technique for nonlinear harmonic generation of THz waves based on phonon polariton-enhanced giant THz nonlinearity in a 2D-topologically protected valley photonic microcavity.Effective THz harmonic generation has been observed in both noncentrosymmetric and centrosymmetric nonlinear materials.These results can provide a valuable reference for the generation and control of THz high-harmonics,thus developing new nonlinear devices in the THz regime.

谷边缘态作为连续域中的束缚态

Bound states in the continuum(BICs) are spatially localized states with energy embedded in the continuum spectrum of extended states. The combination of BICs physics and nontrivial band topology theory givs rise to topological BICs, which are robust against disorders and meanwhile, the merit of conventional BICs is attracting wide attention recently. Here, we report valley edge states as topological BICs, which appear at the domain wall between two distinct valley topological phases. The robustness of such BICs is demonstrated. The simulations and experiments show great agreement. Our findings of valley related topological BICs shed light on both BICs and valley physics, and may foster innovative applications of topological acoustic devices.

Valley-resolved transport in zigzag graphene nanoribbon junctions

Applying the transfer matrix and Green’s function methods,we study the valley-resolved transport properties of zigzag graphene nanoribbon(ZGN_(R))junctions.The width of the left and right ZGN_(R)s are N_(L)and N_(R),and N_(L)≥N_(R).The step/dip positions of the conductance G,the intravalley transmission coefficients(TKKand TK’K’),and the valley polarization efficiency PK’K correspond to the subband edges of the right/left ZGN_(R)that are controlled by N_(R)/N_(L).The intervalley transmission coefficients(TKK and TK’K)exhibit peaks at most of the subband edge of the left and right ZGN_(R)s.In the bulk gap of the right ZGN_(R),TKK’=TK’K=0,and PKK’=±1,the valley polarization is well preserved.As N_(R)increases,the energy region for PK’K=±1 decreases.When N_(L)is fixed and N_(R)decreases,G,TKK,TK’K’and PKK’exhibit more and more dips,and the peaks of TKK’(TK’K)become more and more high,especially when(N_(L)-N_(R))/2 is odd.These characters are quite useful for manipulating the valley dependent transport properties of carriers in ZGN_(R)junctions by modulating N_(L)or N_(R),and our results are helpful to the design of valleytronics based on ZGN_(R)junctions.

Tunable hexagonal boron nitride topological optical delay line in the visible region

Tunability,ultracompact design,high group index,low loss,and broad bandwidth are desired properties for integrated optical delay lines(ODLs).However,those properties are challenging to achieve simultaneously in the visible region.This paper proposes a tunable hexagonal boron nitride topological optical delay line(ODL)in the visible region based on valley photonic crystals.The topological edge state from the beard-type boundary allows the achievement of an ultralow group velocity close to zero,which results in a large group index of 629 at 645 nm.Moreover,we demonstrate tuning of the slow-light wavelength and optical delay times with electrically tunable liquid crystals by applying external voltage.The device has an ultracompact size of 5μm×2.7μm with an optical delay distance of 25a(a is the lattice constant)and a delay time of 12 ps.Our design can provide a new possibility for designing ODLs working in the visible region for optical communication and quantum computing systems.