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.

Random-Gate-Voltage Induced Al'tshuler–Aronov–Spivak Effect in Topological Edge States

Helical edge states are the hallmark of the quantum spin Hall insulator. Recently, several experiments have observed transport signatures contributed by trivial edge states, making it difficult to distinguish between the topologically trivial and nontrivial phases. Here, we show that helical edge states can be identified by the randomgate-voltage induced Φ_(0)/2-period oscillation of the averaged electron return probability in the interferometer constructed by the edge states. The random gate voltage can highlight the Φ_(0)/2-period Al'tshuler–Aronov–Spivak oscillation proportional to sin^(2)(2πΦ/Φ_(0)) by quenching the Φ_(0)-period Aharonov–Bohm oscillation. It is found that the helical spin texture induced π Berry phase is key to such weak antilocalization behavior with zero return probability at Φ = 0. In contrast, the oscillation for the trivial edge states may exhibit either weak localization or antilocalization depending on the strength of the spin-orbit coupling, which has finite return probability at Φ = 0. Our results provide an effective way for the identification of the helical edge states. The predicted signature is stabilized by the time-reversal symmetry so that it is robust against disorder and does not require any fine adjustment of system.

Quantum transport signatures of non-trivial topological edge states in a ring-shaped Su–Schrieffer–Heeger double-chain system

In the ring-shaped Su–Schrieffer–Heeger(SSH)double-chain,the quantum interference between the two different electron tunneling paths of the upper and lower chains has an important influence on the electron transport properties of non-trivial topological edge states.Here,we have studied the electron transport signatures of non-trivial topological edge states in a ring-shaped SSH double-chain system based on the wave-guide theory and transfer-matrix method.In the ringshaped SSH double-chain with the upper chain being different from the lower one,it is demonstrated that the electron transmission probability displays the four and two resonance peaks associated with the non-trivial topological edge states in the weak and strong coupling regimes,respectively.Whereas in the case of the upper chain being the same as the lower one,the two transmission resonance peaks associated with the non-trivial topological edge states in the weak coupling regime are only found,and that in the strong coupling regime disappear that originated from the destructive interference between the two different electron tunneling paths of the upper and lower chains.Consequently,the variation of the number of transmission resonance peaks associated with the non-trivial topological edge states in the weak and strong coupling regimes suggests that an alternative scheme for detecting non-trivial topological edge states in the ring-shaped SSH doublechain system.

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.

Actively Reconfigurable Valley Topological Edge and Corner States in Photonic Crystals Based on Phase Change Material Ge2Sb2Te5

The immunity of topological states against backscattering and structural defects provides them with a unique advantage in the exploration and design of high-precision low-loss optical devices.However,the operating bandwidth of the topological states in certain photonic structures is difficult to actively tune and flexibly reconfigure.In this study,we propose a valley topological photonic crystal(TPC)comprising two inverse honeycomb photonic crystals,consisting of hexagonal silicon and Ge2Sb2Te5(GST)rods.When GST transitions from the amorphous phase to the crystalline phase,the edge band of the TPC appears as a significant redshift and is inversed from a“∪”to an“∩”shape with topological phase transition,which enables active tuning of the operating bandwidth and propagation direction of topological edge states.Both the topological edge and corner states in a triangular structure constructed using TPCs can be simultaneously adjusted and reconfigured via GST phase transition,along with a change in the group number of corner states.Using the adjustability of topological edge states and electromagnetic coupling between two different topological bearded interfaces,we develop a multichannel optical router with a high tuning degree of freedom,where channels can be actively reconfigured and their on/off states can be freely switched.Our study provides a strategy for the active regulation of topological states and may be beneficial for the development of reconfigurable topological optical devices.

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.

Highly efficient conversion from classical guided waves to topological chiral edge states

Electromagnetic topological chiral edge states mimicking the quantum Hall effect have attracted a great deal of attention due to their unique features of free backscattering and immunity against sharp bends and defects.However,the matching techniques between classical waveguides and the topological one-way waveguide deserve more attention for real-world applications.In this paper,a highly efficient conversion structure between a classical rectangular waveguide and a topological one-way waveguide is proposed and demonstrated at the microwave frequency,which efficiently converts classical guided waves to topological one-way edge states.A tapered transition is designed to match both the momentum and impedance of the classical guided waves and the topological one-way edge states.With the conversion structure,the waves generated by a point excitation source can be coupled to the topological one-way waveguide with very high coupling efficiency,which can ensure high transmission of the whole system(i.e.,from the source and the receiver).Simulation and measurement results demonstrate the proposed method.This investigation is beneficial to the applications of topological one-way waveguides and opens up a new avenue for advanced topological and classical integrated functional devices and systems.

Energy-resolved spin filtering effect and thermoelectric effect in topological-insulator junctions with anisotropic chiral edge states

Topological edge states have crucial applications in the future nano spintronics devices.In this work,circularly polarized light is applied on the zigzag silicene-like nanoribbons resulting in the anisotropic chiral edge modes.An energy-dependent spin filter is designed based on the topological-insulator(TI)junctions with anisotropic chiral edge states.The resonance transmission has been observed in the TI junctions by calculating the local current distributions.And some strong Fabry–Perot resonances are found leading to the sharp transmission peaks.Whereas,the weak and asymmetric resonance corresponds to the broad transmission peaks.In addition,a qualitative relation between the resonant energy separation TR and group velocity vf is derived:TR=πhvf n/L,that indicated TR is proportional to vf and inversely proportional to the length L of the conductor.The different TR between the spin-up and spin-down cases results in the energyresolved spin filtering effect.Moreover,the intensity of the circularly polarized light can modulate the group velocity vf.Thus,the intensity of circularly polarized light,as well as the conductor-length,play very vital roles in designing the energy-dependent spin filter.Since the transmission gap root in the Fabry–Perot resonances,the thermoelectric(TE)property can be enhanced by adjusting the gap.A schedule to enhance the TE performance in the TI-junction is proposed by modulating the electric field(Ez).The TE dependence on Ez in the nanojunction is investigated,where the appropriate Ez leads to a very high spin thermopower and spin figure of merit.These TI junctions have potential usages in the nano spintronics and thermoelectric devices.

Efficient and stable wireless power transfer based on the non-Hermitian physics

As one of the most attractive non-radiative power transfer mechanisms without cables,efficient magnetic resonance wireless power transfer(WPT)in the near field has been extensively developed in recent years,and promoted a variety of practical applications,such as mobile phones,medical implant devices and electric vehicles.However,the physical mechanism behind some key limitations of the resonance WPT,such as frequency splitting and size-dependent efficiency,is not very clear under the widely used circuit model.Here,we review the recently developed efficient and stable resonance WPT based on non-Hermitian physics,which starts from a completely different avenue(utilizing loss and gain)to introduce novel functionalities to the resonance WPT.From the perspective of non-Hermitian photonics,the coherent and incoherent effects compete and coexist in the WPT system,and the weak stable of energy transfer mainly comes from the broken phase associated with the phase transition of parity-time symmetry.Based on this basic physical framework,some optimization schemes are proposed,including using nonlinear effect,using bound states in the continuum,or resorting to the system with high-order parity-time symmetry.Moreover,the combination of non-Hermitian physics and topological photonics in multi-coil system also provides a versatile platform for long-range robust WPT with topological protection.Therefore,the non-Hermitian physics can not only exactly predict the main results of current WPT systems,but also provide new ways to solve the difficulties of previous designs.

Underwater acoustic metamaterial based on double Dirac cone characteristics in rectangular phononic crystals

We theoretically construct a rectangular phononic crystal(PC) structure surrounded by water with C2vsymmetry, and then place a steel rectangular scatterer at each quarter position inside each cell. The final complex crystal has two forms:the vertical type, in which the distance s between the center of the scatterer and its right-angle point is greater than 0.5 a,and the transverse type, in which s is smaller than 0.5 a(where a is the crystal constant in the x direction). Each rectangular scatterer has three variables: length L, width D, and rotation angle θ around its centroid. We find that, when L and D change and θ is kept at zero, there is always a linear quadruply degenerate state at the corner of the irreducible Brillouin zone. Then, we vary θ and find that the quadruply degenerate point splits into two doubly-degenerate states with odd and even parities. At the same time, the band structure reverses and undergoes a phase change from topologically non-trivial to topologically trivial. Then we construct an acoustic system consisting of a trivial and a non-trivial PC with equal numbers of layers, and calculate the projected band structure. A helical one-way transmission edge state is found in the frequency range of the body band gap. Then, we use the finite-element software Comsol to simulate the unidirectional transmission of this edge state and the backscattering suppression of right-angle, disorder, and cavity defects. This acoustic wave system with rectangular phononic crystal form broadens the scope of acoustic wave topology and provides a platform for easy acoustic operation.

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.

Observation of an acoustic non-Hermitian topological Anderson insulator

The interaction of band topology and disorder can give rise to intriguing phenomena.One paradigmatic example is the topological Anderson insulator,whose nontrivial topology is induced in a trivial system by disorders.In this study,we investigate the efect of purely non-Hermitian disorders on topological systems using a one-dimensional acoustic lattice with coupled resonators.Specifically,we construct a theoretical framework to describe the non-Hermitian topological Anderson insulator phase solely driven by disordered loss modulation.Then,the complete evolution of non-Hermitian disorder-induced topological phase transitions,from an initial trivial phase to a topological Anderson phase and finally to a trivial Anderson phase,is revealed experimentally using both bulk and edge spectra.Interestingly,topological modes induced by non-Hermitian disorders to be immune to both weak Hermitian and non-Hermitian disorders.These findings pave the way for future research on disordered non-Hermitian systems for novel wave manipulation.

Topological Landau–Zener nanophotonic circuits

Topological edge states(TESs),arising from topologically nontrivial phases,provide a powerful toolkit for the architecture design of photonic integrated circuits,since they are highly robust and strongly localized at the boundaries of topological insulators.It is highly desirable to be able to control TES transport in photonic implementations.Enhancing the coupling between the TESs in a finite-size optical lattice is capable of exchanging light energy between the boundaries of a topological lattice,hence facilitating the flexible control of TES transport.However,existing strategies have paid little attention to enhancing the coupling effects between the TESs through the finite-size effect.Here,we establish a bridge linking the interaction between the TESs in a finite-size optical lattice using the Landau–Zener model so as to provide an alternative way to modulate/control the transport of topological modes.We experimentally demonstrate an edge-to-edge topological transport with high efficiency at telecommunication wavelengths in silicon waveguide lattices.Our results may power up various potential applications for integrated topological photonics.

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.

Reconfigurable nested photonic topological loops

Photonic structures with topological edge states and resonance loops are both important in optical communication systems,but they are usually two separate structures.In order to obtain a photonic system combining properties from both,we design multiple-layer nested photonic topological structures.The nested topological loops not only have topological protection immune to structural disorder and defects,but also possess both the properties of unidirectional propagation and loop resonance.Through mode analysis and simulations,we find that the transport can form diverse circulation loops.Each loop has its own resonance frequencies and can be solely excited in the nested layered structure through choosing its resonance frequencies.As a result,this work shows great application prospects in the area of reconfigurable photonic circuits.

Non-Hermitian topological coupler for elastic waves

Non-Hermitian topological systems,by combining the advantages of topological robustness and sensitivity induced by nonHermiticity,have recently emerged and attracted much research interest.Here,we propose a device based on the topological coupler in elastic waves with non-Hermiticity,which contains two topological domain walls and four ports.In this device,topological robustness routes the transmission of waves,while non-Hermiticity controls the gain or loss of waves as they propagate.These mechanisms result in continuous and quantitative control of the energy distribution ratio of each port.A nonHermitian Hamiltonian is introduced to reveal the coupling mechanism of the topological coupler,and a scattering matrix is proposed to predict the energy distribution ratio of each port.The proposed topological coupler,which provides a new paradigm for the non-Hermitian topological systems,can be employed as a sensitive beam splitter or a coupler switch.Moreover,the topological coupler has potential applications in information processing and logic operation in elastic circuits or networks,and the paradigm also applies to other classical systems.