Topological Interface Modes Research Articles

Investigating the robustness of interface topological modes in rods

Topological phononic crystals and metamaterials are structures that can present waveguiding and energy concentration phenomena, which can be of interest in structural dynamics for energy harvesting and passive vibration and noise control. The periodicity of the typical phononic crystals and metamaterials is broken for these structures, which need to present at least two crystal lattices with different topological characteristics. Thus, the topological invariant, such as the Zak phase, which defines the topological characteristic, must be computed. A rod metastructure exhibiting two low-frequency band gaps, each with a topological interface mode, was designed. It has bolt sets whose weights generate variability, which was modeled and inferred. In order to increase variability along the rod metastructure, washers were included or removed. Experiments were performed to validate the simulations. It was observed that the variability of the topological mode in the first band gap is more robust considering its mode shape, natural frequency, and energy concentration at the interface than the second interface mode, at higher frequency. As variability increases, the robustness of the energy concentration at the interface and of the mode shape of both topological modes decreases. The same behavior was observed for the natural frequencies of the topological modes.

Highly Tunable Light Absorber Based on Topological Interface Mode Excitation of Optical Tamm State.

Optical absorbers based on Tamm plasmon states are known for their simple structure and high operational efficiency. However, these absorbers often have limited absorption channels, and it is challenging to continuously adjust their light absorption rates. Here, we propose a Tamm plasmon state optical absorber composed of a layered stack structure consisting of one-dimensional topological photonic crystals and graphene nano-composite materials. Using the four-by-four transfer matrix method, we investigate the structural relationship of the absorber. Our results reveal that topological interface states (TISs) effectively excite the optical Tamm state (OTS), leading to multiple absorption peaks. This expands the number of absorption channels, with the coupling number of the TIS determining the transmission quality of these channels-a value further adjustable by the period number of the photonic crystals. Tuning the filling factor, refractive index, and thickness of the graphene nano-composite material allows for a wide range of control over the device's absorption rate, from 0 to 1. Additionally, adjusting the defect layer thickness, incident angle, and Fermi energy enables us to control the absorber's operational bandwidth and the switching of its absorption effect. This work presents a new approach to expanding the tunability of optoelectronic devices.

Low-frequency multiple topological interface modes in metamaterial beams with quasi-zero-stiffness resonators

To achieve multiple low-frequency topological interface modes (TIMs) while maintaining lightweight and load-bearing capacities in metamaterial beams, we propose novel topological beams equipped with double quasi-zero-stiffness (QZS) resonators. Following the introduction of the negative stiffness (NS) mechanism, we derived the dispersion relations of the topological beams with double QZS resonators using the transfer matrix method (TMM), and performed comparative and parametric analyses of stiffness ratio on folded Dirac cones (DCs) and locally resonant band gaps (LRBGs). Thanks to the NS mechanism and the double degrees of freedom (DOFs) in the QZS resonators, we can realize double low-frequency DCs (< 500 Hz) in metamaterial beams. It is notable that adjusting the stiffness of oblique springs can tune the resonators’ effective stiffness, implying that we can custom the frequency of DCs and LRBGs by adjusting the QZS resonator. By altering the distance between two QZS resonators, we obtain two topologically distinct unit cells. Transmission simulations confirm the presence of multiple low-frequency TIMs at the interface between these two domains. We also find that the effect of mass and geometric defects at various positions on TIMs is minimal. The proposed metamaterial beams could inspire innovative low-frequency vibration energy harvesters and lightweight topological devices.

Multifrequency topological interface modes in a nonlocal acoustic system with large winding numbers

Topological interface states have wide applications for their robustness and energy localization. Multiple topological interface states in 1D acoustic systems are preferred for signal enhancement at specific frequencies. However, previous 1D topological systems with local interactions can realize only one topological interface state in a bandgap. Here, we find that connected acoustic Su–Schrieffer–Heeger (SSH) chains with nonlocal interactions can achieve two or more topological interface states at different frequencies in a single bandgap, even in the subwavelength region. The difference in frequency can be modulated by merely adjusting the structural design at the interface. A mechanical metamaterial with a large winding number is designed to realize multiple nondegenerate topological interface states. This metamaterial can enhance weak acoustic signals at multiple specific frequencies simultaneously and has applications in the fields of acoustic detecting and color imaging.

A novel 3D topological metamaterial for controllability of polarization-dependent multilayer elastic waves

The achievement of high-quality wave manipulation and energy concentration has always been considered as state-of-the-art technologies, especially for integrated photonics, acoustics, and mechanics. The exploration of the topological phase of matter provides abundant design tools for robust waveguiding that is immune to backscattering at small defects and sharp bends. Recent research has extended the elastic wave manipulation from 2D edge waveguiding to 3D planar waveguiding. However, most of them are limited to single-mode and single-frequency wave propagation along the designed plane. This paper introduces a novel 3D topological metamaterial structure whose geometrical parameters are specifically configured to obtain dual-mode topological states at distinct frequencies. Parametric studies are presented to demonstrate the controllability of bandgaps and to provide a design principle for preventing the effects of unwanted modes. Topological interface modes with either high group velocity or near-zero group velocity along the z direction are found. Full-scale finite element simulations are presented to uncover the elastic wave propagation behavior. The interesting layer-locked and layer-unlocked waveguiding based on excitation polarization and frequency for both straight path and zig-zag path are demonstrated. The outcomes of this work suggest abundant potential applications related to elastic wave control such as wave filters, energy harvesters, mechanical computers, and the like. This work may also help inspire future research on more complex and sophisticated multi-mode waveguiding in 3D spaces.

Single-Mode Laser in the Telecom Range by Deterministic Amplification of the Topological Interface Mode.

Photonic integrated circuits are paving the way for novel on-chip functionalities with diverse applications in communication, computing, and beyond. The integration of on-chip light sources, especially single-mode lasers, is crucial for advancing those photonic chips to their full potential. Recently, novel concepts involving topological designs introduced a variety of options for tuning device properties, such as the desired single-mode emission. Here, we introduce a novel cavity design that allows amplification of the topological interface mode by deterministic placement of gain material within a topological lattice. The proposed design is experimentally implemented by a selective epitaxy process to achieve closely spaced Si and InGaAs nanorods embedded within the same layer. This results in the first demonstration of a single-mode laser in the telecom band using the concept of amplified topological modes without introducing artificial losses.

Robust elastic shear wave transport in membrane-type topological metamaterials induced by material difference

Novel membrane-type topological metamaterials induced by material difference are investigated in this work. Different from previous common method to break spatial inversion symmetry and realize topological phase transition, choosing different materials is more convenient and shows more complex topological properties. Not all combinations of different materials can open the topological band gap. Interestingly, not only the topological interface modes but also the conventional interface modes are found in this system. Although strong energy localization capacity is found near the interface, both kinds of interface modes show different robustness against defects. To further enhance adaptability to environmental variations and broaden the working frequency range, the thermal field is introduced in membrane-type topological metamaterials to tune the dispersion relations. Fortunately, not only interface modes can be tuned to a lower frequency range, but also the energy localization of interface modes can be remained at a high level. The temperature can act as a switch to turn on/off the robust shear wave transport in membrane-type topological metamaterials. Given that, novel temperature-controlled topological metamaterials are expected to open new avenues for active elastic multifunctional devices.

Topological elastic interface states in hyperuniform pillared metabeams

Topological states have been receiving a great deal of interest in various wave problems, such as photonic, acoustic, and elastic waves. However, few studies of topological elastic waves in non-periodic systems have been reported. Recently, hyperuniform systems suppressing long-range order while partly maintaining short-range order have provided new opportunities to control waves. In this work, we study the elastic topological interface states appearing between two Su–Schrieffer–Heeger (SSH)-like pillared metabeams where each metabeam, is constituted by a mirror symmetric hyperuniform structure. The SSH-like model is constructed by combining two hyperuniform metabeams with inverted configurations. We demonstrate that this structure could open new bandgaps at low frequencies, of which some are nontrivial and can support topological interface modes. We further show that the number of low-frequency bandgaps supporting the topological modes increases with the level of randomness, hence providing a high number of interface modes in the same structure. The robustness of the topological interface states against random perturbations in the pillars’ positions is further verified. Our work offers a reliable platform for studying topological properties and hyperuniform metamaterials and designing wave control devices for low-frequency wave attenuation and robust energy localization.

Optical bistability modulation based on graphene sandwich structure with topological interface modes.

In this paper, we have investigated optical bistability modulation of transmitted beam that can be achieved by graphene sandwich structure with topological interface modes at terahertz frequency. Graphene with strong nonlinear optical effect was combined with sandwich photonic crystal to form a new sandwich structure with topological interface modes. The light-limiting properties of the topological interface modes, as well as its high unidirectionality and high transmission efficiency, all contribute positively to the reduction of the optical bistability threshold. In addition, the topological interface modes can effectively ensure the stability of the two steady state switching in the case of external interference. Moreover, optical bistability is closely related to the incident angle, the Fermi energy, the relaxation time, and the number of layers of graphene. Through parameter optimization, optical bistability with threshold of 105 V/m can be obtained, which has reached or is close to the range of the weak field.

Active control on topological interface states of elastic wave metamaterials with double coupled chains.

Topological elastic wave metamaterials have shown significant advantages in manipulating wave propagation and realizing localized modes. However, topological properties of most mechanical metamaterials are difficult to change because of structural limitations. This work proposes the elastic wave metamaterials with double coupled chains and active control, in which band inversion and topological interface modes can be achieved by flexibly tuning negative capacitance circuits. Finite element simulations and experiments are performed to demonstrate the topological interface modes, which show good agreements with the theoretical results. This research seeks to provide effective strategies for the design and application of topological elastic wave metamaterials.

Topological photonic crystal fiber with honeycomb structure.

We analyze a new type of photonic crystal fiber which consists of the core and cladding that distinct in topology by tuning the position of air holes in each hexagonal unit cell where the C6v symmetry is respected. The p-d band inversion between the core and cladding leads to topological interface modes inside the band gap, which can propagate along the fiber with a nonzero momentum in perpendicular to the corss section of a fiber. The helical topological interface modes possess the pseudospin-momentum locking effect inherited from the corresonding two-dimensional photonic crystal characterized by the Z2 topology. The wave functions for the topological interface modes are analytically studied and compared successfully to the numerical results, enlighting a novel way to use photonic crystal fiber to transfer information.

Exploring Photonic Crystals: Band Structure and Topological Interface States

The physical mechanisms supporting the existence of topological interface modes in photonic structures, formed with the concatenation of two finite, N-period, one-dimensional photonic crystals, are investigated. It is shown that these mechanisms originate from a specific configuration of bands and bandgaps of topological origin in the band structure of the concatenated structure. Our analysis reveals that the characteristics of such a configuration depend on the structural parameters, including the number, N, of unit cells, and determine the properties of the corresponding resonant transmission peak. It was shown that the width and maximum value of the transmission peaks decrease with N. These results not only provide new physical insight into the origin and nature of such modes, but also can be used to control and manipulate the transmission peak properties, such as peak values, full width at half maximum (FWHM), and Q-factor, which are of special interest in the fields of optical sensing, filters, etc.

New topological rainbow trapping approach for phononic beam-foundation systems

Rainbow trapping is of great significance for frequency-based wave splitting and broadband wave attenuation. By recognizing the deficiency of prevailing gradient rainbow reflection devices in terms of energy concentration and broadband vibration isolation, we design a new topological rainbow trapping device by introducing a topological protected interface mode (TPIM) into the prevailing gradient rainbow device. Therefore, a topological rainbow trapping beam composed of a homogenous beam rested on an alternate and gradient foundation is constructed. Using theoretical and numerical analysis, we perform a unit-cell band structure analysis. The dependence of bandgap region and group velocity on the reference foundation stiffness is investigated. With the help of the topological phase transition and Zak phase analysis, we successfully predict and demonstrate TPIM. A quantitative evaluation of the advancement of topological rainbow devices upon the prevailing gradient device in vibration amplification and broadband wave attenuation is also presented. We believe that the robust one-dimensional topological rainbow trapping beam will be useful in many applications, such as energy harvesting, wave splitting, and vibration control.

Tailoring of interface modes in topologically protected edge states with hourglass lattice metamaterials

Nonreciprocity and topologically protected wave propagation have significant implications on how energy and information are transmitted or guided within materials to control or mitigate its effects. The major challenge in tailoring interface mode arises from challenges related to the customizability and linearity of interface lattice, moreover, there is a scarce of experimental analysis reported in the literature. Our study has focused on obtaining topologically protected nontrivial interface modes at a specific frequency by breaking the inversion symmetry through novel hourglass metastructure both theoretically and experimentally. Detailed work on wave transmission, dispersion, and bandgap analysis are carried out considering topological metamaterials. New cellular configurations based on regular honeycomb and auxetic cells, and variations of their geometric parameters responsible for interface mode tuning are reported here. A generalized theoretical scheme for different combinations of the hourglass lattice is derived at the interface, and consequent energy harvesting and damping prospects are reported. Analytical modeling of topological metamaterial lattice along with numerical simulation, additive layer manufacturing (3D printing), and finally experimental validations are carried out to justify the behavior and reveal the underlying physics responsible for its unique behavior. Three types of configurations including hourglass lattice at the interface define a general framework for introducing lattice-based imperfections in the continuous elastic structure for potential engineering applications. The localized topological interface mode obtained within the bandgap can be tuned significantly with the help of latticed hourglass and may be utilized for the purpose of wave guiding, wave focusing, and energy harvesting within the isolation zone.

Strongly nonlinear topological phases of cascaded topoelectrical circuits

Circuits provide ideal platforms of topological phases and matter, yet the study of topological circuits in the strongly nonlinear regime, has been lacking. We propose and experimentally demonstrate strongly nonlinear topological phases and transitions in one-dimensional electrical circuits composed of nonlinear capacitors. Nonlinear topological interface modes arise on domain walls of the circuit lattices, whose topological phases are controlled by the amplitudes of nonlinear voltage waves. Experimentally measured topological transition amplitudes are in good agreement with those derived from nonlinear topological band theory. Our prototype paves the way towards flexible metamaterials with amplitude-controlled rich topological phases and is readily extendable to two and three-dimensional systems that allow novel applications.

Extended topological interface modes with tunable frequency in the piezoelectric phononic crystal

Acoustic metamaterials have provided a versatile platform to explore more degrees of freedom for tunable topological wave manipulation. Recently, extended topological interface modes (ETIMs) with heterostructure have been proposed to extend the spatial degree of freedom. However, the absence of frequency tunability still restricts the application of the wave transports of ETIMs. Here, we propose a one-dimensional piezoelectric topological phononic crystal (PTPC) with electrically tunable working frequency by introducing external capacitor circuit. With the bandgap frequency actively controlled by appropriately tuning the capacitances, we construct the heterostructured PTPCs possessing high-energy-capacity ETIMs with electrically tunable working frequency range and bandwidth. This work paves the way to wide engineering applications on acoustic sensing enhancement, nondestructive testing, energy harvesting, information processing, and reconfigurable topological wave transports.

Observation of strong backscattering in valley-Hall photonic topological interface modes

The unique properties of light underpin the visions of photonic quantum technologies, optical interconnects and a wide range of novel sensors, but a key limiting factor today is losses due to either absorption or backscattering on defects. Recent developments in topological photonics have fostered the vision of backscattering-protected waveguides made from topological interface modes, but, surprisingly, measurements of their propagation losses were so far missing. Here we report on measurements of losses in the slow-light regime of valley-Hall topological waveguides and find no indications of topological protection against backscattering on ubiquitous structural defects. We image the light scattered out from the topological waveguides and find that the propagation losses are due to Anderson localization. The only photonic topological waveguides proposed for materials without intrinsic absorption in the optical domain are quantum spin-Hall and valley-Hall interface states, but the former exhibit strong out-of-plane losses, and our work, therefore, raises fundamental questions about the real-world value of topological protection in reciprocal photonics.

Controllable subwavelength topological rainbow trapping in water-filling acoustic metamaterials

Due to the great application potential in programmable wave transportation, topological metamaterials have gained enormous research attention in recent decades. This article proposes an acoustic metamaterial that is composed of a perforated nylon substrate and a ceiled air-flowing channel. The holes arranged in a honeycomb lattice are filled with water to tune the resonance frequency and topological phases. Two subwavelength bandgaps are opened by tuning the height of water columns, and controllable bandgap and topological phase transitions are subsequently obtained. Generally, the chirality conflict between different unitcells is designed to generate topological protected interface modes where energy is localized within close vicinity of the interface. After studying on the dependence of topological protected interface mode frequency and quality factor on water height, a design strategy is proposed to obtain high-quality topological protected interface mode at the target frequency. Two waveguiding paths are designed to study the wave propagation behavior along the interface under different excitation frequencies. Topological rainbow trapping which can terminate waves at different frequencies and different locations is finally demonstrated. The controllable bandgap and TPIM allow the topological structural designs to avoid complex structures and high cost.

Subwavelength tunable topological interface modes in metamaterial beams on elastic foundation

In this paper, by the aid of zone folding mechanism, the topological transition point (TTP) is produced in novel metamaterial beams on elastic foundation. Different from the existing topological system, the TTP is located between the locally resonant band gap (LRBG) and the transition zone, which are induced by the local resonance of resonators and Winkler foundation, respectively. The position of TTP can also be tuned effectively by the natural frequency of resonators and critical frequency of Winkler foundation. After opening the TTP by space modulation of resonators, two types of unit cells are produced, and a new topological band gap (TBG) is formed. Besides, topological properties of both types of unit cells are discussed by dispersion analysis. The band inversion and different Zak phase indicate that these two types of unit cells are topologically distinct. Therefore, the topologically protected interface mode (TPIM) will appear at the interface between two domains. The numerical simulation confirms the existence of TPIM. Meanwhile, the robustness of TPIM is investigated, including the influence of damping and defects. In detail, the transmission efficiency of TPIM is reduced with damping, while the frequency and width of TPIM are little affected. Interestingly, the introduction of mass defects is found to improve the transmission efficiency of TPIM. This novel topological system is expected to open new avenues for vibration mitigation and energy harvesting.

Optically controllable coupling between edge and topological interface modes of graphene metasurfaces

Nonlinear topological photonics has been attracting increasing research interest, as it provides an exciting photonic platform that combines the advantages of active all-optical control offered by nonlinear optics with the unique features of topological photonic systems, such as topologically-protected defect-immune light propagation. In this paper, we demonstrate that topological interface modes and trivial edge modes of a specially designed graphene metasurface can be coupled in a tunable and optically controllable manner, thus providing an efficient approach to transfer optical power to topologically protected states. This is achieved in a pump-signal configuration, in which an optical pump propagating in a bulk mode of the metasurface is employed to tune the band structure of the photonic system and, consequently, the coupling coefficient and wave-vector mismatch between edge and topological interface modes. This tunable coupling mechanism is particularly efficient due to the large Kerr coefficient of graphene. Importantly, we demonstrate that the required pump power can be significantly reduced if the optical device is operated in the slow-light regime. We perform our analysis using both ab initio full-wave simulations and a coupled-mode theory that captures the main physics of this active coupler and observe a good agreement between the two approaches. This work may lead to the design of active topological photonic devices with new or improved functionality.