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Schematic of (a) the structural model and (b) the effective medium of a DMR. (c) Resonant frequencies of the multiorder monopole and dipole states. Red dashed and blue dotted lines represent the monopole and dipole states with the effective medium, respectively. Red circles and blue triangles represent the results with structural model. (d) Distributions of the absolute pressure fields and (e) the far-field patterns of the second-order monopole state. (f)-(g) Same as (d)-(e) but of the second-order dipole state.
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Acoustic analogies of topological insulators reside at the frontier of ongoing metamaterials research. Of particular interest are the topological interface states that are determined by the Zak phase, which is the geometric phase characterizing the topological property of the bands in one-dimensional systems. Here we design double-channel Mie reson...
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... design a double-channel Mie resonator (DMR) based on the cylindrical labyrinthine acoustic metamaterials, whose cross-sectional view is shown in Fig. 1(a). The single DMR is composed of two identical semicircular parts and each part consists of a meander channel with a rigid wall thickness t = 1 mm and a slit width w = 2.5 mm. The inner radius of the DMR is R i = 4 mm and the outer radius is defined by R o = R i + N (t + w) + t, with N the curling number that is chosen as N = 8 in this ...
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... number that is chosen as N = 8 in this work. The propagation length of sound waves into DMR is thus multiplied after introducing the aforementioned meander channel. As a result, the size of the unit cell can be designed on the subwavelength scale [39,41]. Additionally, we demonstrate that the DMR is equivalent to an effective medium as shown in Fig. 1(b), which consists of a perforated rigid cylinder connecting two straight channels of ultraslow medium. The velocity and mass density of air are c 0 = 343 m/s and ρ 0 = 1.21 kg/m 3 , respectively. The effective refractive index of the ultraslow medium can be defined as n r = L p /[2(R o − R i )] with L p the total propagation lengths in ...
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... verify the designed model, the calculated eigenfrequencies of the multiorder monopolar and dipolar states in the structural model and the effective medium are illustrated in Fig. 1(c), from which the good agreement between these two models can be inferred. The finite-element software COMSOL MULTI-PHYSICS is utilized in the simulations. Note that there only exist monopolar and dipolar states due to the designed doublechannel structure. To clearly demonstrate the resonant nature, the absolute pressure distributions, ...
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... air, the simulations are recalculated in the acoustic-structure interaction section of the finite-element software COMSOL MULTIPHYSICS. In the simulations, the rigid material is replaced by the steel, of which the mass density, Poisson's ratio and the Young's modulus are ρ = 7800 kg/m 3 , ν = 0.3 and E = 2.1 × 10 11 Pa, respectively. As shown in Fig. 10(a), the degeneracy at the BZ boundary is still lifted after expanding/shrinking the distance between two DMRs in the unit cell. The existence of the topological interface state is also verified by the detected pressure amplitude at the interface between two PnCs as shown in Fig. 10(b), which also reaches about 40 similar to the situation ...
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... 3 , ν = 0.3 and E = 2.1 × 10 11 Pa, respectively. As shown in Fig. 10(a), the degeneracy at the BZ boundary is still lifted after expanding/shrinking the distance between two DMRs in the unit cell. The existence of the topological interface state is also verified by the detected pressure amplitude at the interface between two PnCs as shown in Fig. 10(b), which also reaches about 40 similar to the situation with the rigid materials in Fig. 4(c). distributions of the pressure fields at the frequency of the interface state, which is illustrated in Fig. 10(c), the energy is confined at the interface. To conclude, the existence of the topological interface states based on the proposed ...
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... existence of the topological interface state is also verified by the detected pressure amplitude at the interface between two PnCs as shown in Fig. 10(b), which also reaches about 40 similar to the situation with the rigid materials in Fig. 4(c). distributions of the pressure fields at the frequency of the interface state, which is illustrated in Fig. 10(c), the energy is confined at the interface. To conclude, the existence of the topological interface states based on the proposed labyrinthine acoustic metamaterials in air will not be influenced if the perfectly rigid material is interchanged with steel. However, it must have serious impact on the physics in the proposed labyrinthine ...
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... attenuation coefficient can be reduced to a smaller value, such as 0.005, if the experimental environment is optimized. Figure 11 illustrate the influence of the thermoviscous losses in the proposed systems. Figure 11(a) shows the structure of the 1D PnC composed of eight metamolecules and the calculated transmission is illustrated in Fig. 11(b). ...
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... 11 illustrate the influence of the thermoviscous losses in the proposed systems. Figure 11(a) shows the structure of the 1D PnC composed of eight metamolecules and the calculated transmission is illustrated in Fig. 11(b). We demonstrate that the topological interface state still exists although the thermoviscous losses reduce the transmissions of the interface state and bulk states at the same time. ...
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... The attenuation coefficient can be reduced to a smaller value, such as 0.005, if the experimental environment is optimized. Figure 11 illustrate the influence of the thermoviscous losses in the proposed systems. Figure 11(a) shows the structure of the 1D PnC composed of eight metamolecules and the calculated transmission is illustrated in Fig. 11(b). We demonstrate that the topological interface state still exists although the thermoviscous losses reduce the transmissions of the interface state and bulk states at the same time. The sound pressure level at the frequency of f = 824.1 Hz with α = 0.005 shown in Fig. 11(c) further verifies the presence of the interface state even when ...
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... of eight metamolecules and the calculated transmission is illustrated in Fig. 11(b). We demonstrate that the topological interface state still exists although the thermoviscous losses reduce the transmissions of the interface state and bulk states at the same time. The sound pressure level at the frequency of f = 824.1 Hz with α = 0.005 shown in Fig. 11(c) further verifies the presence of the interface state even when the thermoviscous losses are considered. demonstrates that the transmitted energy is reduced as a result of the increased transport paths for the sound waves in the DMRs. However, the topological interface state still can be clearly observed. Here we demonstrate that there ...
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... the system with the randomly introduced disorder, the absolute pressure is detected at the interface as shown in Fig. 12. Note that the interface states still exist as indicated by red dotted peaks with the negligible frequency shift compared to ordered resonators. Moreover, the enhancement factor of the topological interface state also reaches about 40, which is identical to the unperturbed system. As a result, the convincing robustness of the proposed ...
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... this section, we demonstrate that the designed topological interface state not only is robust against disordered DMRs but also remain resilient to perturbations of the waveguide. As shown in Fig. 13(a), a 10 • bend has been introduced, leaving the topological interface states and the pressure as seen in Fig. 13(b) and Fig. 13(c), respectively, virtually ...
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... this section, we demonstrate that the designed topological interface state not only is robust against disordered DMRs but also remain resilient to perturbations of the waveguide. As shown in Fig. 13(a), a 10 • bend has been introduced, leaving the topological interface states and the pressure as seen in Fig. 13(b) and Fig. 13(c), respectively, virtually ...
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... this section, we demonstrate that the designed topological interface state not only is robust against disordered DMRs but also remain resilient to perturbations of the waveguide. As shown in Fig. 13(a), a 10 • bend has been introduced, leaving the topological interface states and the pressure as seen in Fig. 13(b) and Fig. 13(c), respectively, virtually ...
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... we increase the bend up to 60 • as illustrated in Fig. 14(a) and do also reshape the waveguide into a zigzagged form as seen in Fig. 14(c). Surprisingly, apart from some marginal frequency shifts, the interface states as seen in Fig. 14(b) and Fig. 14(d) prevail rather ...
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... we increase the bend up to 60 • as illustrated in Fig. 14(a) and do also reshape the waveguide into a zigzagged form as seen in Fig. 14(c). Surprisingly, apart from some marginal frequency shifts, the interface states as seen in Fig. 14(b) and Fig. 14(d) prevail rather ...
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... we increase the bend up to 60 • as illustrated in Fig. 14(a) and do also reshape the waveguide into a zigzagged form as seen in Fig. 14(c). Surprisingly, apart from some marginal frequency shifts, the interface states as seen in Fig. 14(b) and Fig. 14(d) prevail rather ...
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Citations
... To validate it, we calculate the Zak phases of the lowest five isolated bands, represented by the purple numbers in Fig. 2 and further calculate sgn½ξ ðmÞ for the lowest four bandgaps. Furthermore, the parity analysis method, which involves observing the parities of the eigenmodes at the band edges (center or boundary of the Brillouin zone) both above and below the mth bandgap, serves as an alternative tool to determine the sgn½ξ ðmÞ [53][54][55][56] . ...
Topological phases in photonic systems have garnered significant attention, often relying on precise structural design for generating non-trivial topological phases. However, this dependency on fixed structures limits their adaptability. This study systematically explores incident angle-induced topological phase transitions in a one-dimensional photonic crystal (PC). Both TE and TM polarized modes undergo topological phase transitions at the same critical transition angles. Additionally, the TM-polarized mode undergoes a unique topological phase transition at the Brewster angle. When these two kinds of transition angles coincide, even if the band structure of the TM-polarized mode undergoes an open-close-reopen process, the topological properties of the corresponding bandgap remain unchanged. Based on theoretical analysis, we design the composite PCs comprising two interfaced PCs having common bandgaps but different topological properties. By tuning the incident angle, we theoretically and experimentally achieve TE-TM splitting of topological interface states in the visible region, which may have potential applications in optical communications, optical switching, photonic integrated circuits, and so on.
... By combining a locally resonant metamaterial and topology, previous studies have successfully reported the emergence of topological states-from 1D locally resonant Su-Schrieffer-Hegger (SSH) [33][34][35][36] models to 2D crystalline-based metamaterials [9,25,[37][38][39][40]. Introducing local resonances enables the realization of subwavelength topological states and the ability to tune topological mode frequencies by controlling the resonators of the constituent metamaterials. ...
We theoretically and experimentally demonstrate singular topological edge states in a locally resonant metamaterial with a configuration based on inversion-symmetric extended Su-Schrieffer-Heeger chains. Such states arise from a topological gap transition from a conventional Bragg-type gap (BG) to a local resonance-induced gap (LRG), accompanied by a topological phase transition. Remarkably, nontrivial topological states can emerge in the vicinity of the singularity in the imaginary parts of the wavenumber within the bandgap, leading to highly localized modes on a scale comparable to a single subwavelength unit cell. We experimentally demonstrate distinct differences in topologically protected modes-highlighted by wave localization-between the BG and the LRG in locally resonant granular-based metamaterials. Our findings suggest the scope of topological metamaterials may be extended via their bandgap nature.
... However, for the absorption of low-frequency sound, the materials inevitably require large thickness and bulky size, which is inconvenient in many circumstances. Recently, the emergency of acoustic metamaterials [4][5][6][7][8][9][10][11][12][13] and metasurfaces [14][15][16][17][18][19][20][21][22][23][24] provides new possibilities for designing lowfrequency acoustic absorbers with a deep sub-wavelength thickness. ...
We report both experimentally and numerically that a low-frequency acoustic absorber is realized by double split-ring resonators backed with a rigid wall. This absorber leverages the impedance matching and dissipation effect, which arises due to the thermal-viscous loss within the dual channels. As a result, this absorber achieves near-perfect sound absorption (the absorption coefficient α = 0.99) at a subwavelength thickness of around λ/23. By assembling six unit cells with distinct structure parameters to form a supercell, the fractional bandwidth (the ratio of the bandwidth to the center frequency) is increased to 40% with an average α of 0.86. Acoustic experiment results validate this exceptional performance, which is also in agreement with the simulation results. Moreover, by employing the supercell, we create an anechoic room demonstrating broadband sound absorption in a wide range of incident angles while occupying significantly less space than traditional sound-absorbing porous materials. Our double split-ring composite design paves the way for broadband acoustic absorbers at the deep subwavelength scale
... 2(a) and 2(b), the calculated Zak phases are labeled on each band, and the topological phase transition can be further confirmed by the inverted Zak phases in these two cases. To analyze the topological properties of the band gaps, the parameter f ðnÞ for the nth bandgap is introduced, whose sign is related to the discrete Zak phases through the following relation: [41][42][43] ...
Over the recent decade, topological insulators, originating from the condensed matter physics, have resided at the frontier in the field of acoustics owing to their novel topological properties for manipulating robust wave propagation, which have also opened an intriguing landscape for potential applications. At the meantime, gradually slowing down acoustic waves with metamaterials allows temporary storage of sound, leading to the exploration of so-called trapped rainbow. However, most of the current studies are reported in a topological trivial context with complex structures, and it is hitherto still a challenge to obtain the high-efficient acoustic rainbow trapping effect in a straightforward setup. Here, we propose an acoustic gradient topological insulator in the one-dimensional system to realize a highly efficient rainbow trapping device. Based on the acoustic analogous Su–Schrieffer–Heeger model, we tune the eigenfrequencies of the topological interface states through modulating the neck widths of Helmholtz resonators. The experimentally measured pressure spectra clearly show that the proposed structure could tightly trap the broad-band sound waves at the target spatial positions. Our proposal may provide versatile possibilities for the design of topological acoustic devices.
... [35][36][37][38][39][40][41][42][43][44] These 2D and 3D ATIs can host topologically protected boundary states that propagate along edges or surfaces robustly against defects and disorder without being localized, a desirable property of information carriers in waveguides and communication devices. On the other hand, one-dimensional (1D) ATIs, [45][46][47][48][49][50][51][52][53][54][55][56][57] instead, host zero-dimensional (0D) topological interface states localized at an interface. While being robust under topological protection, [58][59][60] such 0D topological interface states generally cannot serve as information carriers to deliver information from one location to another due to their intrinsic localization. ...
... Additionally, the 1D ATI can also be achieved by modulating the distance between two resonators. [53][54][55] However, the design of these ATIs is difficult to realize a reconfigurable characteristic. For this case, by rotating resonators in the 1D ATIs, 56,57 the band inversions and their associated interface states can be observed based on the SSH model, which provides a potential feasibility of designing reconfigurable 1D ATIs. ...
Topological acoustic interface states in one-dimensional (1D) acoustic topological insulators (ATIs) are zero-dimensional (0D) topological states localized at an interface. Unlike topological edge states that can propagate to deliver information in acoustic waveguides, the 0D topological interface states generally cannot serve as information carriers to deliver information from one location to another due to their intrinsic localization. Here, we design and demonstrate a 1D ATI with a movable interface, enabling the 0D topological acoustic interface states to deliver information from one location to another. The ATI design is based on two types of elemental building blocks—denoted as “1” and “0”—which are programmable. These elements of 1 and 0, when periodically arranged, can form topologically distinct crystals, whose interface hosts acoustic topological interface states in two bandgaps simultaneously. Since these two types of elements can switch from each other with external control, a programmable 1D dual-band ATI can be constructed. By programming coding sequences of 1 and 0 elements, we can observe dynamically movable 0D topological interface states riding on a moving interface along the 1D ATI in both bandgaps. Our work opens an avenue to develop topological acoustic devices with programmable and dynamic functions, which may have a variety of potential applications in the fields of energy trapping, topological pumping, information processing, and sound communication.
... 45 Hence, the band structure of the PTPC can be tuned by the external capacitance circuit throughout the PZT-5A rod, which is different from the pioneering works where the bandgaps are determined by the geometric parameters. 46,47 In the supplementary material, Note B, we deduce the dispersion relationship (band structure) of the proposed PTPC when R ( a by combining the piezoelectricity equations and the Floquet-Bloch periodic boundary condition, where the effect of the external capacitance on the piezoelectric material is represented as a certain parameter contained in the dispersion equation. ...
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.
... In recent years, condensed matter physics has undergone epochmaking changes due to the introduction of topological classification of matter phases. 1 The concept of topological insulators is also extended to optical [2][3][4][5] and acoustic systems rapidly. In particular, the acoustic topological edge states, in one-dimensional, 6,7 two-dimensional, [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] and three-dimensional 26,27 topological insulators, are of great interest due to their transmission without backscattering and defect-insensitive transport. ...
Backscattering immunity of valley edge states for a monolayer sonic crystal provides a basis for designing devices with unconventional functions. Recently, the valley edge state of a bilayer sonic crystal, regarded as a new degree of freedom, gives a powerful platform for manipulating acoustic waves. In this Letter, we realize valley spin insulators in a bilayer sonic crystal and find that the layer-mixed, layer-polarized, and layer-locked edge states exist on both zigzag and armchair interfaces. There are significant differences between the armchair edge states and the zigzag edge states at the interfaces formed by two domains of distinct acoustic layer-valley Hall phases. Based on the projected dispersion relations for a bilayer sonic crystal, we achieve theoretically and experimentally bilayer multichannel transmission with different layers locking. This paper provides a design approach for applications of bilayer acoustic multichannel communication devices.
... In recent years, several studies have been devoted to investigate the existence of interface Tamm states based on the topological properties of band structures in the considered artificial materials that can be revealed through the Berry phase approach [23]. In 1D periodic systems, the topology of the bands is characterized by the concept of Zak phase, a special kind of Berry phase [24][25][26][27][28]. Recently, topological interface states and Zak phase have been extended to various branches of physics such as photonics [26,[29][30][31][32][33][34], plasmonics [22,35], acoustics and mechanical systems [36][37][38][39] and metamaterials [40,41]. The topological invariant has been successfully applied to predict the existence of interface states from the Zak phases of bulk bands. ...
We investigate the existence of acoustic Tamm states at the interface between two one-dimensional (1D) comblike phononic crystals (PnCs) based on slender tubes and discuss their topological or trivial character. The PnCs consist of stubs grafted periodically along a waveguide and the two crystals differ by their geometrical parameters (period and length of the stubs). We use several approaches to discuss the existence of Tamm states and their topology when connecting two half-crystals. First, we derive a necessary and sufficient condition on the existence of interface states based on the analysis of the bulk band structure and the symmetry of the band edge states. This approach is equivalent to an analysis of the Zak phases of the bulk bands in the two crystals. Indeed, a topological interface state should necessarily exist in any common bandgap of the two PnCs for which the lower (upper) band edges have opposite symmetries. A novelty of our structure consists in the fact that the symmetry inversion results from a band closure (flat band) rather than from a gap closure, in contrast to previous works. Then, such interface states are revealed through different physical quantities, namely: (i) the local density of states (LDOS), which exhibits a high localization around the interface; (ii) sharp peaks in the transmission spectra in the common bandgap when two finite crystals are connected together; (iii) the phases of the reflection coefficients at the boundary of each PnC with a waveguide, which have a direct relationship with the Zak phases. In addition, we show that the interface states can transform to bound states in the continuum (BICs). These BICs are induced by the cavity separating both PnCs and they remain robust to any geometrical disorder induced by the stubs and segments around this cavity. Finally, we show the impossibility of interface states between two connected PnCs with different stub lengths and similar periods. The sensitivity of these states to interface perturbations can find many practical applications in PnC sensors.
... Topological physics and mechanics inspired phononic crystals (PnC) and acoustic metamaterials (AM) have observed a surge of research studies in unusual control of acoustic and elastic waves. Interface states that are related to topological phase inversion [1] of trivial and non-trivial phases provide robust, lossless, immune to backscattering and sharp edges wave transportation at the interface of topologically distinct PnC and AM [2][3][4][5]. Such interface mode provides potential avenues for wave control including wave energy focusing/harvesting [6], vibration and noise control [7,8], topological insulators [9,10], higher order corner states/modes [11,12], and design of other acoustic devices. ...
Inspired by the idea of topological mechanics and geometric phase, the topological phononic beam governed by topological invariants has seen growing research interest due to generation of a topologically protected interface state that can be characterized by geometric Zak phase. The interface mode has maximum amount of wave energy concentration at the interface of topologically variant beams with minimal losses and decaying wave energy fields away from it. The present study has developed a deep learning based autoencoder to inversely design topological phononic beam with invariants. By applying the transfer matrix method, a rigorous analytical model is developed to solve the wave dispersion relation for longitudinal and bending elastic waves. By determining the phase of the reflected wave, the geometric Zak phase is determined. The developed analytical models are used for input data generation to train the autoencoder. Upon successful training, the network prediction is validated by finite element numerical simulations and experimental test on the manufactured prototype. The developed autoencoder successfully predicts the interface modes for the combination of topologically variant phononic beams. The study findings may provide a new perspective for the inverse design of metamaterial beam and plate structures in solid and computational mechanics. The work is a step towards deep learning networks suitable for the inverse design of phononic crystals and metamaterials enabling design optimization and performance enhancements.
... Notably, for the 1D system, the Zak phase θ (i.e., topological phase) of each isolated band can be determined by the symmetry of the eigenfields as [42][43][44][45] θ ...
Topological states of classic waves are fascinating for both fundamental and practical purposes due to their unprecedented wave characteristics. In this paper, we realize the one-dimensional topological insulators for electromagnetic and mechanical waves simultaneously based on phoxonic crystal (PxC) cavity chains. The proposed PxC cavity chains are the analogs to the Su-Schrieffer-Heeger model in condensed-matter physics. The interaction between the neighboring PxC cavities can be described by the tight-binding model, where the coupling or hopping strength between the adjacent cavities can be tuned by varying their distance. Thus, the PxC cavity chains with topologically nontrivial and trivial phases are achieved by changing the cavity distances directly. The topological edge and interface states for the electromagnetic and elastic (or acoustic) waves are observed simultaneously in the finite-sized PxC cavity chains, which exhibit robustness against geometrical imperfections. The topological states of the proposed PxC cavity chains hold promise for designing robust devices in signal processing, sensing, and optomechanics.
