A three-dimensional phononic crystal structure, acoustic supercell, and acoustic device

Abstract

This application relates to the field of acoustics, and in particular to a method for realizing a three-dimensional phononic crystal structure, an acoustic supercell, and an acoustic device. The phononic crystal structure is composed of multiple stacked unit cells; each unit cell includes several resonant cavities and acoustic coupling channels connecting the resonant cavities; the layers are connected by interlayer acoustic coupling channels; the geometric parameters of the resonant cavities and acoustic coupling channels are configured to satisfy a tightly bound model with chiral symmetry, such that the phononic crystal structure forms nodal loops in three-dimensional momentum space and supports higher-order topological hinge states at the rigid boundary edges of the phononic crystal structure. This invention can achieve stable higher-order topological hinge states while maintaining the characteristics of nodal loops, and has the advantages of simple structure and ease of fabrication.

Description

Technical Field

[0001] This application relates to the field of acoustic technology, and in particular to a three-dimensional phononic crystal structure, acoustic supercell, and acoustic device for realizing high-order nodal loops. Background Technology

[0002] Topological acoustics, as an extension of the topological concept in condensed matter physics into classical wave systems, has become a research hotspot in physics and engineering in recent years. Similar to topological insulators and topological half-metals in electronic systems, acoustic topological structures can achieve unique control over sound wave propagation through the topological properties of energy bands. Among them, acoustic topological half-metals possess non-trivial band degeneracy in momentum space, and based on the different dimensions of degeneracy, they can be divided into acoustic Weyl half-metals (zero-dimensional degeneracy points) and acoustic nodal line / nodal surface half-metals.

[0003] For acoustic nodal-line half-metals, their bands intersect in momentum space to form closed nodal-line loops. This structure typically carries a nontrivial Zak phase and supports "tympanic surface states" on its surface. For example, studies in 2019 and 2020 have demonstrated nodal-line half-metals using three-dimensional artificial phononic crystals and observed nonradiative tympanic states. These studies primarily focus on utilizing first-order topological effects, i.e., generating localized states on the material surface using volume-edge correspondences.

[0004] Existing research is mostly limited to exploring first-order topological properties (i.e., volume states corresponding to surface states), with less attention paid to higher-order topological phenomena—such as second-order "hinge states" in three-dimensional systems. Compared to surface states, hinge states have stronger spatial locality and better robustness to structural defects, showing greater application potential in acoustic energy localization and precision acoustic sensing. Simultaneously realizing nodal-ring band structures and higher-order topological boundary states in three-dimensional systems often requires complex spatial symmetry designs or the introduction of metamaterial parameters that are difficult to fabricate precisely, increasing the difficulty of experimental verification and practical applications.

[0005] Therefore, how to induce and realize stable higher-order topological hinge states in three-dimensional phononic crystals while maintaining the characteristics of nodal loops, and how to propose a simple and easy-to-fabricate physical model, are the technical problems that urgently need to be solved in this field. Summary of the Invention

[0006] Therefore, it is necessary to provide an ultrawideband sound absorber that can achieve a stable high-order topological hinge state while maintaining the characteristics of the nodal loop, and that has the characteristics of simple structure and easy fabrication.

[0007] To achieve the above-mentioned objectives of this invention, the technical solution adopted is as follows: A three-dimensional phononic crystal structure for realizing higher-order nodal loops is disclosed. The phononic crystal structure is composed of multiple unit cells stacked in layers. Each unit cell includes several resonant cavities and acoustic coupling channels connecting the resonant cavities. The layers are connected to each other through interlayer acoustic coupling channels. The geometric parameters of the resonant cavities and acoustic coupling channels are configured to satisfy a tight-binding model with chiral symmetry, such that the phononic crystal structure forms nodal loops in three-dimensional momentum space and supports higher-order topological hinge states at the edges of the phononic crystal structure with rigid boundaries.

[0008] Preferably, the unit cell comprises four resonant cavities, namely a first cavity, a second cavity, a third cavity, and a fourth cavity.

[0009] Furthermore, the acoustic coupling channel includes an intracellular coupling channel, an intercellular coupling channel, and an interlayer coupling channel, and their connection relationships are configured as follows: the first cavity and the third cavity, and the second cavity and the fourth cavity are connected horizontally through the intracellular coupling channel and the intercellular coupling channel to construct a two-dimensional topological lattice with angular states; the first cavity and the second cavity, and the third cavity and the fourth cavity are connected vertically through the interlayer coupling channel to achieve interlayer stacking coupling.

[0010] Furthermore, the coupling strength of the acoustic coupling channel is controlled by changing the cross-sectional area or length of the channel; in order to realize higher-order topological phases, the interlayer coupling channel is configured to be weakly coupled, so that the angular states of the two-dimensional topological lattice form a continuous local acoustic field channel in the vertical stacking direction, i.e., the hinge state.

[0011] Furthermore, the Bloch-Hamiltonian of the phonon crystal structure Satisfy the following expression:

[0012] in, To be related to the wave vector The relevant function is determined by the coupling coefficient of the acoustic coupling channel; It represents complex conjugation; this Hamiltonian characterizes the physical property of the system in momentum space where band degeneracy forms nodal loops.

[0013] Furthermore, the resonant cavity is a cuboid or cube structure with a first characteristic dimension; the acoustic coupling channel is a tubular structure connecting the surfaces of the resonant cavity with a second characteristic dimension; by setting different second characteristic dimensions, anisotropic coupling strength is introduced inside and between the unit cells, thereby breaking spatial symmetry to induce a topological phase transition.

[0014] Furthermore, the phononic crystal structure in the Brillouin zone or A plane has quantization The Zak phase indicates the existence of topologically protected diaphragmatic surface states; the higher-order topological hinge states are located within the bandgap frequency range of the phononic crystal structure, and their acoustic pressure field energy is highly localized at the vertical edges of the finite sample of the phononic crystal structure.

[0015] Furthermore, the resonant cavity and acoustic coupling channel are made of an acoustically rigid material, including photosensitive resin, metal, rigid plastic or ceramic; the resonant cavity and acoustic coupling channel are filled with a fluid medium, which is either air or water.

[0016] An acoustic supercell is formed by stacking the aforementioned three-dimensional phononic crystal structure in a regular array in three-dimensional space. The acoustic supercell has a finite physical size and external boundary. When the incident sound wave frequency is within the frequency range where the propagation of the bulk state and surface state of the acoustic supercell is significantly suppressed, the acoustic supercell supports higher-order topological hinge states only in the edge regions formed by the intersection of different surfaces, so that the sound field energy is transmitted locally in the edge regions, while the sound field inside and on the surface regions of the acoustic supercell decays exponentially.

[0017] An acoustic device configured as an acoustic energy harvester, a directional acoustic waveguide, or an acoustic sensor, utilizing the higher-order topological hinge state of the edge region to achieve directional transmission of sound waves or localized energy detection.

[0018] The beneficial effects of this invention are as follows: This invention creatively transforms the angular states of a two-dimensional topological lattice into hinged states distributed along the edges in three-dimensional space by constructing a unit cell containing resonant cavities and acoustic coupling channels, and employing a layered stacking method. This allows the phonon crystal structure to not only possess the properties of nodal-line semimetals in momentum space, but also support second-order topological hinged states at the edges in real space. This design successfully introduces higher-order topological physics mechanisms into a three-dimensional nodal-line semimetal system, providing higher degrees of freedom for the manipulation of sound waves. Furthermore, the structure of this invention mainly consists of periodically arranged resonant cavities and coupling channels, avoiding dependence on complex local resonant units or extremely special material parameters. By adjusting the geometry of the coupling channels, the coupling strength in the tight-binding model can be precisely controlled, thereby inducing a topological phase transition. This structure has extremely high engineering feasibility, lowering the manufacturing threshold for high-performance acoustic topological devices. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of a tight-binding model of a three-dimensional phononic crystal structure in one embodiment.

[0020] Figure 2This is a numerically calculated band structure diagram in one embodiment.

[0021] Figure 3 This is a graph showing the Zak phase calculation results in one embodiment.

[0022] Figure 4 This is a numerical calculation of a three-dimensional band structure in one embodiment.

[0023] Figure 5 This is a projected bandgap diagram in one embodiment.

[0024] Figure 6 This is an angular distribution diagram of a two-dimensional cross-section in one embodiment.

[0025] Figure 7 This is a phononic crystal unit cell model in one embodiment.

[0026] Figure 8 As in one embodiment, along Figure 2 Band diagrams of the same high-symmetry line scan.

[0027] Figure 9 This is an example of angular state distribution.

[0028] Figure 10 This is a band structure projected along the kz direction in one embodiment.

[0029] Figure 11 This is a software-simulated prism of an acoustic supercell in one embodiment. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0031] Example 1 This invention proposes a three-dimensional phonon crystal structure capable of realizing the properties of a high-order nodal loop topological half-metal.

[0032] like Figure 1 As shown, the three-dimensional phonon crystal structure in this embodiment consists of multiple unit cells arranged periodically in the x, y, and z three-dimensional spatial directions. Each unit cell logically contains four resonant cavities, which act as artificial atoms and are interconnected through acoustic coupling channels. Specifically, a unit cell in the tight-binding model is composed of atoms from four nodes: A, B, C, and D. Physically, these nodes are designed as square resonant cavities with specific geometric dimensions.

[0033] In this embodiment, the coupling connection relationship between the cavities is configured as follows in order to construct the required topological band: Intracellular coupling: Within the same protocell, cavities located in the same layer are connected by coupling channels with a first-dimensional characteristic.

[0034] Intercellular coupling: Between adjacent protocells, cavities in the same layer are connected by coupling channels with second-dimensional characteristics.

[0035] Interlayer coupling: In the vertical z-direction, the upper cavity and the lower cavity are connected by a vertical coupling channel with a third dimension feature.

[0036] In this embodiment, the Bloch-Hamiltonian of this structure Forms that satisfy chiral symmetry:

[0037] in, , , , The intracellular coupling strength and extracellular coupling strength are , .

[0038] like Figure 2 Numerical calculations of the band structure diagram show that, under this tight-binding model, bands cross at specific paths, forming the expected degenerate structure.

[0039] This embodiment verifies the first-order topological properties of the phononic crystal structure, namely the tympanic surface states. According to the volume-edge correspondence, the existence of nodal loops is usually accompanied by non-trivial topological invariants. This embodiment utilizes the Wilson Loop method, along... Direction calculated The Zak phase in the plane is calculated as follows: First, define the two band structures for the Berry connection.

[0040]

[0041] The Zak phase integral is defined as follows: for a closed loop (where the loop is taken as...) The sum of the Berry phases within the direction is the Zak phase, which is the sum of the Berry phases at each point along a periodic plane of kx-ky. Calculate the Berry phase along a closed path and perform discrete integration.

[0042] In systems with mirror symmetry and chiral symmetry, the Zak phase has only two values: π (non-trivial with surface states) and 0 (trivial without surface states). Figure 3 The diagram shows the distribution of the calculated Zak phases. The green areas in the diagram represent non-trivial phases of the Zak phase. The gray area represents the Zak phase as 0, which represents the mediocre phase. Figure 4 The three-dimensional band structure plot generated by Mathematica is further demonstrated, visually showing the existence of four closed nodal loops within a Brillouin zone period. The boundary contour of the green region is... Figure 4 The middle-section loops are positioned identically in momentum space projection. This means that within the surface momentum range corresponding to the green region, this phononic crystal structure... The surface of the orientation will support topologically protected tympanic surface states.

[0043] In this embodiment, to verify the higher-order characteristics of the phononic crystal model, the model was subjected to open-boundary processing in Mathematica, and the projected band structure and density of states distribution of the phononic crystal model were calculated and plotted. Figure 5 As shown, the projected band structure of the theoretical model is illustrated. It is clearly observable that isolated energy levels exist within the band gap of the bulk band structure. These energy levels correspond to hinge states, proving that nodal-type half-metals do indeed possess higher-order properties. Figure 6 The density of states distribution diagram shows that, on the two-dimensional cross-section, the 2D angular states are distributed at the four corners of the model.

[0044] In this embodiment, the resonant cavity and acoustic coupling channel are made of an acoustically rigid material, including photosensitive resin, metal, rigid plastic, or ceramic. The resonant cavity and acoustic coupling channel are filled with a fluid medium, which is air or water. The phonon crystal structure is manufactured integrally using 3D printing technology or computer numerical control (CNC) machining technology.

[0045] This embodiment systematically verifies, through theoretical derivation, numerical calculation, and full-wave simulation, that the three-dimensional phononic crystal structure not only possesses first-order topological surface states as a nodal-line ring semimetal, but more importantly, successfully realizes higher-order topological hinge states through a weak interlayer coupling stacking mechanism. This structure is simple to fabricate and can be integrally formed by 3D printing, making it of significant application value in the fields of acoustic waveguides, acoustic energy localization, and acoustic sensing.

[0046] Example 2 In this embodiment, as Figure 7As shown, a three-dimensional phonon crystal model was designed. To achieve higher-order characteristics, this model adopts a double-layer SSH structure, using a Z-direction oblique coupling tube to connect the upper and lower layers. The lattice constant of each unit cell in the xy direction is 33 mm, and its resonant cavity and coupling tube parameters are as follows: , .

[0047] Full-wave simulation of the physical model in this embodiment was performed using COMSOL Multiphysics software. For example... Figure 8 As shown, the band structure scanned along a high-symmetry line is illustrated, and the results are in high agreement with the theoretical model calculations, proving that the physical structure accurately reproduces the design goals of the tight-binding model, namely, in... A closed nodal loop was successfully implemented on the plane.

[0048] like Figure 9 As shown, the physical structure of the three-dimensional phononic crystal is configured with open boundaries in the x and y directions, i.e., 10 unit cells are set in each direction. The calculated projected energy bands are as follows. Figure 10 As shown, around 10.15 kHz, four flat energy bands (red lines in the figure) appear in the bandgap. These four energy bands correspond to the hinge states on the four side edges of the structure. The frequencies of the four lines are respectively... Figure 9 The frequencies of the intermediate-angle states correspond one-to-one.

[0049] Example 3 like Figure 11 As shown, an acoustic supercell is formed by stacking the aforementioned three-dimensional phononic crystal structure in a regular array in three-dimensional space. The acoustic supercell has a finite physical size and external boundary. When the incident sound wave frequency is within the frequency range where the propagation of the bulk state and surface state of the acoustic supercell is significantly suppressed, the acoustic supercell supports higher-order topological hinge states only in the edge regions formed by the intersection of different surfaces, so that the sound field energy is transmitted locally in the edge regions, while the sound field inside and on the surface regions of the acoustic supercell decays exponentially.

[0050] This embodiment presents a numerical simulation of a finite structure of a stacked three-dimensional phononic crystal to verify its characteristic of generating hinge states at a specific frequency. The finite structure consists of 10×10×10 unit cells, with the geometric dimensions of the unit cells consistent with the aforementioned design scheme, and the parameters of the periodic direction remaining unchanged.

[0051] The model was built in COMSOL Multiphysics software, with all unit cells stacked in a regular array to form a cubic supercell. To simulate the actual situation of finite samples, rigid wall boundary conditions were applied to the model in two directions, while soft acoustic field boundaries were set in the remaining directions to eliminate the influence of the external acoustic field and highlight the distribution characteristics of the internal topological modes. To excite possible hinge states, Place a point sound source at the middle of a vertical edge at the bottom of the model, such as... Figure 11 The yellow star in the image indicates that this point source operates in a sweepable frequency mode, covering the bandgap region where the first-order mode of the unit cell is located. A steady-state frequency domain solver is used in the simulation to calculate the sound pressure field distribution and local energy characteristics at each frequency.

[0052] The calculation results show that at a frequency of 10.166 kHz, the sound pressure energy in the model is mainly concentrated in the four edge regions distributed along the z-direction, forming a distinct local sound field channel. At this point, the sound field intensity in the bulk region and surface region is significantly reduced, indicating that the sound energy is confined to the edge regions, exhibiting typical hinged state characteristics. This result is consistent with the predictions of the theoretical model, verifying that the proposed stacked three-dimensional phononic crystal can stably generate and maintain hinged states within the designed frequency band. This phenomenon further demonstrates that the structural design of this invention not only possesses high-order topological properties in theory but can also be effectively excited and observed in actual physical models, providing a reliable basis for the experimental realization of topological acoustic devices.

[0053] Example 4 An acoustic device configured as an acoustic energy harvester, a directional acoustic waveguide, or an acoustic sensor, utilizing the higher-order topological hinge state of the edge region to achieve directional transmission of sound waves or localized energy detection.

Claims

1. A three-dimensional phononic crystal structure for realizing high-order nodal loops, characterized in that, The phononic crystal structure is composed of multiple unit cells stacked in layers; each unit cell includes several resonant cavities and acoustic coupling channels connecting the resonant cavities; the layers are connected by interlayer acoustic coupling channels; the geometric parameters of the resonant cavities and acoustic coupling channels are configured to satisfy a tight-binding model with chiral symmetry, such that the phononic crystal structure forms nodal loops in three-dimensional momentum space and supports higher-order topological hinge states at the edges of the phononic crystal structure with rigid boundaries.

2. The three-dimensional phononic crystal structure for realizing higher-order nodal loops according to claim 1, characterized in that, The unit cell contains four resonant cavities, namely the first cavity (A), the second cavity (B), the third cavity (C), and the fourth cavity (D).

3. A three-dimensional phononic crystal structure for realizing higher-order nodal loops according to claim 2, characterized in that, The acoustic coupling channels include intracellular coupling channels, intercellular coupling channels, and interlayer coupling channels, and their connection relationships are configured as follows: the first cavity (A) and the third cavity (C), and the second cavity (B) and the fourth cavity (D) are connected via intracellular coupling channels ( ) and intercellular coupling channels ( The first cavity (A) and the second cavity (B), and the third cavity (C) and the fourth cavity (D) are connected at the horizontal level to construct a two-dimensional topological lattice with angular states; the interlayer coupling channels connect the first cavity (A) and the second cavity (B), and the third cavity (C) and the fourth cavity (D). They are connected in the vertical direction to achieve interlayer stacking coupling.

4. A three-dimensional phononic crystal structure for realizing higher-order nodal loops according to claim 3, characterized in that, The coupling strength of the acoustic coupling channel is controlled by changing the cross-sectional area or length of the channel; in order to realize higher-order topological phases, the interlayer coupling channel is configured to be weakly coupled, so that the angular states of the two-dimensional topological lattice form a continuous local acoustic field channel in the vertical stacking direction, i.e., the hinge state.

5. A three-dimensional phononic crystal structure for realizing higher-order nodal loops according to claim 2, characterized in that, The Bloch-Hamiltonian of the phonon crystal structure Satisfy the following expression: in, To be related to the wave vector The relevant function is determined by the coupling coefficient of the acoustic coupling channel; It represents complex conjugation; this Hamiltonian characterizes the physical property of the system in momentum space where band degeneracy forms nodal loops.

6. A three-dimensional phononic crystal structure for realizing higher-order nodal loops according to claim 1, characterized in that, The resonant cavity is a cuboid or cubic structure with a first characteristic dimension ( The acoustic coupling channel is a tubular structure connecting the surfaces of the resonant cavity, having a second characteristic dimension (). By setting different second feature sizes, anisotropic coupling strengths are introduced inside and between the unit cells, thereby breaking spatial symmetry to induce topological phase transitions.

7. A three-dimensional phononic crystal structure for realizing higher-order nodal loops according to claim 1, characterized in that, The phononic crystal structure in the Brillouin zone or A plane has quantization The Zak phase indicates the existence of topologically protected diaphragmatic surface states; the higher-order topological hinge states are located within the bandgap frequency range of the phononic crystal structure, and their acoustic pressure field energy is highly localized at the vertical edges of the finite sample of the phononic crystal structure.

8. A three-dimensional phononic crystal structure for realizing a high-order nodal loop according to claim 1, characterized in that, The resonant cavity and acoustic coupling channel are made of an acoustically rigid material, including photosensitive resin, metal, rigid plastic or ceramic; the resonant cavity and acoustic coupling channel are filled with a fluid medium, which is either air or water.

9. An acoustic supercell, characterized in that: The acoustic supercell is formed by stacking the three-dimensional phononic crystal structure in a regular array in three-dimensional space. The acoustic supercell has a finite physical size and external boundary. When the incident sound wave frequency is within the frequency range where the propagation of the bulk state and surface state of the acoustic supercell is significantly suppressed, the acoustic supercell supports higher-order topological hinge states only in the edge regions formed by the intersection of different surfaces. This allows the sound field energy to be transmitted locally in the edge regions, while the sound field inside and on the surface of the acoustic supercell decays exponentially.

10. An acoustic device, characterized in that: The acoustic device is configured as an acoustic energy harvester, a directional acoustic waveguide, or an acoustic sensor, utilizing the higher-order topological hinge state of the edge region to achieve directional transmission of sound waves or localized energy detection.

Images