Microstructure-based two-dimensional acoustic crystal and acoustic frequency beam splitter

Abstract

The invention discloses a two-dimensional acoustic crystal based on a microstructure. A functional material layer of the two-dimensional acoustic crystal comprises square acoustic cells which are periodically arranged in an xy plane according to a square lattice; a scatterer in the acoustic cell has rotational symmetry and is composed of a cross structure and four identical semicircles, the cross structure is composed of two identical rectangular strips in an orthogonal mode, the diameter of the semicircle is collinear with the short edge of the rectangular strip at the tail end where the semicircle is located, and the diameter of the semicircle is larger than the length of the short edge of the rectangular strip. The rotation angle of the scatterer is matched with the geometric parameter of the scatterer, so that the physical energy band structure of the two-dimensional acoustic crystal generates a triple degeneracy point formed by the first three physical energy bands at the M point of the Brillouin region, and further a stable boundary state with global characteristics is realized. Furthermore, an acoustic frequency beam splitter is constructed on the basis of the boundary state, and sound waves of different frequency bands are split to form included angles of 180 degrees and 90 degrees.

Description

Technical Field

[0001] This invention belongs to the field of acoustic wave transmission control technology, and specifically relates to an acoustic frequency beam splitter based on a microstructure and its design method. Background Technology

[0002] The discovery of Weyl semimetals sparked a surge of research into topological semimetals. A key characteristic of Weyl semimetals is the presence of Weyl points in their band structures, characterized by linear double degeneracy between the conduction and valence bands, with each band carrying a topological charge of ±1. Besides linear dispersion, Weyl points can exhibit other types of dispersion, such as quadratic and cubic dispersion. A Weyl point with quadratic dispersion exhibits quadratic dispersion in two directions and linear dispersion in the third, carrying a topological charge of ±2, and can be considered as a merger of two Weyl points with the same topological charge. In addition to double degeneracy points, multi-band degeneracy points, such as triple, hexa-, and even octet degeneracy points, have been proposed and extensively studied. A typical triple degeneracy point is characterized by three bands linearly intersecting at the same point, carrying a topological charge of ±2. Projecting these degeneracy points onto the Brillouin zone boundary reveals boundary states connecting the degeneracy points, and the properties of these boundary states are correlated with the topological charge of the degeneracy points. These boundary states at unconventional degenerate points often exhibit more unique physical effects, such as topological self-collimation and topological birefringence. Among them, the boundary states that run through the entire Brillouin zone are particularly interesting and are called "toroidal surface states" in three-dimensional systems.

[0003] Currently, these topological degenerate points and their corresponding boundary states have been extensively studied in three-dimensional systems. In the two-dimensional case, these degenerate points can be viewed as projections of a synthetic three-dimensional system constructed with one system parameter as another degree of freedom. The calculation of the topological charge is then transformed into the integral of the Bailey connection on the ring containing the point, characterized by the Bailey phase. However, since only two-dimensional irreducible representations exist in a two-dimensional space group, triple degenerate points can only be realized through accidental degeneracy. As mentioned earlier, projecting a pair of Pyl points onto the Brillouin zone boundary connects them to boundary states, called Fermi arcs. However, the distribution of these boundary states in the Brillouin zone is sensitive to the boundary conditions. Under zigzag or whisker-shaped boundary conditions, the distribution of these boundary states in the Brillouin zone exhibits complementary characteristics and occupies only a portion of the momentum space. This sensitivity reflects the limitations of traditional boundary states, further highlighting the potential advantages of boundary states with stable and global properties, and these boundary states are expected to have wider applications. However, in the two-dimensional case, especially in the case of isolated degenerate points, such globally characteristic boundary states are relatively rare.

[0004] To realize these unique boundary states that possess both stability and global properties, attention can be focused on unconventional degeneracy points. Since the Weyl points and triple degeneracy points of quadratic dispersion carry zero topological charge in the two-dimensional case, boundary states at these degeneracy points have been less studied. Although there are theoretical calculations of globally characteristic boundary states in condensed matter physics materials, observing them experimentally remains challenging due to the complexity of preparing materials with high actual purity. Summary of the Invention

[0005] To address the aforementioned problems, this invention provides an acoustic crystal based on a microstructure. A scatterer with C4 rotational symmetry is designed, and by adjusting the rotation angle and geometric parameters of the scatterer, its band structure achieves a triple degeneracy point, thereby realizing a stable boundary state with global characteristics. Furthermore, this invention also constructs an acoustic frequency beam-splitting device based on this boundary state, splitting sound waves of different frequency bands at angles of 180° and 90° respectively.

[0006] The technical solution of this invention includes the following aspects: The first aspect of this invention discloses a two-dimensional acoustic crystal based on a microstructure, comprising a functional material layer, wherein the functional material layer includes acoustic cells arranged periodically in a square lattice in the xy plane; the acoustic cells are square, comprising a scatterer and air filling the space surrounding the scatterer; the scatterer has… The scatterer exhibits rotational symmetry, consisting of a cross structure and four identical semicircles circumscribed at the ends of the cross structure. The cross structure is formed by two identical orthogonal rectangular strips, whose centers of symmetry coincide with the center of the square lattice. The diameter of each semicircle is collinear with the short side of the rectangular strip at its end, and its center coincides with the midpoint of the outer side. The diameter is greater than the length of the short side of the rectangular strip. A non-zero rotation angle exists between the central axis of the scatterer's cross structure and one side of the square lattice. The rotation angle Matching the geometric parameters of the scatterer, the bulk band structure of the two-dimensional acoustic crystal produces a triple degeneracy point at point M in the Brillouin zone, formed by the first three bulk bands, which are defined as the first three modes that increase sequentially along the high-frequency direction starting from zero frequency.

[0007] As an alternative, the material of the scatterer satisfies that its acoustic impedance is greater than or equal to 10 times that of air; the material of the scatterer is any one of photosensitive resin, acrylic, metal, and organic plastic.

[0008] As an alternative, the thickness of the functional material layer is determined by the height of the scatterer in the acoustic cell; the height of the scatterer , The wavelength of the sound wave corresponding to the operating frequency of the acoustic crystal.

[0009] As an alternative, the acoustic cell has a period number of not less than 10 in the x and y directions.

[0010] As an alternative, the lattice constant of the acoustic cell The length of the long side of the rectangular strip is 15 mm. It is 10 mm, the length of the short side 4mm, rotation angle It is 28.93°; the radius of the semicircle It is 3mm.

[0011] A second aspect of this invention discloses an acoustic frequency beam splitter with a beam splitting angle of 180°, comprising a top surface, a bottom surface, and a main structure between the top and bottom surfaces. The main structure is selected from the microstructure-based two-dimensional acoustic crystal described in the first aspect of this invention or any alternative embodiment thereof. One side of the acoustic frequency beam splitter is configured as a hard boundary, and the hard boundary has adjacently arranged first and second working boundaries. The shear length of the first and second working boundaries is... Each satisfies 0 0.5 and 0.5 , The lattice constant of the acoustic cell; all other boundaries outside the working boundary in the acoustic frequency beam splitter are open boundaries; the acoustic frequency beam splitter has one input port and two output ports, the input port is arranged between the first and second working boundaries, and the output ports are respectively arranged at the ends of the first and second working boundaries away from the input port.

[0012] A third aspect of this invention discloses an acoustic frequency beam splitter with a beam splitting angle of 90°, comprising a top surface, a bottom surface, and a main structure between the top and bottom surfaces. The main structure is selected from the microstructure-based two-dimensional acoustic crystal described in the first aspect of this invention or any alternative embodiment thereof. Two adjacent sides of the acoustic frequency beam splitter are set as hard boundaries, one side being a first working boundary and the other a second working boundary. The shear length of the first and second working boundaries is... Each satisfies 0 0.5 and 0.5 , The lattice constant of the acoustic cell; all other boundaries outside the working boundary in the acoustic frequency beam splitter are open boundaries; the acoustic frequency beam splitter has one input port and two output ports, the input port is arranged between the first and second working boundaries, and the output ports are respectively arranged at the ends of the first and second working boundaries away from the input port.

[0013] As an alternative, the acoustic frequency beam splitter is generally rectangular or square.

[0014] As an alternative, the number of periods in the acoustic crystal regions at different working boundaries is greater than or equal to 10 in both the x and y directions.

[0015] As an alternative, the shear length of the first working boundary and the second working boundary They are 0.25 respectively. and 0.68 The acoustic frequency beam splitter operates in the range of 7.6-15.0 kHz; wherein the acoustic wave with a frequency range of 7.6-9.8 kHz propagates along the first working boundary; and the acoustic wave with a frequency range of 11.3-15.0 kHz propagates along the second boundary.

[0016] Compared with the prior art, the present invention has the following beneficial effects: (1) In the acoustic crystal system, the invention achieves a triple degeneracy point in its band structure by adjusting the rotation angle and geometric parameters of the scatterer in the acoustic cell. The stable boundary state brought about by the degeneracy point makes the device have stable characteristics during sound wave transmission.

[0017] (2) It is particularly important to note that the three bands of the triple degeneracy point achieved in this invention have large directional band gaps, thus enabling a wider operating frequency range, from 7.6 to 15.0 kHz. This frequency range is entirely within the range of human hearing and has outstanding advantages in data transmission capability, device integration and compatibility, as well as environmental adaptability and anti-interference capability. Therefore, it has excellent application potential and applicable scenarios in the field of audible sound.

[0018] (3) The present invention provides a two-dimensional acoustic crystal based on microstructure, which is constructed by stretching a two-dimensional system to three dimensions, thus having a small volume and being beneficial to the integration of related acoustic devices.

[0019] (4) The acoustic frequency beam splitter design method proposed in this invention can realize two types of devices with different beam splitting angles, thereby significantly expanding the application potential of the device.

[0020] (5) This invention not only enriches the study of triple degenerate point boundary states, but also provides new approaches and methods for controlling and applying acoustic boundary states. Attached Figure Description

[0021] Figure 1(a) is a schematic diagram of the cell structure of a two-dimensional acoustic crystal based on microstructure; (b) is a schematic diagram of the location and morphology of the triple degeneracy point of the acoustic crystal band in the Brillouin zone; (c) is the band structure of the acoustic crystal obtained by specific calculation.

[0022] Figure 2 (a) A schematic diagram of the supercell structure constructed for calculating the projected band structure, and the shear length. (b) is for illustration; 0.25 The projected energy bands are calculated using a supercell, where the purple spheres represent the locations of triple degeneracy points, the gray lines represent the projection of the bulk energy bands, and the green lines represent the dispersion of the boundary states. The attached figure on the right shows the field distribution of the boundary states at the orange rhombus location; (c) shows the field distribution of the boundary states at the location of the orange rhombus. 0.68 The projected energy bands are calculated using the supercell; the attached figure on the right shows the field distribution of the boundary states at the orange rhombus positions.

[0023] Figure 3 (a) is to take The existence of boundary states is characterized by the topological indices (Zak phase) of bands 1 and 2, calculated from the center of the cross-shaped scatterer, corresponding to 0. 0.5 (a) the situation; (b) to take The topological indices (Zak phase) of band 1 and band 2, calculated with the center located at the midpoint of the upper boundary of the square lattice, correspond to 0.5. The situation.

[0024] Figure 4 (a) An acoustic frequency beam splitter with a beam splitting effect of 180° at two specific operating frequencies ( 14.9kHz and The field distribution at 8.2 kHz corresponds to the propagation of high-frequency sound waves to the left and low-frequency sound waves to the right within the operating frequency range; the green pentagram represents the input port of the sound wave, the orange circle represents the two output ports, and the color legend represents the sound pressure density; (b) shows the acoustic frequency beam splitter with a beam splitting effect of 90° at two specific operating frequencies ( 14.9 kHz and The field distribution at 8.2 kHz corresponds to the propagation of high-frequency sound waves to the right and low-frequency sound waves downward within the operating frequency range. Detailed Implementation

[0025] The technical solution of the present invention will now be clearly and completely described with reference to specific embodiments and accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0026] In the description of this invention, the use of terms such as "upper," "lower," "left," "right," "front," "rear," "inner," "outer," "top," and "bottom," indicating orientation or positional relationships, is based on the orientation or positional relationships shown in the accompanying drawings. These terms are used solely for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the use of terms such as "first" and "second" is used to distinguish similar objects and is not necessarily used to describe a specific order or relative importance. Those skilled in the art can understand the specific meaning of the above terms in this invention in conjunction with the specific circumstances. In addition, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion, but rather to include other units not explicitly listed or inherent to these products or devices.

[0027] Phononic crystals, with their ease of fabrication and flexible control, are becoming an ideal platform for manipulating the topological states of matter. Based on this, this invention constructs a boundary state with stable and global properties by evolving the Weyl point of quadratic dispersion to a triple degeneracy point. That is, it utilizes a microstructure-based acoustic crystal to construct a boundary state with stable and global properties. Furthermore, it leverages the characteristic of this boundary state to flip across different band gaps to realize an acoustic frequency beam splitter. Moreover, this invention also verifies the relevant performance of this acoustic frequency beam splitter through theoretical characterization and numerical calculations.

[0028] Embodiment 1 of the present invention discloses a two-dimensional acoustic crystal based on microstructure, wherein the core functional material layer is composed of acoustic cells arranged periodically in a square lattice in the xy plane.

[0029] like Figure 1As shown in (a), the acoustic cell is square, and its geometry consists of a scatterer located at the center of the square lattice and air filling the space surrounding the scatterer. The scatterer consists of a cross structure and four semicircles connecting its four ends, with the center of symmetry of the scatterer coinciding with the center of the square lattice. The cross structure is formed by two identical orthogonal rectangular bars, with their centers of symmetry coinciding. The diameters of the four semicircles are equal and greater than the width of the rectangular bars. The diameters of the four semicircles coincide with the outer sides of the cross structure (i.e., the short sides of the rectangular bars), and their centers are located on the central axis of the rectangular bars, that is, the centers coincide with the midpoint of the outer sides of the cross structure.

[0030] In structural design, the scatterer has Rotational symmetry, and rotating about its center of symmetry, with the direction of deflection determined by the rotation angle. These structural parameters are determined. For ease of understanding, in this invention, the edges of the square lattice are defined to align with the xy coordinate axes. Correspondingly, the rotation angle... It can be defined as the angle between the central axis of a specified rectangular strip in the cross structure of the scatterer and the positive x-axis. Due to the C4 rotational symmetry of the scatterer, equivalently, given that the edges of the square lattice align with the coordinate axes, the rotation angle... It can also be defined as the angle between the central axis of a specified rectangular strip in the cross structure of the scatterer and any side of the square lattice.

[0031] It is worth noting that the rotation angle of the scatterer should match its geometric parameters so that the bulk band structure of the acoustic crystal produces a triple degeneracy point at point M in the Brillouin zone, formed by the first three bulk bands. In other words, the first, second, and third bulk bands of the acoustic cell achieve a triple degeneracy point at point M in the Brillouin zone through accidental degeneracy. The first, second, and third bulk bands are defined as the first three modes, increasing sequentially along the high-frequency direction from zero frequency.

[0032] The scatterer structure of the acoustic cell can be made of any material that can be considered as an acoustic hard boundary, such as photosensitive resin, acrylic, metal, or organic plastic, and is fabricated using 3D printing technology. The selected material should have an acoustic impedance much higher than that of air; for example, .

[0033] The thickness of the functional material layer is determined by the height of the scatterer in the acoustic cell. , This refers to the wavelength of the acoustic wave corresponding to the operating frequency of the acoustic crystal. The reason for this is that the mode along the z-axis should not affect the operating mode along the xy-plane. Generally, the smaller the height of the acoustic crystal along the z-axis, the higher the frequency of its mode along the z-axis, and the smaller the influence.

[0034] Acoustic cells have Due to rotational symmetry, its volume band has a Weyl point with quadratic dispersion at point M in the Brillouin zone. This can be regarded as the superposition of two Weyl points with opposite topological charges, so the topological charge carried by this quadratic dispersion Weyl point is 0.

[0035] Since the frequency of the quadratic Weyl point exists only at this single degeneracy point, a boundary state with global characteristics can exist, meaning the boundary state spans the entire Brillouin zone. However, this boundary state changes with the shear length, disappearing when the shear length reaches a certain range, thus lacking stability. Stability, on the other hand, refers to the property that remains stable regardless of the shear length of the boundary cell. Regardless of the value, the boundary state always exists; the global characteristic means that the boundary state runs through the entire Brillouin zone, containing all momentum information, which is more beneficial for information transmission. The stability and global characteristics of the boundary state are calculated based on its projected energy bands in the kx and ky directions in momentum space, and the calculation of the projected energy bands is obtained by calculating the eigenstates of the supercell.

[0036] To further realize boundary states with stable properties, this can be achieved by connecting Weyl points of quadratic dispersions with different topological properties. Specifically, during the transformation of Weyl points between two different quadratic dispersions, the energy bands undergo accidental degeneracy to achieve a triple degeneracy point, corresponding to... Figure 1 As shown in (b).

[0037] For a specific model, for example, the lattice constant of an acoustic cell is... 15 mm; the length of the rectangular strips forming the cross structure 10 mm, width 4mm; Angle between the cross structure and the positive x-axis direction 28.93°; radius of the semicircle 3mm. The thickness of the functional material layer is 5mm. It's understandable that the length corresponds to the length of the long side of the rectangle, and the width corresponds to the length of the short side of the rectangle.

[0038] By adjusting the rotation angle of the entire scatterer This is to achieve the transformation of the degeneracy point at point M in the Brillouin zone, that is, the accidental degeneracy of the Weyl point of quadratic dispersion to a triple degeneracy point. When At 28.93°, the Weyl points of the quadratic dispersion realize in the second and third bands, and the global boundary states exist at 0.5. The situation; when At 28.93°, the Weyl point of the quadratic dispersion is realized in the first and second energy bands, and the global boundary state exists at 0. 0.5 The situation; when At 28.93°, the triple degeneracy point is formed by the first three energy bands and can be considered as the phase transition point of the Weyl points of two types of quadratic dispersion. Its energy bands are as follows: Figure 1 As shown in (c), the triple degeneracy point is located at point M in the Brillouin zone at a frequency of 10.12 kHz, exhibiting a large directional bandgap. Therefore, the boundary states obtained further will also have a relatively larger bandwidth. Specifically, the maximum directional bandgap between the first and second bands is 4.72 kHz, and the maximum directional bandgap between the second and third bands is 5.18 kHz.

[0039] The specific composition of a supercell is as follows: Figure 2 As shown in (a), this is obtained by arranging individual acoustic cells along the x-axis or y-axis. Generally, the period of the array is no less than 10 to ensure more accurate calculation of the boundary states. The shear length of the boundary cells in the supercell is also considered. The illustration is shown in the upper right corner.

[0040] Here, without loss of generality, we take the period of the supercell to be 15, and calculate the shear length. By considering the projected band structure for different values, the following conclusions can be drawn: When 0 0.5 At this time, the boundary states of the global characteristics are located between the band gaps of the first and second energy bands; when 0.5 At this point, the boundary state of the global characteristic is located between the band gaps of the second and third energy bands. Therefore, from the appearance, the boundary state of the triple degeneracy point has stable characteristics.

[0041] Pick 0.25 At that time, the projection band is as follows Figure 2 As shown in (b), the boundary state represented by the green line is located between the band gaps of the first and second energy bands and broadens to 2.72 kHz. The attached figure on the right shows the field distribution at the position of the yellow rhombus. It can be seen that the sound field is basically localized on the boundary and propagates along the boundary.

[0042] when 0.68 At that time, the projection band is as follows Figure 2 As shown in (c), the boundary state represented by the green line is located between the band gaps of the second and third energy bands, with a broadening of 4.98 kHz.

[0043] The physical mechanism by which this boundary state is stable will be demonstrated through further theoretical calculations.

[0044] Here, we characterize the bulk band by calculating its topological number, the Zak phase. A non-zero Zak phase of a bulk band reflects the presence or absence of boundary states in the band gap above it. In the Brillouin zone, a certain bulk band in each... The Zakphase of a slice can be calculated using the following formula: ; In the formula, For acoustic crystals in the Brillouin zone The eigenstate at that location; This represents an integration operation; For along Differential of direction; This indicates that the integral is performed over the entire Brillouin zone. (for a fixed value); It is the imaginary unit.

[0045] The above formula will only yield a quantized solution 0 or 0 if the chosen cell is symmetric. , respectively corresponding to 0 and 0.5 And this quantization is precisely due to This is due to the symmetry (combining the symmetry of a 180-degree rotation and a time-reversal operation). Since this triple degeneracy point has two band gaps, both the first and second bulk bands must be considered.

[0046] It is worth noting that the above formula cannot be defined and calculated at band degeneracy points, therefore we will The calculation point at that location, which is the position projected onto by the triple degenerate point, has been moved to the left and right respectively. The calculated results are as follows: Figure 3 (a) and Figure 3 As shown in (b), these correspond to the selected cells respectively. 0 and 0.5 As can be seen, the two calculated results are exactly opposite, further illustrating... 0.5 This represents the phase transition point of the entire shearing process.

[0047] for 0 In this case, the calculated band 1 Zak phase is the same throughout the entire projected Brillouin zone. The Zak phase of band 2 is 0, indicating that there are boundary states in the band gap between band 1 and band 2, but no boundary states in the band gap between band 2 and band 3.

[0048] for 0.5 In this case, the calculated Zak phase of band one is 0 throughout the entire projected Brillouin zone, while the Zak phase of band two is... This indicates that there are no boundary states in the band gap between band 1 and band 2, but there are boundary states in the band gap between band 2 and band 3, meaning that the boundary states flip from the first band gap to the second band gap.

[0049] Therefore, the stability of the triple degenerate point boundary state was proved by calculating the topological number Zak phase of the energy band, i.e., regardless of the shear length. No matter how the value is chosen, the boundary state always exists, it's just that... 0.5 Before and after, the distribution of boundary states in the two band gaps is different.

[0050] Furthermore, Embodiment 2 of the present invention discloses a design method for designing an acoustic frequency beam splitter based on the two-dimensional acoustic crystal with microstructure described in Embodiment 1. The resulting acoustic frequency beam splitter includes a top surface, a bottom surface, and a functional body between the top and bottom surfaces. The functional body of the acoustic frequency beam splitter is constructed based on the two-dimensional acoustic crystal described in Embodiment 1.

[0051] The boundary conditions for the acoustic frequency beamsplitter are set as follows: the working boundary of the frequency beamsplitter is a hard boundary, forming a channel for stable sound wave transmission, while the remaining non-working boundaries are open boundaries. The working boundary is obtained by shearing the complete acoustic cell at the boundary. The top and bottom surfaces use acoustic hard boundary materials to restrict sound wave propagation in the xy plane.

[0052] The acoustic frequency beam splitter is configured with three ports on the channel, including one input port and two output ports, wherein the input port is located at the interface between two different operating boundaries, i.e. Figure 4 The location is indicated by the green star. The output port is located at the other end of the working boundary, away from the input port, that is, the end in contact with the air. Figure 4 The location is indicated by the orange circle in the middle.

[0053] Set the shear length of the working boundary to The two working boundaries must be adjacent to each other, and the shearing length... Each satisfies 0 0.5 and 0.5 .

[0054] The acoustic frequency beam splitter is rectangular or square in shape. For acoustic crystal regions with different working boundaries, the number of periods in both the x and y directions is greater than or equal to 10.

[0055] Furthermore, based on the stable and global boundary states of the triple degeneracy point of the acoustic crystal, Embodiment 3 of the present invention also constructs an acoustic frequency beam splitter.

[0056] The design method described in Example 2 can yield two types of acoustic frequency beamsplitters that separate low-frequency and high-frequency sound waves at 180° and 90° respectively within the operating range. The main structural difference between the different types of acoustic frequency beamsplitters lies in the included angles of the working boundaries obtained by shearing the boundary cells, which are 180° and 90° respectively.

[0057] Because the boundary state of the triple degeneracy point is 0.5 Since the front and rear sections are located in different band gaps, the splicing is 0. 0.5 and 0.5 By defining two boundaries within a certain range, sound waves within a specific frequency range can be beamed. Based on the fact that the acoustic crystal is a square lattice, two types of beam splitters can be designed, namely, two working planes that are parallel or perpendicular, which can respectively split the sound waves within the working frequency along 180° and along 90°.

[0058] Understandably, when the boundary states have greater broadening, the frequency beam splitter will have a larger operating range. Therefore, two shear lengths for the two operating boundaries can be selected as follows: 0.25 and 0.68 The boundary state dispersion morphology in this case is as follows: Figure 2 (b) and Figure 2 As shown in (c). The following section will describe these two types of acoustic frequency beam splitters in detail.

[0059] First, let's consider the case where the beam splitting angle (i.e., the angle between the working boundaries) is 180°. The specific device structure is as follows: Figure 4 As shown in (a), the device was initially obtained by arranging acoustic cells 20 times along the x-direction and 10 times along the y-direction. The upper boundary was chosen as the working boundary, which was then divided into two parts: the left 10 cycles formed a single unit with the same shear length, and the right 10 cycles formed a single unit with the same shear length. Without loss of generality, the left working boundary was chosen. 0.68 Right working boundary 0.25 All working boundaries are hard boundaries, while the remaining boundaries—the lower, left, and right boundaries—are open boundaries. For the working port settings, the input port is located between the left and right working boundaries, but not too close to the interior; it needs to be close to the working boundaries to more efficiently excite boundary states and improve device efficiency. Figure 4As shown by the green star in (a). The output ports are located at the other two ends of the working boundary, namely the upper left and upper right corners of the entire device, as shown in [example image]. Figure 4 (a) is shown in the orange circle.

[0060] Calculations using COMSOL finite element simulation software show that the device can split sound waves in the range of 11.3-15.0 kHz to propagate along the left (i.e., the negative x-axis direction), with a working bandwidth of 3.7 kHz; and split sound waves in the range of 7.6-9.8 kHz to propagate along the right (i.e., the positive x-axis direction), with a working bandwidth of 2.2 kHz. Figure 4 (a) The two figures above and below show the field distribution at two different operating frequencies. It can be seen that the beam splitting effect is better at different operating frequencies, and the sound waves basically propagate along the operating boundary. It should be noted that the descriptions of frequency ranges in this invention all include endpoint values.

[0061] For a beam splitting angle of 90°, the specific device structure is as follows: Figure 4 As shown in (b), the device was initially obtained by arranging acoustic cells 10 times along the x and y directions, resulting in a smaller volume compared to the device with a 180° beam split. In this case, the working boundary can be selected by choosing any two adjacent right angles; here, the upper left corner is used for device description, meaning the left and upper boundaries are the working boundaries. Similarly, for these two working boundaries, different shear lengths are chosen, with the upper working boundary being selected. 0.68 Left working boundary 0.25 All boundaries are hard boundaries. The remaining boundaries, namely the right and bottom boundaries, are left unprocessed and are considered open boundaries. The input port is located at the upper left corner (right angle) to facilitate triggering boundary transmission mode, such as... Figure 4 As shown by the green star in (b); the two output ports are located in the lower left and upper right corners respectively, as shown in the image. Figure 4 (b) is shown in the orange circle.

[0062] Calculations using COMSOL finite element simulation software show that the operating frequency of this device is the same as that of a device with a beam splitting angle of 180°. This device splits sound waves in the range of 11.3-15.0 kHz into propagation along the right (i.e., the positive x-axis direction) and splits sound waves in the range of 7.6-9.8 kHz into propagation along the down (i.e., the negative y-axis direction). Figure 4 (b) The two figures above and below also show field distributions at two different working frequencies. It can be seen that the beam splitting effect is better at different working frequencies, and the sound waves basically propagate along the working boundary.

[0063] It is particularly noteworthy that the three bands of the triple degeneracy point achieved in this invention have relatively large directional band gaps, thus possessing an operating frequency range of 7.6 to 15.0 kHz. This frequency range falls entirely within the human hearing range of 0.02 to 20 kHz, therefore the broadened frequency band significantly enhances the device's application potential and applicable scenarios in the audible sound field.

[0064] The advantages of this frequency range mainly include the following three aspects: 1) Higher data transmission capability: A wider frequency range means that more data streams can pass through simultaneously, improving the data transmission rate; 2) Stronger device integration and compatibility: Wideband design allows a single device to replace the functions that could only be performed by multiple original narrowband devices, which is conducive to system simplification and multi-functional integration; 3) Stronger environmental adaptability and anti-interference capability: Wideband devices can select the sub-frequency band with the best quality to operate, effectively avoiding noise or interference in specific frequency bands, thereby ensuring smooth communication in changing environments.

[0065] In summary, this invention achieves its effect by adjusting the properties of a two-dimensional acoustic crystal. By utilizing the rotation angle of a symmetric scatterer and the transformation process of two quadratic dispersive Weyl points with different topological properties, a triple degeneracy point is achieved through accidental degeneracy, thereby realizing a boundary state with global and stable characteristics. Furthermore, based on the characteristic that this boundary state with global and stable characteristics can be located in different band gaps, this invention also proposes acoustic frequency beamsplitters with beam-splitting angles of 180° and 90°, exhibiting a large operating frequency range. This device also possesses advantages such as tunability, ease of fabrication, and stable properties. Therefore, this invention provides guidance for the design of acoustic transmission devices using topological acoustics.

[0066] Finally, it should be noted that although the embodiments of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the specific embodiments and application fields described above. The specific embodiments described above are merely illustrative and instructive, and not restrictive. Those skilled in the art, guided by this specification, can make many other forms without departing from the scope of protection of the claims of the present invention, and all of these are within the scope of protection of the present invention.

Claims

1. A two-dimensional acoustic crystal based on a microstructure, comprising a functional material layer, characterized in that, The functional material layer comprises acoustic cells arranged periodically in a square lattice in the xy plane; The acoustic cell is square and includes a scatterer and air filling the space around the scatterer; The scatterer has Rotational symmetry is achieved by a cross structure and four identical semicircles circumscribed at the ends of the cross structure. The cross structure is formed by two identical rectangular strips orthogonally, with their centers of symmetry coinciding with the center of the square lattice. The diameter of each semicircle is collinear with the short side of the rectangular strip at its end, and its center coincides with the midpoint of the outer side. The diameter of each semicircle is also greater than the length of the short side of the rectangular strip. The scatterer cross structure has a non-zero rotation angle between one of its central axes and one side of the square lattice. The rotation angle Matching the geometric parameters of the scatterer, the bulk band structure of the two-dimensional acoustic crystal produces a triple degeneracy point at point M in the Brillouin zone, formed by the first three bulk bands, which are defined as the first three modes that increase sequentially along the high-frequency direction starting from zero frequency.

2. The two-dimensional acoustic crystal as described in claim 1, characterized in that, The material of the scatterer satisfies that its acoustic impedance is greater than or equal to 10 times that of air; the material of the scatterer is any one of photosensitive resin, acrylic, metal, and organic plastic.

3. The two-dimensional acoustic crystal as described in claim 1, characterized in that, The thickness of the functional material layer is determined by the height of the scatterer in the acoustic cell; the height of the scatterer , The wavelength of the sound wave corresponding to the operating frequency of the acoustic crystal.

4. The two-dimensional acoustic crystal as described in claim 1, characterized in that, The number of periods of the acoustic cell in the x and y directions is not less than 10.

5. The two-dimensional acoustic crystal according to any one of claims 1 to 4, characterized in that, The lattice constant of the acoustic cell The length of the long side of the rectangular strip is 15 mm. It is 10 mm, the length of the short side 4mm, rotation angle It is 28.93°; the radius of the semicircle It is 3mm.

6. An acoustic frequency beam splitter with a beam splitting angle of 180°, characterized in that, It includes a top surface, a bottom surface, and a main structure between the top surface and the bottom surface, wherein the main structure is selected from the two-dimensional acoustic crystal based on microstructure as described in any one of claims 1 to 5; One side of the acoustic frequency beam splitter is set as a hard boundary, and the hard boundary has a first working boundary and a second working boundary arranged adjacent to each other, the shear length of the first working boundary and the second working boundary being... Each satisfies 0 0.5 and 0.5 , The lattice constant of the acoustic cell; All boundaries outside the working boundary in the acoustic frequency beam splitter are open boundaries. The acoustic frequency beam splitter has one input port and two output ports. The input port is arranged between the first and second working boundaries, and the output ports are respectively arranged at the ends of the first and second working boundaries away from the input port.

7. An acoustic frequency beam splitter with a beam splitting angle of 90°, characterized in that, It includes a top surface, a bottom surface, and a main structure between the top surface and the bottom surface, wherein the main structure is selected from the two-dimensional acoustic crystal based on microstructure as described in any one of claims 1 to 5; The acoustic frequency beam splitter has two adjacent sides defined as hard boundaries, one side being a first working boundary and the other a second working boundary. The shear length of the first and second working boundaries is... Each satisfies 0 0.5 and 0.5 , The lattice constant of the acoustic cell; All boundaries outside the working boundary in the acoustic frequency beam splitter are open boundaries. The acoustic frequency beam splitter has one input port and two output ports. The input port is arranged between the first and second working boundaries, and the output ports are respectively arranged at the ends of the first and second working boundaries away from the input port.

8. The acoustic frequency beam splitter as described in claim 6 or 7, characterized in that, The acoustic frequency beam splitter is generally rectangular or square.

9. The acoustic frequency beam splitter as described in claim 6 or 7, characterized in that, The number of periods in the acoustic crystal regions at different working boundaries is greater than or equal to 10 in both the x and y directions.

10. The acoustic frequency beam splitter as described in claim 6 or 7, characterized in that, The main structure is selected from the two-dimensional acoustic crystal based on microstructure as described in claim 5; the shear lengths of the first working boundary and the second working boundary are... They are 0.25 respectively. and 0.68 The acoustic frequency beam splitter operates in the range of 7.6-15.0 kHz; wherein the acoustic wave with a frequency range of 7.6-9.8 kHz propagates along the first working boundary; and the acoustic wave with a frequency range of 11.3-15.0 kHz propagates along the second boundary.

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