Broadband topology slow sound protection method based on Brillouin region multiple winding modulation

Abstract

The invention discloses a broadband topology slow sound protection method based on Brillouin region multi-winding modulation, and the method employs a topological photonic crystal and resonant cavity coupling structure to achieve broadband topology slow sound protection based on Brillouin region multi-winding modulation, and the coupling structure comprises a topological photonic crystal and a resonant cavity. The topological photonic crystal comprises a honeycomb lattice and an acoustic topological insulator, and the resonant cavities are periodically placed along the lower edge of the acoustic topological insulator to construct a resonant cavity array. According to the invention, coupling of a near-flat band and a topological edge state dispersion band in a Brillouin region is realized by utilizing resonance induction, so that novel hybrid edge state dispersion is formed. The synergistic interaction of the plurality of flat bands enables the topology edge state dispersion band to form a plurality of windings in the Brillouin region, thereby achieving the broadband topology slow sound phenomenon. The mechanism not only has multi-dimensional adjustability and robustness, but also can actively tune the sound wave group velocity by independently adjusting resonator parameters, and can cooperate with multi-parameter tuning.

Description

Technical Field

[0001] This invention belongs to the field of topological phononic crystal applications and relates to a broadband topological slow-motion protection method, specifically a broadband topological slow-motion protection method based on multiple winding modulation in the Brillouin zone. Background Technology

[0002] In recent years, topological phononic crystals have opened a new chapter in the field of acoustics due to their ability to efficiently transmit and manipulate sound waves. The manipulation of sound wave characteristics, particularly the ability to control sound wave propagation and achieve low group velocities, has become an increasingly important research area. This capability is crucial for improving time-domain signal processing and enhancing the interaction between sound waves and matter. Slowing down sound waves results in delays, allowing them to be temporarily stored in resonator structures, enabling new applications such as superabsorption and rainbow trapping. While significant progress has been made in slowing down sound waves through various methods such as resonance, band-edge models, and helical metamaterials, these techniques face challenges of high backscattering losses and narrow bandwidths, limiting their applicability in practical applications. Therefore, minimizing losses and backscattering simultaneously for slow sound waves over a wide frequency range remains an unresolved problem. Acoustic topological insulators offer an effective approach to addressing this challenge. This stems in part from the fact that unique topological edge states are naturally unaffected by backscattering and localization caused by disturbances, making them ideal for stable acoustic transmission. Topologically protected states enable many unique phenomena and significant applications, including wave filtering, sensors, stable acoustic wave transmission, and directional antennas. In topological phononic crystals, the propagation speed of acoustic waves is determined by the slope of the Brillouin zone dispersion band; achieving slow waves involves adjusting the dispersion band. According to the volume boundary correspondence, modifications near the edge of a topological phononic crystal do not affect the existence of topological edge states, but only change their dispersion curves. Summary of the Invention

[0003] To address the limitations of traditional slow-sound schemes due to structural perturbations and backscattering vulnerability, which hinder broadband performance, this invention provides a broadband topological slow-sound protection method based on multiple winding modulation in the Brillouin zone. This method utilizes resonance-induced coupling between near-flat bands and topological edge-state dispersion bands within the Brillouin zone to form a novel hybrid edge-state dispersion. The synergistic interaction of multiple flat bands causes the topological edge-state dispersion bands to form multiple windings in the Brillouin zone, thereby achieving the broadband topological slow-sound phenomenon. This mechanism not only possesses multidimensional tunability and robustness but also allows for active tuning of the sound wave group velocity through independent adjustment of resonator parameters and can be coordinated with multi-parameter tuning.

[0004] The objective of this invention is achieved through the following technical solution:

[0005] A topological phonon crystal coupled to a resonant cavity based on the synthesis dimension includes a acoustic synthesis Weyl system and a resonant cavity, wherein:

[0006] The acoustic synthesis Weyl system is a topological phononic crystal, comprising a honeycomb lattice and an acoustic topological insulator. The unit cells of the honeycomb lattice are made of photosensitive resin (density ρ = 1169 kg / m³). 3 It consists of a sound velocity c = 2079 m / s and an equilateral triangular scatterer, with a lattice constant a = 25 mm and a side length l = 0.6a for the equilateral triangular scatterer;

[0007] The resonant cavities are periodically placed along the lower edge of the acoustic topological insulator to construct a resonant cavity array, and the topological edge state dispersion band is modulated by the resonant modes of the cavities.

[0008] A design method for the above-mentioned topological phononic crystal coupled with a resonant cavity based on the synthesis dimension includes the following steps:

[0009] Step 1: In a two-dimensional topological phonon crystal, combine the two-dimensional Bloch wave vector k x k y And additional structural parameters θ, construct a synthetic three-dimensional parameter space (k x , k y , θ);

[0010] Step 2: By constructing a resonant cavity array at the edge of the topological phononic crystal, the dynamic equation of the nth resonance is:

[0011]

[0012] in, It is the first The normalized amplitude in each resonant element, ω0 is the resonant center frequency, γ is the leakage rate, and Ω is the evanescent coupling rate between adjacent resonators. It is the coupling coefficient between the resonant cavity and the edge states; combining Bloch's theorem and the CMT identity, we obtain its hybrid dispersion relation and group velocity as follows:

[0013]

[0014]

[0015] Where, k x k is the propagation constant of the entire system. ω Let be the propagation constant of the topological edge state before coupling with the resonant cavity, γ be the leakage rate of the resonant cavity, ω be the system frequency, ω0 be the resonant frequency of the resonant cavity, and v be the propagation constant of the topological edge state before coupling with the resonant cavity. g Let be the group velocity of the sound waves in the entire system;

[0016] Step 3: Use the hard acoustic field at the lower edge of the synthesized Weyl phonon crystal to truncate and induce edge states;

[0017] Step 4: By changing the coupling strength between the resonant cavity and the topological edge states (the size of the resonant cavity opening), the dispersion curve of the mixed topological edge states is affected, thereby reducing the sound velocity;

[0018] Step 5: Adjust the range of slow-motion frequencies and the operating space by changing different parameters of the resonant cavity (such as width, height, and opening).

[0019] Step Six: By designing resonant cavities of different sizes, the difference in resonant frequency leads to different cutoff frequencies of sound waves, thereby achieving effective guidance and spatial separation of sound waves, demonstrating the rainbow capture effect, and providing diversity for precise manipulation of sound waves in the frequency and spatial domains.

[0020] A broadband topology slow-motion protection method based on multiple winding modulation in the Brillouin zone using the above coupling structure includes the following steps:

[0021] Step 1: Through the synergistic interaction of multiple flat bands in the resonant cavity, the topological edge state dispersion bands are entangled in the Brillouin zone, thereby realizing the broadband topological slow sound phenomenon.

[0022] Step 2: Adjust the operating frequency range and bandwidth of the slow-motion sound by coordinating the control of multiple parameters of the resonant cavity;

[0023] Step 3: Customize the sound velocity based on the inverse proportional relationship between sound velocity and the number of windings;

[0024] Step 4: Acoustic rainbow capture is achieved by spatially modulating the group velocity of the edge states. Edge waves of different frequencies will stop at different locations, generating spatial separation along the straight interface.

[0025] Compared with the prior art, the present invention has the following advantages:

[0026] Topological phononic crystals, with their efficient transmission and manipulation capabilities for sound waves, provide an effective method for manipulating acoustic characteristics, particularly controlling sound wave propagation and achieving low group velocities. This invention utilizes the synergistic interaction of multiple flat bands to create multiple entanglements of the topological edge state dispersion bands in the Brillouin zone, thereby realizing broadband topological slow-motion phenomena. Taking a relative bandwidth of ~7% and a velocity of 0.04c0 (where c0 is the speed of sound in air) as an example, this significantly outperforms traditional methods. Furthermore, this invention exhibits multidimensional tunability and robustness, allowing for active tuning of the sound wave group velocity through independent adjustment of resonator parameters, and enabling synergistic multi-parameter tuning. By designing different resonant cavities and utilizing the ability to control the sound velocity, this invention achieves effective spatial separation, demonstrating an acoustic topological rainbow and providing diversity for precise manipulation of sound waves in the frequency and spatial domains. This not only establishes a theoretical framework for the manipulation of broadband slow-motion waves in topological phononic crystals but also paves the way for the development of high-performance acoustic devices. Attached Figure Description

[0027] Figure 1 The diagram shows the coupling structure of the synthesized Weyl phonon crystal and the resonant cavity.

[0028] Figure 2 The band diagrams are shown for the near-flat band and topological edge states induced by the resonant cavity under coupled and uncoupled conditions.

[0029] Figure 3 Dispersion bands and sound velocities under different coupling strengths (different resonant cavity openings).

[0030] Figure 4 The figures show the fitted curves of sound velocity and winding number, (a) the sound velocity of a broadband topological slow sound wave achieved through multiple windings in the Brillouin zone; and (d) the simulation data and nonlinear fitting of sound velocity and relative bandwidth under different winding numbers. Black marks represent the magnitude of the sound velocity, numerical simulation data, and purple lines represent nonlinear fitting, as shown on the right y-axis. Relative bandwidth (bandgap width and bandgap center frequency) The ratio is displayed on the left y-axis, with blue squares marking simulated data and solid lines representing nonlinear fitting.

[0031] Figure 5 To independently adjust the resonator parameters and actively tune the acoustic group velocity. Detailed Implementation

[0033] The technical solution of the present invention will be further described below with reference to the accompanying drawings, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.

[0034] This invention constructs a topological phonon crystal and resonant cavity coupling structure based on the synthesis dimension, such as... Figure 1 As shown, the coupling structure includes a topological phononic crystal with a honeycomb lattice and a resonant cavity, wherein: the unit cell of the honeycomb lattice consists of photosensitive resin and equilateral triangular scatterers embedded in an air medium, and the scatterers (dark gray area) are modeled as rigid bodies relative to the surrounding air. The lattice constant a = 25 mm, and the side length l = 0.6a of each equilateral triangular scatterer. In the two-dimensional phononic crystal, combined with the two-dimensional Bloch wave vector k... x k y And additional structural parameters θ, construct a synthetic three-dimensional parameter space (k x , k y (θ). A resonant cavity array is constructed at the edge of the acoustic synthesis Weyl system. The flat bands induced by the resonant cavities and the dispersion bands of the topological edge states are intertwined within the Brillouin zone, enabling the modulation of broadband slow acoustic waves, whose energy bands are as follows: Figure 2 As shown.

[0035] This invention considers a physical configuration in which resonators are periodically placed at the lower edge of an insulator, isolated from each other and coupled to a waveguide, such as... Figure 2 As shown. Using coupled-mode theory, the dynamic equation for the nth resonance is:

[0036] (1)

[0037] Where c is the normalized amplitude in the nth resonant unit, w0 is the resonant center frequency, γ is the leakage rate, and Ω is the evanescent coupling rate between adjacent resonators. This is the coupling coefficient between the resonant cavity and the edge states. The resonators are isolated from each other, so the evanescent coupling of the resonators is zero (Ω=0). Combining Bloch's theorem and the CMT identity, we can derive its hybridized dispersion relation and group velocity as follows:

[0038] (2)

[0039] (3)

[0040] When a resonant mode couples to a propagating edge state, the group velocity of the hybrid edge state decreases, with its minimum occurring at the center frequency. Lower group velocities can be achieved over a wide frequency range by adding more resonant frequencies.

[0041] The finite element method is used to calculate the opening parameters and tuning velocity of the resonant cavity, such as... Figure 3 As shown. When the cavity opening width t = 0, there is no coupling between the resonant mode and the topological edge state, resulting in no hybridization. Therefore, the dispersion curves of the resonant mode and the topological edge state intersect, as shown. Figure 3As shown in (a), the coupling strength increases with increasing t. This causes the intersection points of the dispersion curves to separate, and the topological edge states and near-horizontal bands connect to form new hybrid topological edge states, such as... Figure 3 As shown in (c). Furthermore, in Figure 3 In (d), the hybrid topological edge states exhibit a significant decrease in group velocity after circling the Brillouin zone once. Further increasing t leads to stronger coupling, resulting in significant changes in both the near-horizon and hybrid edge states, and a further decrease in group velocity.

[0042] To further reduce the group velocity of edge states and realize broadband topological slow acoustic waves, this invention increases the Brillouin zone winding number to explore winding in high momentum space. Figure 4 (a) and Figure 4 (b) Edge dispersion configurations with 2 and 8 resonant cavities, respectively, with cavity parameters m = 0.99a, h = 0.5a, t = 0.18a, arranged along the y-direction. As the number of resonant cavities increases, the dispersion of the mixed topological edge states around the Brillouin zone increases. The synergistic effect of multiple flat bands allows the topological edge state dispersion bands to form multiple entanglements in the Brillouin zone. Since the group velocity corresponds to the slope of the dispersion curve, multi-entangled edge dispersion naturally leads to a slower group velocity, such as... Figure 4 As shown in (c), with the increase of the number of windings within BZ, the speed is negatively correlated with the number of windings w, and the fitted function relationship is v. g = c0(A+B / (w+C)), such as Figure 4 As shown in (d). Furthermore, multi-wound banding offers a wider operating frequency range than single-wound banding, with the bandwidth tending to be constant. For example, in this optimized configuration (w = 20), the sound velocity can be significantly reduced to below 0.089c0 (c0 is the speed of sound in air, which is 343 m / s), and the bandwidth is approximately 6.72% (the ratio of bandgap width to bandgap center frequency). Therefore, the speed of sound can be further reduced without sacrificing bandwidth by increasing the number of windings. A fitted curve of sound speed versus number of windings provides the possibility of customizing the sound speed.

[0043] This invention further tunes the size of the resonant cavity to adjust the dispersion curve. Here, we take the resonant cavity width *m* as an example. After changing the resonant cavity width, the resonant modes exhibit a monotonic change, such as... Figure 5 As shown in (a), four widths are selected to display the frequency shift; the resonant frequency monotonically increases as m decreases. Here, widths m are selected as 0.93a, 0.95a, 0.97a, and 0.99a. Figure 5As shown in (b), four resonant cavities are used as an example. The parameters of each cavity are h = 0.5a and t = 0.18a, respectively. The widths of the resonant cavities are m1, m2, m3, and m4. By changing the size of the resonant cavities, the velocity of sound waves in different frequency ranges can be effectively adjusted, such as... Figure 5 As shown in (b). For example, when the width of the first cavity is adjusted (m1 = 0.97a), the sound velocity is effectively reduced in the range of 7.26 kHz to 7.35 kHz, as... Figure 5 As shown in (b1). When m2 = 0.97a, the frequency range shifts to 7.09 kHz ~ 7.19 kHz (as shown in Figure 1). Figure 5 (b2) shows); when m3 = 0.97a, the frequency range shifts to 6.97 kHz ~ 7.03 kHz (as shown in b2). Figure 5 (as shown in (b3)). This invention can not only achieve wide slow sound waves through multi-cavity coupling, but also customize the speed of slow sound waves within the desired frequency band by adjusting the width of the resonator.

[0044] The coupling mechanism of this invention can effectively reduce the speed of sound over a wide frequency range and allow sound waves to be temporarily stored in the resonator structure, providing a good solution for designing acoustic devices with multiple functions. As an example, this invention demonstrates rainbow edge waves, using the gradient magnitude of different resonator cavity lengths m (0.91a, 0.93a, 0.96a, 0.99a), represented by colored resonator cavities, while the height and opening (h = 0.5a, t = 0.22a) of all resonator cavities are fixed, as shown in Figure 6(a). Due to the gradient of the resonator cavity length, the shift of its resonant flat band leads to a shift in the dispersion curve of the hybrid edge state, as shown in Figure 6(b). Figure 6(c) shows that the first hybrid edge mode exhibits a cutoff frequency at the tail end of the group velocity curve, at which the group velocity becomes zero. By placing a point source on the left, at the four rainbow capture frequencies ( = 7.545 kHz, = 7.440 kHz, = 7.240 kHz, The absolute sound pressure distribution at 7.035 kHz is clearly shown in the left image of Figure 6(d), where the sound wave is captured at the corresponding interface. We obtained its corresponding absolute sound pressure value distribution (yellow dashed line in the left image of Figure 6(d)) and plotted it in the right image of Figure 6(d). As shown, the sound pressure field outside the capture area is almost zero, and the area where the sound wave stops and amplifies gradually moves to the right of the interface, achieving spatial separation of the sound wave. This is expected to promote the development of fields such as spatial frequency component decomposition, energy harvesting, and selective filtering, with smaller size and higher performance levels.

Claims

1. A synthetic dimension based topological phononic crystal and resonator coupling structure, characterized in that The coupling structure comprises a sound synthetic Weyl system and a resonant cavity, wherein: The sound synthetic Weyl system is a topological phononic crystal, which comprises a honeycomb lattice and an acoustic topological insulator; The resonant cavity is periodically placed along the lower edge of the acoustic topological insulator, and a resonant cavity array is constructed, and the topological edge state dispersion band is regulated by the resonant mode of the cavity.

2. The synthetic dimension based topological phononic crystal and resonator coupling structure of claim 1, wherein The unit cell of the honeycomb lattice is composed of a photosensitive resin and an equilateral triangle scatterer, the lattice constant a = 25 mm, and the side length l of the equilateral triangle scatterer is 0.6a.

3. A method for designing a synthetic-dimension-based topological phononic crystal and resonator coupling structure according to any one of claims 1-2, characterized in that The method comprises the following steps: Step one, in two-dimensional topological phononic crystal, combining two-dimensional Bloch wave vector k x , k y and additional structural parameters θ, a synthetic three-dimensional parameter space (k x , k y , θ) is constructed; Step two, constructing a resonant cavity array on the edge of the topological phononic crystal, and the dynamic equation of the nth resonant is: wherein, is the normalized amplitude in the mth resonator, ω0is the resonance center frequency, γ is the leakage rate, Ω is the evanescent coupling rate between adjacent resonators, is the coupling coefficient between the resonator and the edge state; combining the Bloch theorem with the CMT identity with it, the dispersion relation and group velocity after hybridization are obtained; Step three, inducing the edge state by truncating the hard sound field on the lower edge of the synthetic Weyl phononic crystal; Step four, affecting the hybrid topological edge state dispersion curve by changing the coupling strength between the resonant cavity and the topological edge state, so as to reduce the sound velocity; Step five, adjusting the range of slow sound frequency and operation space by changing different parameters of the resonant cavity; Step six, by designing resonant cavities of different sizes, the difference in resonant frequency causes the cutoff frequency of the sound wave to be different, thereby realizing effective guidance and spatial separation of the sound wave, and showing the rainbow capture effect, and providing diversity for accurately manipulating the sound wave in the frequency and spatial domains.

4. The method of designing a synthetic-dimension-based topological phononic crystal and resonator coupling structure according to claim 3, wherein In step two, the dispersion relationship and group velocity after hybridization are: where k x is the propagation constant of the whole system, k ω is the propagation constant of the topological edge state before coupling with the resonator, γ is the leakage rate of the resonator, ω is the system frequency, ω0 is the resonant frequency of the resonator, and v g is the group velocity of the sound wave in the whole system.

5. A method for implementing a wideband topology slow acoustic protection based on the Brillouin zone multiple winding modulation by using the synthetic dimension based topological phononic crystal and resonant cavity coupling structure according to any one of claims 1-2, characterized in that The method comprises the following steps: Step one, by the synergistic interaction of multiple flat bands of the resonant cavity, multiple windings of the topological edge state dispersion band are formed in the Brillouin zone, so as to realize the wideband topological slow sound phenomenon; Step two, by the synergistic regulation of multiple parameters of the resonant cavity, the slow sound working frequency range and bandwidth are adjusted; Step three, according to the inverse proportional relationship between the sound velocity and the winding number, the sound velocity is customized; Step four, by spatially modulating the group velocity of the edge state, the sound wave rainbow capture effect is realized, and the edge waves of different frequencies will stop at different positions, and spatial separation is generated along the straight line interface.

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