Multidirectional acoustic wave transmission via artificial periodic structures

1 Introduction

Directional acoustic transmission enables precise manipulation of acoustic energy along predefined propagation paths, serving as a fundamental technique for modern acoustic functional systems. It has found extensive applications in acoustic communication [1–3], industrial non-destructive testing [4–6], acoustic energy harvesting [7, 8], and biomedical ultrasonic imaging [9]. Conventional acoustic wave manipulation techniques, including geometric lenses and structural sound barriers, suffer from bulky dimensions, single functionality, and low energy efficiency, which largely limit their practical applicability. As artificially engineered periodic composites, acoustic metamaterials exhibit extraordinary effective parameters absent in natural materials, such as negative mass density and negative bulk modulus. By overcoming the inherent limitations of traditional acoustic regulation schemes, acoustic metamaterials have become a promising platform for high-precision and efficient acoustic wave control [10–13].

The development of acoustic metamaterials is significantly inspired by electromagnetic metamaterials, a relatively mature research field. As fundamental classical wave motions, acoustic and electromagnetic waves share analogous propagation and modulation characteristics. Accordingly, effective medium theory and parametric design principles originally established for electromagnetic systems have been extended to acoustic research, providing reliable theoretical guidance for the design of advanced acoustic functional structures. Current studies mainly focus on the development of double-negative acoustic metamaterials that replicate the unique wave-manipulating properties of their electromagnetic counterparts. Such structures enable flexible tailoring of acoustic wavefronts and propagation directions, offering new opportunities for high-performance directional acoustic transmission [14–22].

A milestone advance in this field was the proposal of locally resonant phononic crystals by Liu et al. in 2000 [23]. By embedding resonant units periodically within elastic media, subwavelength low-frequency bandgaps can be realized, breaking the lattice-size constraints of conventional Bragg scattering. This pioneering work unlocked subwavelength acoustic manipulation and greatly promoted the development of low-frequency acoustic metamaterials. However, the original multilayer resonant structure imposes considerable challenges to practical fabrication. To address this issue, Yang et al. proposed a simplified membrane-mass resonant configuration and experimentally verified the negative mass density effect near the resonant frequency, facilitating low-cost and feasible fabrication of subwavelength acoustic metamaterials [24].

Alongside structural optimization, continuous progress in theoretical modeling has further improved the analytical framework of acoustic metamaterials. Sharma et al. developed a rigorous analytical formalism for soft media embedded with dense spherical cavities, providing a self-consistent homogenization method for monopole-scattering acoustic metamaterials [25]. Based on these theoretical and structural foundations, Li et al. achieved simultaneous negative effective mass density and bulk modulus via rational resonant configuration design. The resulting double-negative effect supports exotic acoustic behaviors such as negative refraction, which is essential for high-efficiency directional acoustic transmission [26]. Subsequently, Ghasemi Baboly et al. designed 90° bent phononic crystal waveguides utilizing bandgap characteristics, achieving preliminary directional acoustic transmission [27].

Despite these advances, existing metamaterial-based directional transmission structures still face several limitations. Most reported designs only support fixed single-path transmission with limited robustness and poor adaptability to complex acoustic environments, restricting their practical deployment. To overcome these challenges, this work proposes a novel artificial periodic acoustic metamaterial structure to realize multidirectional acoustic focusing and low-loss, high-stability directional acoustic transmission.

The proposed structure adopts a two-dimensional three-component unit cell consisting of a lead core, rubber cladding, and epoxy matrix. The unit cell exhibits resonant dynamics consistent with a double-spring vibrator model, yielding simultaneous negative effective mass density and bulk modulus near the resonant frequency. The induced double-negative characteristic produces a negative refraction effect within a specific frequency range, enabling efficient multidirectional focusing and convergence of diffuse acoustic waves. Furthermore, line defects are introduced into locally resonant phononic crystal arrays to construct customized acoustic waveguides. Benefiting from phononic bandgap confinement, acoustic energy is well localized within defect channels to implement low-loss directional propagation. By modulating channel widths, the designed structure achieves multifunctional acoustic manipulation, including path-selective transmission and acoustic beam splitting [29–31].

Moreover, topological design is incorporated to further enhance the transmission robustness and anti-scattering capability of system. A hexagonal lattice with broken six-fold symmetry is constructed to generate topologically protected edge states, which effectively suppress acoustic backscattering and improve acoustic energy transmission efficiency. Featuring broadband operability, structural flexibility, and functional versatility, the proposed metamaterial system not only provides an effective strategy for acoustic wave manipulation along complex trajectories, but also expands the application prospects of phononic crystal metamaterials in acoustic communication, directional signal detection, and acoustic energy harvesting. The proposed design is further validated by 500 kHz underwater acoustic experiments on a fabricated Z-shaped topological waveguide sample.

It is worth emphasizing that the three functionalities above are realized on a single base lattice configuration rather than through independently designed structures. In previous studies, negative-refraction focusing typically requires dedicated optimization of lattice dispersion curves and equifrequency surfaces to obtain a negative effective refractive index [26], while bandgap-based directional transmission demands lattice redesign to open acoustic band gaps [28]; different application scenarios thus often rely on multiple mutually independent phononic crystal structures, resulting in long design cycles [32, 33]. In contrast, this work demonstrates that one two-dimensional three-component base lattice can satisfy the negative-refraction dispersion condition, the bandgap-opening condition, and the topological edge-state condition simultaneously through modest tuning of lattice size, array arrangement, and operating frequency. Such a unified platform eliminates material and fabrication discrepancies among different configurations, shortens the design and fabrication cycle, and improves the generality and scalability of the structural design system.

2 Unit cell design and effective parameters

2.1 Resonant dynamics and double-negative parameters

The two-dimensional three-component phononic crystal unit cell adopted in this study is schematically illustrated in Figure 1a. The composite structure consists of a central lead core, an intermediate rubber coating layer, and an outer epoxy resin matrix. Specifically, the lead core has a radius of R ₁ = 0.5 mm, and the rubber layer is fabricated with a thickness of R ₂-R ₁ = 0.2 mm. When incident acoustic waves act on the periodic structure, the epoxy matrix undergoes forced vibration, which sequentially transfers dynamic energy to the rubber layer and the inner lead core. This coupling vibration behavior of multi-layer components dominates the dynamic response of the unit cell and can be well described by a classical double-spring vibration model. The corresponding theoretical relationships are defined as follows (Equations 1–3): where M 1 and M 2 represent the equivalent masses of the outer and inner vibrating components of the double-spring system, respectively. M e f f denotes the effective dynamic mass of the unit cell, ω is the operating angular frequency, and a corresponds to the lattice constant between adjacent structural units.

ω 2 = 4 K M eff − 1 ⁡ sin 2 ⁡ k a (1)

M eff = M 1 + M 2 ω 0 2 / ω 0 2 − ω 2 (2)

ω 0 = 2 G / M 2 (3)

In this multi-component configuration, the high-density lead core and the outer epoxy matrix are equivalent to the inner and outer mass blocks of the vibration system, while the highly elastic rubber layer serves as the flexible spring with stiffness coefficient G. Accordingly, the effective masses of the lead core and epoxy matrix can be quantitatively calculated based on their geometric dimensions and material densities (Equations 4, 5):

m lead = ρ lead π R 1 2 (4)

m epoxy = ρ epoxy a 2 − π R 2 2 (5)

Substituting the structural parameters, the inherent resonant frequency of the unit cell and the frequency-dependent effective mass can be further derived (Equations 6, 7):

ω 0 = 2 G / ρ lead π R 1 2 (6)

M eff = ρ lead π R 1 2 ω 0 2 / ω 0 2 − ω 2 − ρ epoxy − a 2 + π R 2 2 (7)

As demonstrated in Equation 7, the effective mass of the proposed unit cell is strongly frequency dispersive. When the frequency of incident acoustic waves approaches the inherent resonant frequency of the structure, the vibration phase of the high-density lead core reverses relative to the external excitation force. In this case, the acceleration direction of the unit cell opposes the applied load, resulting in an abnormal negative effective mass effect. Such resonant-induced dynamic inversion provides the fundamental condition for realizing acoustic negative refraction.

The formation mechanism of double-negative parameters can be physically explained by the coupling resonance of multi-layer materials. Near the resonant frequency, the dynamic response of the high-density lead core dominates the overall vibration behavior, yielding negative effective mass density. Meanwhile, the hyperelastic rubber layer undergoes severe deformation under acoustic excitation, which counteracts the stiffness of the epoxy matrix and further induces negative effective bulk modulus. The coexistence of negative mass density and negative modulus enables the structure to exhibit negative refractive characteristics, which is the core mechanism for achieving extraordinary acoustic wave manipulation.

To systematically analyze the wave propagation characteristics and bandgap properties of the periodic array, finite element simulations were performed using COMSOL Multiphysics 5.4 with Floquet periodic boundary conditions. All numerical calculations were implemented in the pressure acoustic module, with water serving as the background medium. The detailed material parameters adopted in the simulation are listed as follows: ρ water = 1 , 000 kg / m 3, c water = 1 , 500 m / s, ρ lead = 11 , 600 kg / m 3, c lead = 2 , 160 m / s, ρ epoxy = 1 , 180 kg / m 3, c epoxy = 2 , 680 m / s, ρ rubber = 980 kg / m 3, c rubber = 300 m / s. As shown in Figure 1B, the simulation results reveal several bandgaps within which acoustic waves are prohibited from propagating through the periodic structure. These bandgaps offer a viable mechanism for tailored wave guiding and manipulation.

2.2 Nonlocal inter-cell coupling correction

The negative effective parameter behavior described by the aforementioned double-spring model is a local resonant response of the unit cell. And the acoustic response of each structural element depends solely on its own geometric and material parameters, without any inter-cell coupling. However, for realistic periodic metamaterials, the near-field interactions between adjacent unit cells become non-negligible at high filling fractions or under strong resonant conditions. In such cases, the effective parameters must be characterized by a nonlocal constitutive relation. To incorporate the inter-cell coupling effect into the effective mass density, a coupling correction term can be introduced into the double-spring framework. u n and U n are the displacement of the inner mass block and displacement of the outer matrix in the n-th unit cell, respectively. The equations of motion can then be written as (Equations 8, 9): where κ n m and λ n m are the coupling stiffness coefficients between the inner masses and between the outer matrices, respectively. By applying the Bloch periodic conditions u n = u 0 e xp i k n a − ω t and U n = U 0 e xp i k n a − ω t, the above discrete equations are transformed into a wave-vector dependent dispersion relation (Equation 10):where the Fourier transforms of the coupling terms are given by κ ∼ k = ∑ m ≠ 0 κ 0 m 1 − e xp i k m a and λ ∼ k = ∑ m ≠ 0 λ 0 m 1 − e xp i k m a. Consequently, the effective dynamic mass M e f f depends not only on the angular frequency ω, but also explicitly on the acoustic wave vector k, as expressed in Equation 11:

M 2 u ¨ n + G u n − U n + ∑ m ≠ n κ n m u n − u m = 0 (8)

M 1 U ¨ n + G U n − u n + ∑ m ≠ n λ n m U n − U m = F e x t − n (9)

M 2 u ¨ n + G u n − U n + ∑ m ≠ n κ n m u n − u m = 0 (10)

M e f f ω , k = M 1 + M 2 ω 0 2 + κ ∼ k / M 2 ω 0 2 − ω 2 + κ ∼ k / M 2 (11)

Thus, when κ ∼ k is sufficiently large, both the central frequency and bandwidth of negative-mass region are modulated by inter-cell coupling strength. This provides an additional degree of freedom for the engineered design of negative-parameter frequency bands by tuning the lattice constant a and the filling fraction.

3 Directional acoustic focusing

This section investigates the directional acoustic focusing performance enabled by artificially designed triangular arrays composed of the aforementioned three-component resonant unit cells. The unit cells are periodically arranged to form triangular lattices in a water background medium, and their local resonant characteristics are exploited to reshape and converge incident acoustic wavefields. The underlying focusing mechanism originates from the resonant-induced negative refractive index of the proposed metamaterial unit, which enables unconventional wavefront modulation distinct from conventional acoustic media.

3.1 Triangular focusing lens via negative refraction

As typical classical wave fields, acoustic and electromagnetic waves obey analogous refraction principles under linear propagation conditions, both of which can be described by Snell’s law. For acoustic wave propagation across medium interfaces, the refraction relationship is expressed as (Equation 12):where n 1 and n 2 represent the acoustic refractive indices of two adjacent media, and θ 1 and θ 2 denote the incident and refracted angles, respectively. The equivalent acoustic refractive index of a homogeneous medium is defined based on its effective density and elastic modulus (Equation 13):where ρ and E correspond to the effective mass density and effective elastic modulus of the metamaterial medium. In conventional natural materials, these two parameters are always positive, leading to a positive refractive index and regular wave refraction behavior. In contrast, the designed locally resonant metamaterial achieves simultaneous negative ρ and E near its resonant frequency. The dual-negative parametric characteristic produces a negative refractive index, thereby reversing the conventional acoustic refraction trajectory.

n 1 ⁡ sin ⁡ θ 1 = n 2 ⁡ sin ⁡ θ 2 (12)

n = ρ / E (13)

The working principle of the triangular acoustic focusing lens is illustrated in Figure 2a. When spherical acoustic waves radiated from a point source impinge on the metamaterial lens, the negative refraction effect modulates the transmission direction of the acoustic wavefront, giving rise to wave interference within the lens. Wave superposition inside the lens generates a stable focal region, which acts as a secondary acoustic source for secondary wave radiation. The transmitted waves undergo negative refraction again at the lens–water interface and eventually converge at the vertex of the triangular array. Such wave convergence behavior is closely related to the strong dispersion of the phononic crystal structure: near resonance, the phase velocity and group velocity of acoustic waves are modulated oppositely, and the energy propagation direction governed by the group velocity is reversed, which macroscopically presents as an effective negative refraction effect.

Numerical simulations of acoustic pressure fields were conducted to verify the focusing capability of the proposed lens structure, as depicted in Figures 2B–D. The simulation results confirm that the designed metamaterial configuration can effectively focus diffuse incident acoustic waves, which verifies the negative refraction-based focusing mechanism. Nevertheless, the pressure amplitude at the focal point is slightly lower than that of the original point source. This moderate energy attenuation is attributed to the radiation characteristics of the point source: part of the acoustic energy propagates downward and dissipates into the surrounding water medium without participating in lens focusing, while only upward-propagating energy is captured and converged by the triangular lens.

3.2 Enclosed configurations for omnidirectional focusing

To suppress energy dissipation and realize high-efficiency omnidirectional acoustic focusing, two optimized lens configurations with hexagonal and triangular layouts are further proposed, as depicted in Figures 3a,c. In these designs, the point source is fully enclosed by surrounding metamaterial lens arrays, ensuring that nearly all radiated acoustic energy interacts with the resonant structure. Driven by local resonance and negative refraction effects, the acoustic energy is efficiently concentrated at each vertex of the polygonal arrays, achieving low-loss multi-directional focusing. The acoustic pressure amplitude at each focal point is comparable to that of the original source, demonstrating excellent energy retention performance.

Furthermore, multi-beam directional transmission can be realized by adjusting the array topology. The simulated acoustic pressure fields reveal that the energy is effectively partitioned into multiple directional beams, and the number of focal points corresponds to the number of lens vertices. Owing to the conservation of acoustic energy, the hexagonal array with more focal vertices presents a slightly lower pressure amplitude at each individual focal point compared with the triangular configuration, as confirmed by the pressure field amplitudes shown in Figures 3b,d. This topological modulation strategy provides a flexible and efficient approach for multi-directional acoustic wave manipulation, showing promising application potential in acoustic energy harvesting, high-precision signal detection, and directional acoustic communication systems.

4 Bandgap-guided directional transmission

Based on the bandgap characteristics of locally resonant phononic crystals, artificially introduced line defects can construct customized acoustic waveguide channels, enabling flexible regulation of acoustic wave propagation trajectories. This section investigates the directional transmission performance of straight, curved, and Y-shaped beam-splitting waveguides realized via structural defect engineering, and further explores the influence of channel geometric parameters on acoustic transmission efficiency and functional modulation.

4.1 Straight and curved defect waveguides

The straight waveguide configuration constructed by single-line defects is displayed in Figure 4a. A linear acoustic source is placed at the inlet of the defect channel to excite incident acoustic waves. Benefiting from the complete bandgap effect of the surrounding periodic phononic crystal array, acoustic waves are confined within the defect region and prohibited from transverse leakage, thus achieving stable unidirectional transmission. Numerical simulations are performed at three typical frequencies of 450 kHz, 550 kHz, and 600 kHz to verify the broadband adaptability of the designed waveguide. The acoustic pressure field distributions in Figures 4a–c demonstrate effective acoustic energy localization and low-loss directional transmission across the above frequency bands, confirming the favorable broadband working performance of the proposed structure.

The normalized acoustic pressure distribution along the straight propagation channel is quantitatively analyzed in Figure 4g. The results indicate that the acoustic pressure amplitude increases gradually with the elevation of operating frequency. Such frequency-dependent characteristics stem from the matching relationship between acoustic wavelength and channel size (see Appendix A). Higher frequencies correspond to shorter wavelengths, which enable tighter energy confinement within the defect channel and thereby produce higher focal pressure intensity. In contrast, relatively long-wavelength acoustic waves at low frequencies induce slightly dispersed energy distribution and weakened peak pressure.

In addition to straight-channel transmission, the defect-based waveguide strategy supports arbitrary trajectory design. As illustrated in Figures 4d–f, curved waveguides are constructed by tailoring the line defect path. The simulated pressure fields verify that acoustic waves can propagate smoothly along preset curved routes without obvious energy leakage, proving the excellent structural flexibility and path adaptability of the proposed phononic crystal waveguide. This design provides a feasible solution for planar acoustic transmission systems requiring complex propagation paths.

4.2 Y-shaped beam splitter with tunable functionality

It is worth noting that the coupling effect between channel width and incident wavelength plays a decisive role in energy transmission efficiency and wavefield distribution. Mismatched geometric parameters may cause uneven energy distribution and partial wave leakage. To further explore the multifunctional regulation capability of the defect waveguide, a Y-shaped phononic crystal beam splitter is constructed in this study. The structure consists of one horizontal incident channel and two symmetric output channels, with widths defined as w 1, w 2 and w 3, respectively as illustrated in Figure 5a. Plane acoustic waves are vertically incident from the input port, and the transmission behavior is modulated by adjusting the width matching of each channel.

Two typical channel width configurations are compared to reveal the functional switching mechanism. When w 1 = w 2 < w 3, the geometric mismatch between the incident channel and output channels leads to asymmetric energy transmission. Acoustic energy preferentially propagates along the well-matched Output 1, while negligible energy passes through Output 2, thereby realizing path-selective directional transmission, as shown in Figure 5b. By contrast, when all channel widths are identical, i.e., w 1 = w 2 = w 3, the incident acoustic energy is uniformly divided into the two output ports, achieving high-performance acoustic beam splitting, as depicted in Figure 5c. The above results demonstrate that the proposed waveguide can flexibly switch between selective transmission and beam splitting functions only through simple size modulation, exhibiting prominent multifunctional integration advantages.

5 Topologically protected transmission

5.1 Valley topological design and band theory

Traditional defect-type phononic crystal waveguides rely purely on bandgap confinement, which are vulnerable to backscattering interference at structural bends or geometric mutations, resulting in reduced transmission robustness. To address this limitation, topological protection mechanisms are further introduced in this work to enhance the anti-interference capability of the acoustic transmission system. A hexagonal lattice with broken six-fold symmetry is designed by assembling scaled resonant unit cells, which breaks the original spatial symmetry and constructs topologically protected acoustic transmission interfaces.

The band structure of negative parameter in metamaterials not only governs the propagation and prohibition of acoustic waves, but also enables its topological properties and the emergence of topologically protected edge states, along which acoustic waves can propagate without back-scattering even in the presence of defects or disorder. In periodic systems, the topological invariants of the energy bands are characterized by the Berry phase and the Chern number. For the nth band, the Berry phase is defined as the closed loop integral over the first Brillouin zone (Equation 14):where A n k = i φ n k ∇ k φ n k is the Berry connection and | φ n k denotes the Bloch eigenstate. The corresponding Chern number of the nth band is given by Equation 15:which is an integer topological invariant. When the effective mass density ρ e f f or the effective bulk modulus K e f f of the metamaterial crosses zero, a topological phase transition occurs. The energy bands reconnect in the Brillouin zone, accompanied by a jump in the Chern number. Specifically, as ρ e f f → 0 or 1 / K e f f → 0, the dispersion relation ω k exhibits degeneracy near k = 0. The opening or closing of the band gap at this degeneracy signals the onset of the topological phase transition. For two-dimensional acoustic metamaterials, the critical frequency ω c of the phase transition satisfies Equation 16:

Φ = ∮ A n k · d k (14)

C n = 1 2 π ∮ ∇ k × A n k · d 2 k (15)

ρ e f f ω c = 0 or 1 K e f f ω c = 0 (16)

Across the transition frequency, the topological invariant of the system changes, giving rise to topologically protected edge states within the band gap. These edge states possess unidirectional propagation characteristics and exhibit inherent robustness against defects and perturbations. Combining the design of negative effective parameters with topological band theory offers a promising route for acoustic information processing and wave manipulation at subwavelength scales.

5.2 Robust transmission in straight and Z-shaped waveguides

Two types of phononic crystal arrays with opposite valley Chern numbers are arranged alternately to form straight waveguide channels. The topological edge states generated at the heterogeneous interface can effectively suppress acoustic backscattering, enabling stable and efficient energy transmission even at structural boundaries as shown in Figure 6. Furthermore, a Z-shaped topological waveguide with continuous bending trajectories is constructed to verify the robustness of the system. As demonstrated in Figure 7, acoustic waves propagate along the pre-designed Z-shaped path with negligible energy leakage and backscattering, fully demonstrating the superior anti-defect interference capability of the topologically optimized structure. Compared with traditional bandgap-confined waveguides, the proposed topological design significantly improves the stability and practicability of directional acoustic transmission. The transmission performance of the Z-shaped topological waveguide is further experimentally verified in the 'Experimental Validation' section.

6 Experimental validation

To further verify the feasibility of the proposed design, a Z-shaped topological waveguide sample was fabricated and characterized on a self-built underwater acoustic testing platform.

6.1 Sample fabrication

The three-component sample was fabricated through a three-step process, as illustrated in Figure 8. First, the epoxy-resin matrix shell was fabricated by three-dimensional (3D) printing (Figure 8a). Second, the rubber cladding structures were obtained by casting molding, which can be nested with the printed epoxy shell (Figure 8b). Finally, customized cylindrical lead rods were inserted into the central holes of the rubber structures, completing the Z-shaped topological waveguide (Figure 8c). This modular fabrication route is compatible with the three-component unit design and ensures precise alignment of the resonant cores within the periodic array.

6.2 Experimental setup

A center-frequency 500 kHz underwater acoustic testing platform was constructed, as shown in Figure 9. The transmitting unit consists of a DYW-500-01E ultrasonic transducer (Fuzhou Dayu Electronics Co., Ltd.), a custom DYSTM32F4 high-frequency ultrasonic development board that generates the excitation signal and drives the transducer, and a Suin SK3325 constant-voltage power supply providing DC power to the development board. The receiving unit employs a TDH-83 tubular hydrophone (500 kHz) to capture the underwater acoustic signal, which is acquired and analyzed by a Suin SA9232-TGP spectrum analyzer.

6.3 Results and discussion

The output end of the Z-shaped waveguide was scanned along the z-axis with the hydrophone (Figure 10a), and the received acoustic pressure was normalized against its maximum value. As shown in Figure 10b, the measured normalized acoustic pressure exhibits a pronounced peak at the position of the waveguide output port, indicating that the acoustic energy is efficiently guided along the Z-shaped path. The measured distribution is consistent with the simulated acoustic intensity field shown in Figure 7b, verifying the acoustic transmission characteristics of the Z-shaped topological waveguide and demonstrating the robustness of the fabricated sample against bending-induced backscattering. Given that the topological waveguide involves the most demanding fabrication and alignment requirements among the three demonstrated functionalities, its successful experimental operation further supports the viability of the unified three-component lattice platform.

7 Conclusion

This work presents a multifunctional acoustic modulation strategy based on locally resonant phononic crystals. Utilizing the dual-negative parameters and bandgap features of a three-component unit cell, a single unified lattice platform is demonstrated to support three distinct acoustic functions—negative-refraction multidirectional focusing, bandgap-guided directional transmission, and topologically protected transport—through modest tuning of the lattice dimensions, array arrangement, and operating frequency, effectively addressing the functional simplicity and poor adaptability of conventional acoustic metamaterials.

Owing to the resonance-induced negative refraction effect, triangular and polygonal metamaterial arrays achieve efficient multidirectional focusing of diffuse acoustic waves. Optimized enclosed layouts greatly reduce energy dissipation, yielding high-intensity focal signals and enabling high-efficiency directional acoustic convergence. Line-defect-engineered phononic crystal waveguides support stable broadband acoustic transmission along arbitrary straight and curved paths via bandgap confinement. By adjusting channel widths, the waveguide achieves switchable functions of path-selective transmission and acoustic beam splitting, demonstrating excellent multifunctional modulation capability. Furthermore, a symmetry-broken hexagonal topological lattice is designed to generate valley-protected edge states, which suppress acoustic backscattering. This design guarantees robust low-loss transmission along bent trajectories, significantly improving the anti-interference performance of directional acoustic channels. The transmission characteristics of the fabricated Z-shaped topological waveguide were further verified by 500 kHz underwater acoustic experiments.

Featuring broadband operation, structural flexibility and functional versatility, the proposed metamaterial system offers an effective solution for acoustic wave control along complex trajectories. It holds promising application potential for acoustic communication, signal detection and energy harvesting, and can be further extended to the design of various advanced multifunctional acoustic devices.

We note that the present experimental validation focuses on the Z-shaped topological waveguide, which involves the most demanding fabrication and alignment requirements among the three demonstrated functionalities; its successful operation indirectly supports the applicability of the same base lattice to negative-refraction focusing and bandgap waveguiding. Future work will extend the experimental characterization to the focusing and beam-splitting configurations, and will further investigate the influence of fabrication tolerances and the viscoelastic losses of the rubber components on the transmission efficiency.

Generative AI statement

The author(s) declared that generative AI was not used in the creation of this manuscript.

Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Footnotes

Edited by: Fengxian Xin, Xi’an Jiaotong University, China

Reviewed by: Chao Wang, Nanjing University of Science and Technology, China

Mohammed Sallah, Mansoura University, Egypt