Hybrid Metasurfaces for Perfect Transmission and Customized Manipulation of Sound Across Water–Air Interface

Abstract Extreme impedance mismatch causes sound insulation at water–air interfaces, limiting numerous cross‐media applications such as ocean‐air wireless acoustic communication. Although quarter‐wave impedance transformers can improve transmission, they are not readily available for acoustics and are restricted by the fixed phase shift at full transmission. Here, this limitation is broken through impedance‐matched hybrid metasurfaces assisted by topology optimization. Sound transmission enhancement and phase modulation across the water–air interface are achieved independently. Compared to the bare water–air interface, it is experimentally observed that the average transmitted amplitude through an impedance‐matched metasurface at the peak frequency is enhanced by ≈25.9 dB, close to the limit of the perfect transmission 30 dB. And nearly 42 dB amplitude enhancement is measured by the hybrid metasurfaces with axial focusing function. Various customized vortex beams are experimentally realized to promote applications in ocean‐air communication. The physical mechanisms of sound transmission enhancement for broadband and wide‐angle incidences are revealed. The proposed concept has potential applications in efficient transmission and free communication across dissimilar media.


DOI: 10.1002/advs.202207181
many engineering fields such as wireless communication, [7,8] energy transfer, [9] detection, [10,11] and imaging. [12,13] Full manipulation of the wave across dissimilar media means that both the amplitude and phase of transmitted waves are controllable. [14,15] However, the extremely low transmission across the interface due to impedance mismatch between dissimilar media first poses a huge challenge on the modulation of amplitude. One of the most common examples is sound transmission through the water-air interface. [16] Due to the sharp contrast in acoustic impedance (≈3600 times), only 0.1% of the acoustic energy can be naturally transmitted between water and air. [17] Whereas, sound waves are by far the only practical means of underwater wireless communication because of their low attenuation compared to electromagnetic waves. [18][19][20] If an efficient water-to-air sound transmission is realized, the ocean covering 70% of Earth's surface and atmosphere will be effectively connected by sound waves. [21] Light-weight aerial loudspeakers can be immersed underwater to efficiently emit sound waves, and high-sensitivity microphones can also be exploited to achieve high signal-to-noise ratio detection. [22] The realization of cross-media extreme transmission and manipulation will significantly improve the performance of underwater acoustic devices and facilitate wireless underwater to air communications. [21,22] To enhance sound transmission through the water-air interface, several efforts have been made during the past few years. Rigorous theoretical derivations suggest that acoustic energy carried by spatially decaying waves, such as inhomogeneous or evanescent plane waves, can be effectively transmitted across the interface. [23,24] This is mainly attributed to that the decaying component introduced to the incident wave results in a nonzero propagating wave component in the transmitted fields. [23,24] In addition, it is theoretically and numerically demonstrated that tunable sound transmission at an impedance-mismatched fluidic interface can be achieved by dynamically adjusting the impedance characteristics of a composite waveguide. [25] Metasurfaces, [26][27][28][29][30] which have been used to achieve high-efficiency reflection, [31,32] transmission, [33][34][35][36] absorption, [37,38] and isolation [39,40] in the homogeneous background medium, were also applied to solve the www.advancedsciencenews.com www.advancedscience.com extreme mismatch at the water-air interface. [21,22,41,42] By employing a loaded membrane-type metasurface, it is experimentally observed that nearly 30% of incident acoustic power at around 700˜Hz was transferred from water to air in a tube. [22] Based on a mechanically-rigid metasurface composed of resonancematching and labyrinthine-shaped components, sound intensity enhancement exceeding 38 dB is experimentally measured at 8 kHz by combining a focusing phase distribution, realizing the remote water-to-air eavesdropping with a large signal-to-noise ratio. [41] Besides, metasurfaces made of coupled resonant bubbles immersed underwater are proven to be another effective way to improve the sound transmission at the interface. [21,[42][43][44][45] The underlying mechanisms of high-efficiency transmissions are described by the mass-spring resonance models. [21,44] However, due to the strict dependence of resonant frequency on the bubble size and immersion depth, the operating frequency of bubble-type metasurfaces is generally restricted below 4 kHz in the existing experiments. [21] For the enhanced transmission at intermediate frequencies around 10 kHz, an artificial lotus metasurface composed of a superhydrophobic aluminum plate is proposed based on a similar principle. [42] The immersing part of the superhydrophobic aluminum plate in water can form μm-scale air layers to make up the mass-spring resonance system. [42] But the necessary hydrophobic treatment on metal materials inevitably brings some tedious operations to large-scale fabrication and preparation of samples. [42] In general, alternative simple and practical approaches with the aid of new physical mechanisms remain to be explored.
Actually, the classical quarter-wavelength theorem [46,47] indicates that perfect energy transmission across dissimilar media can be realized when the matched layer has a particular acoustic impedance of √ Z 1 Z 2 and a certain thickness d = d /4, where Z 1 , Z 2 , and d are the characteristic acoustic impedances of the two different media and the wavelength in the matched layer, respectively. Hence, it is possible to provide a general solution to solve ultra-low transmission at the interface. [3,48] However, for the water-to-air case, such a matched layer with acoustic impedance about 60 times to that for air is hardly available in nature. [22] How to explore a viable way to construct the matched layer with extreme material properties is of great significance. Apart from this, previous studies have mainly focused on improving sound transmission between water and air. [21,[42][43][44][45] Wavefront manipulation of transmitted sound waves across the water-air interface has always been an overlooked but essential issue, which can bring a broad range of remarkable functionalities. [41,49] In addition, based on the effective medium approximation, the transmission phase will be locked to ± /2 for full transmission, disabling the wavefront phase control ability. Therefore, how to achieve phase manipulation of a wave under full transmission is still a rather challenging task.
In this work, we theoretically propose a universal approach to address the challenges of transmission enhancement and phase modulation on sound propagation across the water-air interface. These two functions are well integrated by exploiting hybrid metasurfaces (labeled as MS 1 and MS 2 ) on the decoupled control of transmitted amplitude and phase across the water-air interface. The topology optimization is applied to systematically develop an inverse design method to separately design the hybrid metasurfaces with unitary transmission (MS 1 ) and desired phase shifts (MS 2 ). The proposed MS 1 consists only of a singlephase solid material. The inversely designed MS 2 is encoded and then assembled by discrete unit cells with unitary transmission and four desired phase shifts according to the customized phase distribution. Multiple acoustic functions involving axial focusing and vortex beams carrying various orbital angular momentums are implemented to demonstrate the ability of wavefront manipulation under enhanced transmission. Water-to-air acoustic experiments are further conducted to validate the performance of hybrid metasurfaces. The underlying physical mechanism of MS 1 for enhancing water-to-air sound transmission is also revealed. The presented coalescence of high-efficiency transmission and customized wavefront manipulation greatly demonstrates the full-wave tailoring capabilities of metasurfaces, and paves the way for applications of advanced transmedia devices in wireless communications, medical monitoring, smart sensors, and so on. Figure 1A illustrates the schematic diagram for achieving perfect transmission and customized manipulation by hybrid metasurfaces. MS 1 floating on the water acts as an impedance-matched layer between water and air to enhance sound transmission. A digital coding metasurface (MS 2 ), placed on top of MS 1 , has customized phase distribution to arbitrarily tailor wavefronts without transmission attenuation. In this case, the detector in the air can easily collect sound signals sent by underwater unmanned vehicles (UUV), and bulky underwater acoustic systems can also be avoided in communication between UUVs by exploiting efficient air-water-air sound propagation. To demonstrate the practicability of the proposed concept, a multi-layer sound transmission model is established based on the effective medium theory. [46] Both metasurfaces are approximately regarded as a layer of homogeneous medium with thickness d, effective wavenumber k, and characteristic acoustic impedance Z. Based on the transfer matrix method, the transmission relationships through the hybrid metasurfaces can be derived as

Theory of Achieving Perfect Transmission and Phase Shifting
where p i and p r are the complex amplitudes of the incident and reflected sound waves in the water; p t is the complex amplitude of sound wave transmitted to the air. The transfer matrices T and represent the enhanced transmission by MS 1 and the phase modulation by MS 2 with a unitary transmission, respectively, and where the subscripts w and a indicate the media of water and air, respectively; the subscripts m 1 and m 2 represent MS 1 and MS 2 , respectively; d m 1 and d m 2 are the thickness of MS 1 and MS 2 , respectively; d m 12 depicts the distance between MS 1 and MS 2 ; and Z m 2 = Z a is assumed for simplicity. The detailed derivations of T and can be seen in Note S1, Supporting Information. Then the reflection and transmission coefficients (R and T) of the hybrid metasurfaces can be easily derived as The reflection and transmission sound intensity coefficients (I R and I T ) can be further calculated by To achieve the full transmission, the reflected sound intensity of the hybrid metasurfaces in the lossless case should be zero (I R = 0), that is, Since Z w ≠ Z a , cos 2 (k m 1 d m 1 ) and (Z w Z a − Z 2 m 1 ) 2 should be zero. Therefore, the full-transmission conditions for the hybrid metasurfaces can be described as In this case, the transmission coefficient T can be simplified as Equation (7) indicates T is no longer purely imaginary. The transmitted phase shift under the full transmission can be flexibly adjusted by changing the propagation wavenumber k m 2 of MS 2 , thus eliminating the limitation of locked phase shift. It should be noted that other solutions can also be found when the constraint of Z m 2 = Z a is not satisfied, but the strong coupling between MS 1 and MS 2 should be considered. [3] However, for the case described by Equation (6), MS 1 and MS 2 are independent of each other since both can achieve full transmission between different media (water/air and air/air, respectively). This means that the full transmission across dissimilar media can be achieved just by MS 1 , and arbitrary phase manipulation under the full transmission can be further achieved by cascading MS 2 . In this way, the transmission enhancement and phase modulation are decoupled with each other, making it more convenient for the inverse design of hybrid metasurfaces. This also implies that the proposed concept of hybrid metasurfaces for manipulating sound across the water-air interface is feasible in principle.

Decoupled Inverse Design of Hybrid Metasurfaces
To break the confinement of perfect transmission and phase shift, it is only necessary to separately design MS 1 and MS 2 based on the above theoretical analysis. Here, we propose a singlephase solid unit cell to construct MS 1 . The required acoustic impedance is expected to be dynamically satisfied by fully taking advantage of the fluid-solid interactions. Different from previous works, [21,22,42] we can avoid strong resonances of tiny air bubbles or narrow air cavities, which may introduce thermoviscous losses to seriously weaken the transmitted sound intensity. [21,22] Topology optimization method based on the genetic algorithm [50,51] is adopted to find appropriate topological configurations for MS 1 .
The optimization problem for the inverse design of MS 1 can be described as where  denotes the fitness of objective function for the topological distribution Ω D ; I R (Ω D ) is the reflection sound intensity coefficient without viscosity losses; I ′ T (Ω D ) is transmitted sound intensity coefficient with viscosity losses; S R = 200 and S T = 100 represent the weight coefficients of I R (Ω D ) and I ′ T (Ω D ), respectively; Ω D (n y , n z ) = 1 or 0 indicates the solid (1) or air (0), respectively; and N y = 24 and N z = 12 are the numbers of discrete pixels in the width and thickness directions, respectively. It is noted that I R (Ω D ) and I ′ T (Ω D ) instead of Z m 1 and k m 1 is involved in the optimization just for convenience. The retrieving method for I R (Ω D ) and I ′ T (Ω D ) is presented in Note S2, Supporting Information. Meanwhile, the smoothing process by chamfering is employed inside MS 1 unit cells to improve the convergence of finite element calculation. The target frequency is selected as 10 kHz, and the width and thickness of MS 1 unit are a = 2/3 a and d m 1 = a ∕3 , respectively, with a being the wavelength in air. It is noted that it is very difficult to achieve full transmission via MS 1 with loss. By finding the optimal solution to Equation (8), the optimized MS 1 with or without loss promises the highest possible sound transmission at the water-air interface. This will facilitate proof of principle and experimental observations.
Regarding the inverse design of MS 2 , two-bit coding unit cells with unitary transmission are expected. 3/10 , 8/10 , 13/10 , and 18/10 phase shifts (a phase interval of /2, encoded as 00, 01, 10, and 11) are chosen for ease of optimization. The optimization problem for MS 2 can be described as where ϕ and t are the phase and transmission of unit cell, respectively; ϕ c is the target phase shift of each coding unit cell; S ϕ = 4000 and S t = 10 represent the weight coefficients of phase and transmission, respectively; and S p (t) = 500 is a penalty term imposed on the transmission when |t| < 0.5 to facilitate simultaneous optimization of ϕ and t. The detailed calculation and optimized process for MS 1 and MS 2 are illustrated in Note S3, Supporting Information. Figure 2 gives the optimized geometrical configurations for the MS 1 and MS 2 unit cells and the corresponding water-to-air sound transmission. The normalized sound pressure field shown in Figure 2A suggests that perfect sound transmission between water and air is achieved by the optimized MS 1 unit cell. In addition, we further calculate the effective acoustic impedance and wavenumber of MS 1 unit cell. The strict impedance-matching conditions given by Equation (6) for MS 1 can be well satisfied (see Note S4, Supporting Information). It indicates that the quarterwave impedance transformer between water and air is successfully designed by the proposed optimization strategy. Figure 2B shows the water-to-air sound transmission when the four optimized unit cells of MS 2 are hybridized with MS 1 unit cell, respectively, where the distance d m 12 between them is only a /100. As expected, the hybrid MS 1 and MS 2 exhibit nearly full sound transmission from water to air and provide the expected phase shifts at the same time. The perfect transmission with phase shift is mainly attributed to the weak coupling between MS 1 and MS 2 unit cells resulting from the air gap (see Note S5, Supporting Information). This guarantees the feasibility of individual design for MS 2 units and may allow MS 2 to achieve the nonlocal design with perfect transmission based on the lattice diffraction theory. [33,52]

Experimental Verification
Due to the decoupled modulation of sound for MS 1 and MS 2 , the enhanced transmission performance of MS 1 will be checked independently. The mechanism of enhancing water-air acoustic transmission will be revealed through vibration tests. Wavefront manipulation under enhanced transmission through hybrid metasurfaces will then be demonstrated. Figure 1B shows the photography of the experimental setup for water-to-air acoustic experiments. The photograph of the fabricated MS 1 sample with a partially enlarged view of the crosssection is shown in Figure 1C. Note that MS 2 (with axial focusing function as an example) shown in Figure 1D is not involved in the enhanced water-to-air sound transmission experiment. A broadband pulse with bandwidth from 8 to 16 kHz is emitted by the underwater transducer. The transmission amplitude enhancement (ET) by MS 1 with respect to the bare water-air interface is calculated by ET = 20 log 10

Enhanced Water-to-Air Sound Transmission
where |p | are the measured sound pressure amplitudes at each sampling point through MS 1 and the waterair interface, respectively; and I = J = 21 represents the numbers of sampling points along the x and y-axes in a 20 cm × 20 cm area (xy-plane) above the center of MS 1 . Figure 3A plots the variation of ET as a function of frequency. The measured transmission amplitudes through the MS 1 and bare water-air interface are presented in Note S6, Supporting Information. It can be observed that MS 1 exhibits above 20 dB (ten times) amplitude enhancement from 9.84 to 11.53 kHz. The measured peak frequency is found to be around f e peak = 10.45 kHz with ≈25.9 dB (nearly 20 times) transmission enhancement, close to the perfect transmission of 30 dB. The time-domain sound signals received at a test point, as shown in Figure 3B, further exhibit the sharp contrast between sound pressure amplitudes transmitted by MS 1 and the bare water-air interface. A more intuitive presentation is also provided in Movies S1 and S2, Supporting Information. They dynamically demonstrate the enhancement (reduction) of the sound pressure when MS 1 is placed on (removed from) the water surface under broadband pulse or peak frequency incidence.
Furthermore, we measure the sound pressure fields transmitted through MS 1 and bare water-air interface at the peak frequency f e peak = 10.45 kHz, as shown in Figure 3C,D, respectively. It can be clearly observed that the sound waves emitted from underwater transducer are converted into uniform plane waves after passing through MS 1 , and the transmission amplitudes through MS 1 over the entire measurement area are greatly improved compared to the bare water-air interface. This mainly benefits from the transmission enhancement of MS 1 under wide-angle incidence. According to Snell's law (k w sin w = k a sin a with w and a being incident angle in water and refracted angle in air, respectively), the transmitted angles in air are less than 13.2°w ithin ±90°oblique incidences from water. Quantitative analysis for transmission enhancement of MS 1 under oblique incidences is presented in Note S7, Supporting Information. It suggests that MS 1 can maintain over 98.05% sound transmission within ±60°oblique incidence. These enhanced plane waves in air are very helpful for the subsequent phase manipulation by the hybrid MS 2 . In addition, we also measure the sound fields near the peak frequency (11 kHz). Similar enhanced performance is also clearly observed, see Note S8, Supporting Information. The measured peak frequency slightly deviates from the simulated one f s peak = 10 kHz. This may originate from deviations in material parameters. As we have checked, the peak frequency will shift upward as Young's modulus of MS 1 increases, see Note S9, Supporting Information. Overall, the experimental results effectively validate the excellent performance of MS 1 for enhanced sound transmission across the water-air interface. Figure 4A shows the photograph of the experimental setup for the vibration test of MS 1 . Four different positions (labeled as positions 1, 2, 3, and 4, respectively) on one unit cell are chosen as the test points, as shown in Figure 4B. Figure 4C presents the measured vibrations of MS 1 at different frequencies f, and the corresponding simulated results of a single unit cell are given on the right for comparison. A complete animation is provided in Movie S4, Supporting Information. Good agreement is observed between the measured and simulated results. Vibrations at the notch (positions 3 and 4) are more pronounced and significantly stronger than on both sides (positions 1 and 2) when f = f e peak (or f s peak ). At the same time, an anti-phase vibration mode can be clearly observed at the masses (position 3) and the thin wall (position 4), which will induce a resonance state of compression and expansion in the inner air cavity. In this case, the collaborative resonance of the masses and thin wall at positions 3 and 4 seems to act as an energy converter, absorbing the underwater acoustic energy and then radiating it into the air. However, when the incident frequency is away from the peak one, such as 8.6 and 14.3 kHz, the collaborative vibration at the notch becomes unapparent. So, the enhanced water-to-air sound transmission by MS 1 may be attributed to the unique flexural vibrations of the solid unit cell, which gives rise to the required sound impedance by inducing compression and expansion of the inner air cavity.

Mechanism Demonstration of Enhanced Sound Transmission
Quantitative analysis is further made by comparing the outward mechanical energy flux generated by the solid vibration at the notch and the total outward sound energy flux on the unit cell surface. The boundaries (Γ s and Γ a ) for calculating the energy flux and the corresponding unit normal vectors are marked in Figure 4D. The outward energy flux E s induced by the flexural vibration and water-to-air sound energy flux E a are calculated by where S m = 1 2 Re(− mn u * t n ) and I m = 1 2 Re(p m v * m ) with m = n = x, y representing the components of mechanical energy flux and sound intensity along x or y axis, respectively; and u t are the stress tensor and velocity field of the solid domain, respectively; p and v are the sound pressure and velocity of air domain, respectively; and Re and * represent the real part and conjugate operations, respectively. Figure 4E plots the water-to-air transmission T s = √ E s ∕E 0 and T a = √ E a ∕E 0 at the boundaries Γ s and Γ a , where E 0 = a|p i | 2 ∕(2Z w ) = 7.62 × 10 −9 W m −1 (|p i | = 1 Pa) represents the incident energy. It can be seen that the maximal outward mechanical energy flux from solid vibrations is also concentrated near the peak frequency, showing a good consistency with the sound energy flux curve. This suggests that almost all acoustic energy transmission from water to air is contributed by the solid vibrations at the notch. It is noted that there is a small amplitude deviation between the both because the solid vibrations far from the notch are not taken into account.

Enhanced Water-Air Sound Wavefront Manipulation
We start with the experimental demonstration of enhanced 3D axial sound focusing by hybrid metasurfaces. For convenience, the operating frequency of hybrid metasurfaces is chosen at f m = 11 kHz near the peak frequency. The ideal phase distribution Ψ F on the exit surface of MS 2 can be expressed as [53,54] where (x 0 , y 0 ) = (0, 0) is the center of MS 2 ; and the focal length F 0 is chosen as 3 a ≈ 93.5 mm with a being the wavelength in air. Following the principle of proximity, the ideal phase distribution Ψ F is approximated by the two-bit coding unit cells with unitary transmission and phase shifts of 3 /10, 8 /10, 13 /10, and 18 /10, respectively. Figure 5A depicts the photograph of fabricated sample MS a 2 for axial focusing with the corresponding coding phase sequence. It can be seen that the encoded phase sequence is centrosymmetric and has a parabolic gradient distribution along the radial direction, which can ensure that the transmitted sound waves are concentrated in the axial direction of MS 2 .
To better demonstrate the focusing characteristics, we perform numerical simulations on the air-to-air transmitted sound field through MS a 2 . The background field with uniform plane wavefronts is used as the incidence. Figure 5B presents the simulated normalized sound intensity distributions on the xz-and yzplanes. Excellent focusing performance is exhibited in the prescribed focal point, showing the good ability of MS a 2 on phase modulation. The measured normalized intensity fields and the corresponding simulated results (obtained from Figure 5B) on the three orthogonal planes are illustrated in Figure 5C, and the measured real parts are presented in Note S10, Supporting Information. As expected, the sound waves emitted from underwater transducer are well gathered around the prescribed focus after transmission enhancement and phase manipulation of the hybrid MS 1 and MS a 2 . The measured sound amplitude at the preset spot (z = 3 a ) is enhanced by nearly 42 dB (about 125 times) compared with the bare water-air interface, showing the distinguished focusing features (see Movie S3, Supporting Information). To further quantitatively characterize the focusing performance, we measure the pressure intensity distributions along x-and y-axis directions through the prescribed focal spot, and plot the normalized results in Figure 5D. It can be seen as a 2 from air to air for sound axial focusing and vortex beam self-focusing, respectively, where the normalized pressure |p 0 | is chosen as 11|p i | and 6.2|p i | in panels (B) and (F) for simulation, respectively. Panels (C) and (G) present the measured sound fields from water to air in different planes through hybrid MS 1 and MS 2 at 11 kHz for axial focusing and vortex beams focusing, respectively. The corresponding simulated results obtained from panels (B) and (F) are also given for comparison. The normalized pressure |p 0 | is chosen as 4.1 and 2.5 Pa in panels (C) and (G) for experiments, respectively. z 0 = 3 a = 93.5 mm, x 0 = y 0 = 0 mm, z ± = z 0 ± 60 mm, x ± = x 0 ± 60 mm, and y ± = y 0 ± 60 mm. Panels (D) and (H) plot the measured and simulated intensity distributions on two transverse lines along x-axis and y-axis in xy-plane through the point (0, 0, 3 a ) for axial focusing and vortex beams focusing, respectively. good agreement with the simulated one. The full width at halfmaximum (FWHM) in the x-and y-axis directions are about 0.56 a and 0.54 a , respectively, close to the diffraction limit of 0.5 a . In addition, we also measure the pressure intensity distribution on the central axis along z-axis. It is found that the actual focal length is slightly larger than the preset one. This may be due to the fact that unavoidable boundary reflections inside water tank result in inhomogeneous amplitudes of transmitted sound field from water to air. Overall, the experimental and simulated results verify the enhanced axial focusing performance of hybrid metasurfaces across the water-air interface.
It is emphasized that the principle of phase modulation under enhanced transmission is general and applicable to other complex wavefront manipulation across the water-air interface, such as vortex fields with orbital angular momentum (OAM). OAM is regarded as an additional spatial degree of freedom to promote the channel capacity of acoustic communication owing to the perfect orthogonality between different topological charges. [55] Benefiting from the decoupled modulation by hybrid metasurfaces, the realization of desired sound fields with the enhanced trans-mission is just required to replace the phase-encoded sequence of MS 2 rather than redesign new unit cells. To generate the vortex beams with spiral wavefronts, the required phase distribution Ψ V on MS 2 can be expressed as [56] Ψ V (x, y) = L V ⋅ arctan(y∕x) (13) where L V represents the expected topological charge of OAM. However, the vortex beams propagating in free space are inherently divergent. To extend the sound energy to the desired location, we consider the generation of self-focusing vortex beams. The total phase distribution Ψ VF can be obtained by superposing a parabolic phase profile along the radial direction according to the digital convolution theorem, [56,57] namely Here, OAM with L V = 1 and focus length F 0 = 3 a are chosen for demonstration.
www.advancedsciencenews.com www.advancedscience.com Figure 5E shows the fabricated sample of MS b 2 for vortex beam self-focusing with the corresponding encoding-phase sequence. It can be observed that the spiral phase variation around the center superposes a non-uniform gradient distribution along the radial direction to effectively gather the generated sound vortex beam. The simulated intensity fields on xz-and yz-planes from air to air by MS b 2 are depicted in Figure 5F. Different from one main lobe of the axial focusing shown in Figure 5B, the sound energy of the self-focusing vortex is split into two lobes at each cross-section. This is mainly because of the singularity of the helical phase at the center, which results in a null sound intensity at the center axis. Figure 5G shows the measured and simulated intensity fields on yz-and xy-planes and phase distribution on xy-plane. The measured real parts of transmitted sound fields are presented in Note S10, Supporting Information. Two high-intensity beams can be clearly observed apart from the central axis on xy-plane. Meanwhile, the intrinsic features of vortex beams, such as ring-shaped intensity field and spiral phase distribution, are also clearly observed from the measured and simulated results on xy-plane (z = 3 a ). Furthermore, we also measure the sound intensity distributions along x-and y-axis directions at z = 3 a and plot the results in Figure 5H. Different from axial focusing, the amplitude valleys are located at the center and the sound intensity is concentrated on the two peaks. This shows good consistency with the simulated results. In addition, slight deviations between measured and simulated phase distributions in Figure 5G can be also noticed, possibly due to the differences in incident waves.
Furthermore, we consider the generation of OAM with anisometric radius and higher topological charge from water to air, which is beneficial to acoustic communication with high channel capacity. In this case, we take advantage of the energy concentration of the non-diffraction Bessel beam to reduce the diffusion of the vortex beam in free space. By superposing a uniform gradient phase Ψ B for generating Bessel beam, the final phase distribution Ψ VB implemented on MS 2 can be expressed as [56] Ψ VB (x, y) = Ψ V (x, y) + Ψ B (x, y) (15) where Ψ B (x, y) = k a √ (x − x 0 ) 2 + (y − y 0 ) 2 sin B with B being the cone angle of Bessel beam. In addition, for the generation of a vortex beam with anisometric OAM, the phase profile Ψ V can be extended as where represents the anisometric factor of OAM. By setting other than one, the spiral phase distribution of vortex beam at the center can be switched from a circle to an ellipse, which may bring a new degree of freedom to manipulate the vortex beams. For demonstration, we construct MS d 2 to generate a nondiffraction vortex beam carrying the first-order anisometric OAM. Meanwhile, MS c 2 used to generate the standard first-order OAM is also constructed for comparison. The anisometric factor and the cone angle of the Bessel beam are chosen as = 3 and sin B = 2∕ √ 13. The fabricated samples of MS c 2 and MS d 2 with the corresponding encoded phase sequences for the standard and anisometric are shown in Figure 6A,D, respectively. Compared with the standard spiral phase in Figure 6A, the spiral phase dis-tribution in Figure 6D is apparently stretched to an elliptic shape to carry non-standard OAM. Besides, both phase distributions contain a uniform gradient variation along a radial direction to generate the non-diffraction beam. Figure 6B,E presents the simulated sound intensity fields from air to air of MS c 2 and MS d 2 , respectively. It can be clearly observed from Figure 6B that a hollow beam with less divergent propagation is formed around 4 a . The sound energy is gathered along the central axis and almost evenly distributed on xz-and yz-planes. In contrast, the energy for the anisometric OAM in Figure 6E is only concentrated on the yzplane due to > 1. The measured and simulated sound intensity and phase distributions for the two cases on xy-plane at z = 4 a are shown in Figure 6C,F, respectively, and the corresponding real parts of sound fields are presented in Note S10, Supporting Information. As expected, we can clearly observe that the sound energy for the standard OAM is concentrated on a ring, while the anisometric OAM is concentrated in one direction along the x-axis. The vortex phase in Figure 6F also exhibits an elliptic pattern different from the circular one shown in Figure 6C. The intriguing features are mainly owing to the introduction of an anisometric factor, which changes the sweeping velocity of the phase along the circumferential direction.
Next, we design hybrid metasurfaces to generate a standard fourth-order OAM ( = 1 and sin B = 2∕ √ 13) across the waterair interface. Figure 6G presents the fabricated sample of MS e 2 with the corresponding encoded phase sequence. The simulated intensity field from air to air is presented in Figure 6H, exhibiting the hollow beam with non-diffractive propagation. Then the measured and simulated intensity and phase fields on xy-plane at z = 4 a are shown in Figure 6I. Four spiral phase patterns and the ring-shaped energy distribution are also clearly observed, thus validating the proposed concept for cross-media transmission manipulation.

Conclusions
In this work, we theoretically propose and experimentally validate the concept of hybrid metasurfaces for the transmission enhancement and phase manipulation of sound across the waterair interface. An inverse-design strategy based on the topology optimization is systematically developed to separately design the hybrid metasurfaces. To achieve perfect transmission between water and air, MS 1 is successfully optimized to have an effective acoustic impedance of about 60 times that of air. Experimental results suggest that ≈25.9 dB (nearly 20 times) transmission enhancement across the water-air interface is obtained by MS 1 at the peak frequency. The physical mechanism of enhanced transmission is that the fluid-solid interactions induce the specific vibration modes of MS 1 to dynamically satisfy the required impedance-matching condition. The optimized MS 1 also exhibits good performance of broadband and wide-angle transmission enhancement. In addition, the water-to-air perfect transmission is further achieved by a thinner MS 1 (whose thickness is 1/10 of the wavelength in the air). When the losses are considered, more than 50% energy transmission can also be obtained (see Note S11, Supporting Information).
Furthermore, four discrete unit cells with unitary transmission and /2 phase shift interval are inversely optimized to construct  Figure S14, Supporting Information. Panels (B), (E), and (H) show the corresponding 3D full-wave simulated intensity fields from air to air of MS c 2 , MS d 2 , and MS e 2 for generating the three types of non-diffracting sound vortex beams, respectively, where the normalized pressure |p 0 | is chosen as 4.5|p i |, 5.6|p i |, and 2.8|p i | in panels (B), (E), and (H) for simulation, respectively. Panels (C), (F), and (I) present the measured sound intensity and phase fields from water to air in xy-plane (z = 4 a ) through hybrid MS 1 and MS 2 at 11 kHz for the three types of vortex beams, respectively. The normalized pressure |p 0 | is chosen as 1.8, 2.2, and 1.08 Pa in panels (C), (F), and (I) for experiments, respectively. z 0 = 4 a = 124.7 mm, x 0 = y 0 = 0 mm, z ± = z 0 ± 60 mm, x ± = x 0 ± 60 mm, and y ± = y 0 ± 60 mm.
the coding MS 2 with wavefront manipulation ability. Based on the digital convolution theorem, various customized sound fields are well realized by modifying the encoded phase sequences on MS 2 . Cross-media (water-to-air) experiments also fully demonstrate that the sound waves in the water are effectively transmitted to the air and reshaped as the desired distributions through the hybrid metasurfaces. Nearly 42 dB (about 125 times) amplitude enhancement is experimentally observed at the preset focus through the hybrid metasurfaces with axial focusing function. Meanwhile, the ability to generate arbitrary sound vortex beams from water to air is also explored. Good agreements between the experimental and simulated results effectively validate the flexibility and universality of hybrid modulations.
Generally, the presented inverse-design strategy allows us to customize the structure design on demand, such as different operating frequencies, thinner thickness, etc. Meanwhile, the separate implementation of hybrid metasurfaces will also bring more flexibility and expansibility. Controllable digital-coding metasurfaces [57,58] can be allowed to be integrated with the MS 1 . This will play a significant role in some potential and promising engineering applications such as high-speed ocean-air wireless communications, etc. In addition, the proposed strategy and model for cross-media wave manipulation can also be applied to other dissimilar media, such as air/solid, water/solid, or different solids, thus beneficial to the design of novel trans-media wave devices.

Experimental Section
Numerical Simulations: The numerical simulations were performed with the commercial finite element software, COMSOL Multiphysics. For the water-to-air sound transmission calculation in Figure 2, pressure acoustics and solid mechanics modules were applied to solve the sound pressure and displacement fields, respectively. The interfaces between water/air and solid were imposed on acoustic-structure boundary conditions, that is, the continuity of the normal acceleration and traction with the vanishing of tangential traction at the interfaces. Floquet periodic boundary conditions were applied to the lateral boundaries of the calculation domains. Perfectly matched layers were employed to the top and bottom to eliminate boundary reflections. A uniform plane wave background field was used as the incident wave and applied to the water domain at the bottom of MS 1 . 3D quadratic Lagrange (serendipity) elements for acoustics (solids) were built by sweeping the free triangular meshes on the cross section. The maximum element sizes of the MS 1 and MS 2 unit cells, air, and water domains were taken as a /144 (≈1/4 the height of the pixel grid), a /10, and w /40, respectively, to ensure the accuracy of the numerical calculations. For the simulated vibration modes shown in Figure 4C, the results were obtained by extracting the displacement fields in the calculation of the sound intensity coefficient for MS 1 at different frequencies (see Note S2, Supporting Information). For the full-wave simulations on MS 2 in Figures 5 and 6, the solid components of MS 2 were considered to be rigid due to the huge impedance contrast between air and solid. Only the pressure acoustics module was used to perform the calculation. The solid boundaries of MS 2 unit cells were set as the sound hard boundary to reduce the computational cost. The sound velocity and density were set as c w = 1500 m s −1 and w = 1000 kg m −3 for water and c a = 343 m s −1 and a = 1.21 kg m −3 for air, respectively. The material of solid metasurface was epoxy resin with density m = 1140 kg m −3 , Young's modulus E m = 3 GPa, and Poisson's ratio μ m = 0.41. When viscosity is considered, Young's modulus of solid material was set as E ′ m = (1 + 0.05i)E m . Experimental Apparatus: The samples of hybrid metasurfaces were fabricated by 3D printing technology. MS 1 included 24 identical unit cells along the y-axis and was stretched by 520 mm along the x-axis. MS 2 was made of 24 × 24 unit cells. The water-to-air acoustic experimental setup is shown in Figure 1B. An underwater transducer with 10 cm in diameter (Model T313, Neptune Sonar Limited) to emit sound waves was placed on the bottom of the water tank (dimensions 1600 mm × 1500 mm × 800 mm) equipped with sponge and rubber wedges. MS 1 was assembled in a metal framework and floating at the water-air interface. MS 2 was placed on top of MS 1 with about 4.2 mm air gap. A 1/4 inch microphone (Type 4939, Brüel & Kjaer) was fixed on the scanning platform to measure the sound fields in the air. The experimental setup of the vibration test for MS 1 is shown in Figure 4A. A flat mirror was fixed on the platform to adjust the path of the laser beam emitted by the laser head. The displacement component u z was measured by using the PSV scanning vibrometer. The scan area was located in the center of MS 1 , which covered four unit cells along the y-axis and was around 20 cm along the x-axis. For the scanned sound fields in Figures 3D,E, 5C,G, and 6C,F,I, the transmitted amplitudes and phases of 961 scanned points (31 × 31 array) on each plane were collected by the microphone in the air.
Statistical Analysis: All statistical analyses were performed with MAT-LAB software. Details of normalization for the collecting data were separately provided in each figure caption. For quantitative analysis of the performance for MS 1 , 21 × 21 sampling points were selected on the xy-plane. The quadratic mean ratio of measured results with and without MS 1 was calculated by Equation (10) and presented in Figure 3A. The maximum, minimum as well as data at each sampling point are provided in Note S6, Supporting Information.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.