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Remote Water-to-air Eavesdropping through Phase-Engineered Impedance Matching Metasurfaces

Efficiently receiving underwater sound remotely from air is a long-standing challenge in acoustics hindered by the large impedance mismatch at the water-air interface. Here we introduce and experimentally demonstrate a technique for remote and efficient water-to-air eavesdropping through phase-engineered impedance matching metasurfaces. By judiciously engineering an ultrathin mechanically-rigid boundary, we make the water-air interface acoustically transparent and at the same time we are able to pattern the transmitted wavefront, enabling efficient control over the effective spatial location of a distant airborne sensor such that it can measure underwater signals with large signal-to-noise ratio as if placed close to the physical underwater source. Such airborne eavesdropping of underwater sound is experimentally demonstrated with a measured sensitivity enhancement exceeding 38 dB at 8 kHz. We further demonstrate opportunities for orbital-angular-momentum-multiplexed communications and underwater acoustic communications. Our metasurface opens new avenues for communication and sensing, which may be translated to nano-optics and radio-frequencies.


INTRODUCTION
What happens under the water-air interface covering 70% of the earth cannot be directly detected through acoustic signals, a challenge that has long been hindering a plethora of applications, such as sonar communications and ocean explorations (1-6). Due to the large ratio in acoustic impedance between water and air (around 3600 times), only 0.1% of the acoustic energy can naturally be transmitted through such a nearly-perfect reflective boundary (namely, 30 dB loss), equivalent to the loss experienced in underwater acoustic propagation accumulated over 30 kilometers at 10 kHz (7).
In comparison to conventional approaches to impedance matching, which feature bulky and impractical devices (8)(9)(10), recently emerging acoustic metamaterials, such as membrane-type (11) and bubble-based (12)(13)(14)(15)(16) artificial materials, among others (17)(18)(19), may enable enhanced transmission between water and air in more efficient and compact platforms. However, their application in real-world systems, requiring mechanical stiffness, high endurance and large transmission efficiency, still remains poorly explored. In addition, beyond the transmission loss at the water-air interface, the signal-to-noise ratio (SNR) measured by a remote sensor in air is also substantially affected by diffraction and dissipation effects in the long-range propagation distance, which may be compensated by manipulating and steering appropriately the transmitted signal to enhance the intensity at the sensor location, and thereby achieve high sensitivity. An effective solution to this challenge is elusive at present, since existing metasurface approaches to steer and direct sound waves only work in homogeneous media (20)(21)(22)(23)(24)(25)(26) or media with weakly-mismatched impedance (27)(28)(29).
In this article, we propose a technique that can overcome both these fundamental limitations and present the experimental demonstration of remote water-to-air eavesdropping through nearly perfect impedance matching metasurfaces, which simultaneously provides wide-angle total transmission at the water-air interface and arbitrarily mold the spatial sound field with flexibility and efficiency. Our mechanism thereby allows an acoustic sensor in one medium to pick up the sound signal emitted from the other medium with large sensitivity, regardless of the sensor location or the monitoring distance. As a practical implementation, we demonstrate a compact mechanically-rigid structure comprising a resonance matching layer that compensates severely mismatched acoustic reactance induced by near fields to enable near-unity transmission, and a labyrinthine-shaped component 3 effectively controlling at the subwavelength scale the sound transmission path. The experimental realization for airborne eavesdropping of underwater low-frequency signals demonstrates energy redistribution near the sensor and a record-breaking enhanced sensitivity over 38 dB. We also demonstrate how this strategy enables novel applications for orbital-angular-momentum (OAM) multiplexing and underwater acoustics, with fundamental relevance for water-to-air remote communication engineering and underwater stealth. Figure 1A schematically shows the common scenario of airborne monitoring of underwater sound.

Operation of the impedance matching metasurface
For simplicity, and without losing generality, we assume that sound is emitted from a point source in water, undergoing nearly-total reflection at the bare water-air interface due to the large impedance contrast. This feature, in addition to unavoidable diffraction of propagating waves, leads to extremely low intensities of the measured signal once sensor and source are separated in the two media. An increase in emitted power or reduction in source-sensor distance, as viable solutions to improve the measured SNR, have negligible impact in improving the connection, due to the large inefficiencies.
Our proposed technique to enhance remote water-to-air eavesdropping through impedance matching metasurfaces can drastically enhance the sensitivity at the sensor location, independent of the distance between sensor and source or of the spatial location of the sensor. As illustrated in Fig. 1B, we judiciously decorate the water-air interface with a tailored artificial layer that supports wideangle total transmission at the otherwise reflective interface, while at the same time enabling arbitrary manipulation of the spatial distribution of the acoustic transmitted energy. This solution compensates for the reduction in signal intensity at the sensor location, and makes it equivalent to moving the sensor to a location very close to the source. By modulating the effective spatial location of the sensor, it is possible to eavesdrop the sound signals with large SNR while keeping a large monitoring distance.
Our proposed acoustic structure for implementing this phenomenon consists of a multi-layered configuration, with an individual unit cell schematically illustrated in Fig. 2A. The proposed unit cell has subwavelength dimensions and a rational design, built by grooving an acoustically-rigid cube 4 with a labyrinthine-like channel filled with air. Such an acoustic architecture overcomes the inherent limitations of existing anti-reflection designs [based for instance on a single layer of bubbles (12), hydrophobic materials (13) or membranes (11)] in terms of low transmission efficiency, short interaction distance and weak mechanical rigidity, as demonstrated in the following. For each unit cell proposed here, layers A and C are coupled to air and water respectively, and the effective acoustic impedance of each layer can be freely adjusted by tuning its air channel width (see Supplementary Materials for design details and geometrical parameters). Layers A and C serve as resonance matching layers that use their strong interaction with the incident wave to enable nearunity transmission. The labyrinthine-shaped layer B, with a length-varying air slit, slows down the sound speed by lengthening the propagation path and thereby introduces a controllable local phase delay to the transmitted wave, patterning at will the transmitted wavefront with subwavelength resolution. We first use numerical simulations to demonstrate the operation of our unit cell: the calculated transmission spectrum, as well as the sound transmission through two particular unit cell designs as shown in Fig. 2B, demonstrates a tunable and linearly continuous phase shift spanning a 2π range with near-unity transmission efficiency. This enables efficient impedance matching at the water-air interface, enhancing the transmission over 850 times compared to the bare interface, and simultaneously modulating the wavefront on the water-air interface within a subwavelength physical dimension, as required by our mechanism. Notice that the special structure design of layer C significantly increases the effective radiation area, and thereby compensates for the acoustic reactance introduced by the higher-order evanescent modes at the surface of the air-filled channel, which is too large to be simply eliminated by shortening the channel length as in conventional airborne metasurface design (see Supplementary Materials for more theoretical analysis and derivation). To verify this effect, we plot in Fig. 2C the enlarged view of the field distribution inside layer C (marked by the black dashed line in Fig. 2B), with the direction of energy flow at the structure-water interface, from which we can observe the typical intensity distribution of a resonant matching layer and significantly enhanced radiation than the one of a conventional air-filled channel.
We also investigate the wide-angle functionality of the device and plot in Fig. 2D the simulated transmission as function of incident angle and length of the labyrinthine path. The results show a high transmission efficiency for a wide range of incident angles, which may be further tuned for the 5 range of angles of interest by tailoring the structural parameters. The resulting artificial matching interface presents a large mechanical stiffness and associated robustness, which are highly desirable for underwater applications. As a feasible implementation, our design makes it possible to effectively and arbitrarily engineer sound waves in media with extremely-mismatched impedance.

Experimental realization of airborne eavesdropping for underwater sound
We will verify the effectiveness of our technique by experimentally demonstrating airborne eavesdropping for underwater sound signals. The working frequency is set to 8 kHz (corresponding to a wavelength λa of 4.3 cm in air and λw of 18.6 cm in water). In order to modulate the effective spatial location of the airborne sensor and significantly enhance its detection sensitivity, the transmitted spatial sound field needs to be transformed to be directively radiated towards the sensor.
In the considered scenario, this is equivalent to focus the otherwise blocked energy on the transmitted side towards the sensor position, which is realized by imposing the phase pattern sound-transparent and phase-engineered metasurface. Our mechanism demonstrates an effective relocation of the sensor in the adjacency of the physical source, thereby enabling eavesdropping with large sensitivity despite the long physical distance. We also explore remote monitoring performance in the far field via numerical simulations, due to the limited size of our experimental setup. The farfield sound pressure level (SPL) is calculated for the cases with and without metasurface in Fig. 3E, showing an average SPL enhancement over angular direction exceeding 25 dB. In addition to the significantly increased sensitivity, omnidirectional acoustic transparency can be observed in the farfield directivity curve, confirming that the impedance matching phenomenon is not limited to a narrow angular range, and paving the way towards various opportunities for acoustic applications.

Applications of water-to-air eavesdropping
We demonstrate the generality and applicability of our technique in more complicated eavesdropping scenarios and consider opportunities to shape the acoustic wave in more complicated scenarios. Recent efforts have shown that OAM beams offer a degree of freedom independent of time and frequency to enable significant boosting of channel capacity and transmission speed, in a convenient form of multiple-input-multiple-output communications. However, to date OAM-enabled high-speed acoustic communications has only been explored in homogeneous media (30)(31)(32). Our metasurface offers the opportunity of properly reshaping the phase profile at the water-air interface, enabling cross-media OAM multiplexing, as demonstrated in Fig. 4 (A and B), and establishing an "acoustic information bridge" linking water and air effectively. From our results, we observe highlyefficient and precise generation of multiplexed OAM beams of desired order, which can serve as independent communication channels through an acoustically impenetrable interface, as evident by the spiral pattern of propagation phase and donut-shaped intensity profile with enhanced amplitude of the transmitted beam. These phenomena overcome the fundamental limitation of existing spatial multiplexing mechanisms that transfer information with significantly-boosted rates but only through a homogeneous medium, offering the possibility for high-speed water-to-air communication and high-security encrypted eavesdropping (31,33,34).
Our technique can also be applied to eavesdropping underwater sound inside an underwater cavity filled with air. Based on this idea, another example of virtual acoustic window for underwater eavesdropping is explored in Fig. 4 (C and D). The results prove that our approach can convert the total reflection at the air cavity into total transmission, focusing the incident energy towards a predesigned spatial position inside the cavity, and resulting in an enhanced sensitivity of over 42 dB.
This effect allows the use of airborne detectors, such as capacitor-type microphones, for underwater high-SNR sound detection, which are generally about 3 orders of magnitude more sensitive than piezoelectric transducers (11). Such a "window" effect, along with the much higher absorption of low-frequency sound in air than in water, may open route to exciting opportunities for underwater detection and camouflage (see Supplementary Materials for details on these two applications).

DISCUSSION
To conclude, here we have proposed and experimentally demonstrated a technique for remote high-SNR water-to-air eavesdropping using impedance matching metasurfaces. As a practical implementation, a compact and mechanically-rigid artificial coupling unit was judiciously designed to make the water-air interface acoustically transparent over a broad range of incident angles and arbitrarily engineer the transmitted wave, which enables effectively steering the sound wave at  (14,35).Our technique can be also applied to monitor airborne sound signals in the underwater environment according to reciprocity. This suggests the potential of our approach in more complicated scenarios, such as active eavesdropping in which the sensor and source are both located in air to detect the underwater objects.
Our methodology provides a promising platform for general water-to-air eavesdropping and it can benefit various applications, such as cross-media communication engineering, remote sensing, underwater vehicle stealthy and beyond. Inset: two specific water-to-air pressure field distributions through designed unit cells (P1 and P2). intensity distributions for underwater eavesdropping inside a square air cavity with and without metasurface, respectively. The white arrows denote the incident waves in water.

SUPPLEMENTARY MATERIALS
Supplementary materials have been attached to this paper.