# A review of acoustic metamaterials for naval and underwater defense applications: from historical concepts to new trends

Charles Croënne, Jerome O. Vasseur, Laetitia Roux, Christian Audoly, Anne-Christine Hladky

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Charles Croënne, Jerome O. Vasseur, Laetitia Roux, Christian Audoly, Anne-Christine Hladky. A review of acoustic metamaterials for naval and underwater defense applications: from historical concepts to new trends. Acta Acustica, 2025, 9, pp.24. 10.1051/aacus/2024086. hal-05025394

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# A review of acoustic metamaterials for naval and underwater defense applications: from historical concepts to new trends

Charles Croënne<fnref n="1" />,*, Jérôme O. Vasseur<fnref n="1" />,*, Laetitia Roux<fnref n="2" />, Christian Audoly<fnref n="2" />, and Anne-Christine Hladky<fnref n="1" />

Received 19 January 2024, Accepted 21 November 2024

**Abstract** – Since World War II, there have been many efforts worldwide to design hull coatings for naval and underwater defense applications in order to reduce either noise radiated from the hull (discretion) or acoustic reflection from the hull (stealth). This paper presents a non-exhaustive review of concepts that have emerged since the iconic Alberich coating and highlights new trends and promising candidates, such as metamaterials, to improve the discretion and stealth performance of underwater defense systems. The need for acoustic materials for naval and underwater applications is first explained, along with some specific design requirements for acoustic coatings. Two coatings technologies, called micro-inclusion coatings and macro-inclusion coatings, are then successively reviewed. New trends in materials design for naval and underwater defense applications are also presented in the following section. This paper concludes by introducing the need for acoustic materials in the frame of new threats to the naval industries as well as other non-naval areas, opening new possibilities for their design.

**Keywords.** Underwater acoustics, Acoustic stealth, Acoustic discretion, Metamaterials

## 1 Introduction

Materials with an acoustic function play a key role in the field of underwater acoustics, for the reduction of near and/or far field radiation in water from vibrating hulls (masking function) and for the reduction of the reflection coefficient of acoustic waves incident on submerged hulls (anechoic function) [1]. The performance of these materials is crucial for the acoustic discretion or stealth of submerged or navigating structures and directly impacts the ability of SONARs to detect, locate and classify them either passively (masking function) or actively (anechoic function). Such materials are mostly used in the fields of acoustic coatings (surface vessels, submarines, drones, mines, oil & gas offshore structures or for renewable marine energies, etc.) and antenna environments (housings such as SONAR domes).

Compared to similar noise control devices for airborne acoustics, the characteristics of the marine environment (acoustic impedance, speed of sound, static pressure, chemical aggressiveness) lead, for the same frequency range, to specific technological solutions and therefore to dedicated materials for the field of underwater acoustics [2].

Most classical acoustic materials used today in underwater acoustics can be considered to be part of the category of metamaterials [3]. “Metamaterial” designates here a class of artificial materials presenting a structuration, with a scale smaller than the wavelength, that gives them the ability to present a behavior that is not found in a natural medium. In many cases, in some specific frequency ranges, they behave just as a homogeneous medium but with unconventional acoustical material parameters that depend on their artificial structuration. For instance, they can be made of constituent elements exhibiting resonances, or of small objects resonating at frequencies such as that the effective wavelength in the surrounding medium is large compared to the object size. These resonances, often quite narrow-band, can occur at very low frequencies and are relatively independent of the periodicity of the structure.

Underwater panels based on metamaterials are either of the micro-inclusion type (injection of compressible microballoons in a visco-elastic matrix with a resonance frequency of the microballoons much higher than the operating frequency, and a random distribution of inclusions), or of the macro-inclusion type (inclusion of resonant structures in the operating range in a viscoelastic matrix, “Alberich” type coating for example).

<footnote n="1">¹Univ. Lille, CNRS, Junia, Univ. Polytechnique Hauts-de-France, UMR 8520 – IEMN – Institut d'Électronique de Microélectronique et de Nanotechnologie, F-59000 Lille, France</footnote>

<footnote n="2">²Naval Group Research, 199 Avenue Pierre-Gilles de Gennes, 83190 Ollioules, France</footnote>

<footnote>*Corresponding author: charles.croenne@junia.com</footnote>
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Concepts of passive and active detection. To avoid detection by passive SONAR, a hull masking coating is employed to reduce the sound radiated by the hull. To avoid detection by active SONAR, an anechoic coating is used to reduce the back-scattered energy.</figcaption></figure>

The technological and scientific challenge for these materials is to achieve a significant improvement in performance with a reduced coating thickness (i.e. small compared to the wavelength). Therefore, work has to be carried out for exploring the potential of new types of resonant inclusions, optimizing the arrangement of layers, as well as seeking manufacturing methods adapted to new types of materials.

In this paper, the second section presents the use of acoustic metamaterials for underwater needs and threats (passive and active detection, masking and anechoic coefficients), as well as the constraints related to underwater environment, specifically for defense applications. The third section is a review of the micro-inclusions technology and the fourth section reports on panels with macro-inclusions, including compliant tube gratings and Alberich coatings with periodic or random distributions of inclusions. The fifth section presents new concepts for underwater panels. Finally, the perspectives address new human activities in the marine environment that require the use of efficient underwater panels, as well as new threats for the defense industry.

# 2 The need for acoustic metamaterials for underwater applications

## 2.1 The context of passive and active detection

For navies and naval industries, underwater sound has always been a crucial matter, since it is the main navigation and communication means for submerged vehicles. Acoustic waves are also used for mine warfare, sea floor characterization and ship or submarine detection

with the help of SONAR (SOund Navigaion and Ranging) systems. Such SONAR systems may be used for passive detection or active detection operations, both concepts being illustrated in Figure 1. In the following, the characteristics and definitions are related to defense applications.

Underwater passive detection consists in the analysis of ambient sound in order to recognize characteristic sounds from a submarine or marine vessel. Those sounds mainly originate from vibrations of items of machinery, engines and propellers, which overall result in radiated noise that can be detected by an adverse passive SONAR system. Against such a threat, the discretion of a submarine or underwater vehicle is crucial. A solution, amongst others, is to place hull masking coatings on the submarine, which significantly reduce noise radiated from the hull. Ideally, coatings should be designed in tandem with hulls, since hull properties can significantly influence their acoustic performance. However, since such a dual design would be highly impractical from an engineering point of view, figures of merit related to an idealized configuration are instead considered in order to select the most promising coating solutions. For passive detection, the intrinsic efficiency of the coating can be evaluated using the masking coefficient [4], also named decoupling coefficient, which is defined here as the ratio of the amplitude S of the pressure wave radiated by the coated vibrating surface to that of the uncoated one S₀ (here, vibrating surface refers to a surface submitted to a forced displacement field), expressed in decibels as:

$$C_M = 20 \cdot \log \frac{|S|}{|S_0|} \qquad (1)$$
Underwater active detection is the other main acoustic threat, consisting in an acoustic wave sent in the underwater environment and in the detection of the potential reflected waves from an obstacle, thus informing on its presence, location and dimensions. The vehicle stealth is thus also essential. Target strength, defined as the ratio between the back-scattered acoustic energy and the incident acoustic energy, can be reduced by adapting the external shape combined with the use of acoustic deflectors, or by applying anechoic coatings made of absorbing materials on the submarine outer hull in order to minimize back-scattered echoes. For stealth, the widely used quantity of interest to estimate the intrinsic efficiency of a coating is the anechoism coefficient [4] which is defined as the ratio of the amplitude A of the reflected wave to the incident wave $p_{inc}$ when the backside of the structure is supposed to be an infinite and perfectly rigid medium:

$$C_A = 20 \cdot \log \frac{|A|}{|p_{inc}|} \qquad (2)$$

Thanks to some assumptions and simplifications, it was shown that these two quantities, relevant to the case of a thick pressure-resistant hull, can be related to the transmission and reflection coefficients of the coating itself immersed in water, without hull backing [4, 5]. Generally speaking, coatings exhibiting very low transmission coefficients ($T$) are ideal for the passive detection (discretion) problem, and coatings with very low values of both reflection ($R$) and transmission are well-adapted to the active detection (stealth) problem. As a consequence, coatings with very high absorption can be interesting candidates for both functions, since they naturally exhibit both low $R$ and $T$. Note that in the case of acoustic deflectors for stealth issues, the reflection and transmission coefficients of the supporting structure (non pressure-resistant) equipped with the coating are also useful performance criteria.

Nevertheless, in actual submarines, the thickness of the hull is limited essentially for weight balance requirements, and in order to support hydrostatic pressure, the hull generally contains periodically spaced stiffeners. The hull can then be assimilated to a ribbed plate. The periodic stiffeners influence the vibratory response of the hull, and in turn induce Bragg diffraction and Bloch-Floquet waves in the back-scattered (for stealth) and radiated (for discretion) far-fields at specific angles and frequencies [6]. For the sake of simplicity, in this paper, the solutions that are proposed assume that the support of the panels is uniform (no ribbed plate) and only normal incidence is considered.

## 2.2 Design requirement of underwater acoustic coatings

The specifications for the underwater panels based on metamaterials concern physical constraints as well as acoustic performance. These two aspects have to

be considered simultaneously in the design of acoustic coatings.

On the one hand, the static compressibility and stability of acoustic performances as a function of immersion depth must be taken into account in the design process of a coating. This can be a critical issue for coatings that include a large volume ratio of air cavities, thus highly compressible. Broadly speaking, in relation to naval architecture constraints (such as the weight and thermal balance of a submarine), the main non-acoustic requirements for the design of coatings are:

- weight, total thickness and compressibility,

- cost, ease of fabrication and integration process, including fire resistance and hydrodynamic criteria (surface roughness, bonds between tiles),

- durability (resistance to sea water, UV, temperature changes, cyclic compressibility, fouling, etc.),

- thermal conductivity.

Note that the requirement for resistance and acoustic performance stability to static pressure may not apply in some cases, for example when the coating is fitted to the hull of a surface ship or for an industrial or marine energy facility operating in shallow waters.

On the other hand, for the design of acoustic coatings, the main requirement is of course the acoustic performance. As introduced previously, there are two main quantities of interest, namely the masking coefficient and the anechoism coefficient. It is also necessary to specify the frequency range of interest with respect to the application, in particular to define the expected coating thickness with respect to the wavelength. As an example, if $\lambda$ is the largest working wavelength in water and $h$ is the panel thickness, acoustic performance is looked for with $h = \lambda/30$ for the masking effect (discretion) and with $h = \lambda/10$ for the anechoism (stealth). Obtaining strong acoustic efficiency over a broadband low frequency range with a reasonably thin coating with respect to the wavelength (i.e. deeply sub-wavelength) remains challenging. Very low frequency performance is especially important for military applications, since active detection systems use lower and lower frequency signals for their long-range propagation properties in the sea. However, some other applications such as mine warfare and underwater communication induce less constraints.

In fact, the properties of the materials designed for masking and anechoic applications differ in terms of acoustic impedance: for a hull masking coating, a strong impedance mismatch is necessary between the material and water to reduce acoustic radiation towards the surrounding water, whereas, for an anechoic coating, impedance matching is required to limit reflection of the incident wave at the water/material interface. Therefore, these two functions (discretion and stealth) are not fulfilled by the same materials, which leads to additional complexity if both functions are required.
<figure><img src="image_3.png" /><figcaption>**Figure 2.** Left: section of unit cell of a compliant tube array. Center: photograph of a panel based on such an array. Right: transmission spectra obtained from numerical simulations (dashed line), measured with a large-area hydrophone (dotted line), and averaged over an array of 11 hydrophones (solid line). The horizontal axis is a normalized frequency, with *k* being the wavenumber in water and *a* the array period (adapted from [21]).</figcaption></figure>

## 3 Acoustic metamaterial panels with micro-inclusions

The first solution for an acoustic coating is a single layer of viscoelastic material without inclusion [7, 8], which is characterized by its thickness, its longitudinal and shear sound speeds, $c_L$ and $c_T$ respectively, that may take frequency-dependent complex values, and its mass density. If the longitudinal speed of sound $c_L$ and the mass density are close to those of water, then the modulus of its longitudinal acoustic impedance matches quite well with that of water and the viscoelastic layer is nearly acoustically transparent in water. Similar approach was considered but with a coating made of several layers [9–12]. Nevertheless, acoustic performances of such homogeneous viscoelastic panels remain relatively low.

A way to improve them is to insert micro-inclusions, such as micro-cavities or soft-wall micro-balloons. There is usually a few percent volume fraction of these micro-inclusions, sometimes among other heavy micro-inclusions, the latter for the adjustment of the overall density. By inserting a random distribution of inclusions in a viscoelastic matrix, and assuming that both the inclusion size and the average distance between adjacent inclusions are small with respect to the wavelength, the imaginary part of the equivalent frequency-dependent complex sound speeds may take larger values and depend on temperature [13]. The effective acoustic properties of such composite materials can be described by quasi-static approaches such as the Kuster–Toksöz model [14]. By an appropriate choice of the volume fraction of air micro-inclusions it is possible to adjust the effective speed of sound, and adding heavy mineral particles in the matrix allows to tune the effective density. In addition, with this technology the design of multilayered coatings is relatively simple and can help improving acoustic performance.

Nevertheless, the air cavities could be deformed under pressure, which could affect the performance of the coating [15–17]. Recent studies focus on the influence of the walls of the micro-inclusions, as micro-balloons embedded

in a polyurethane matrix are generally used for manufacturing reasons. It was shown the effect of these walls may be very significant, in particular at low static pressure [15].

Finally, for higher frequencies, micro-inclusion media can be seen as resonant metamaterials [18, 19] as local resonances may appear. The concept of resonant media is detailed in the next section.

## 4 Acoustic metamaterial panels with macro-inclusions

### 4.1 Compliant tube gratings

Compliant tube gratings were one of the first designs studied as a masking coating in the 1980s in the United States and the Soviet Union. They consist in a periodic distribution of empty tubes with a “flattened” circle cross section (see left panel of Fig. 2), where the tube wall is made of metal or of a resistant composite material. These tubes exhibit resonances at given frequencies and they are also designed to withstand hydrostatic pressure without significantly affecting acoustic performance, up to a given pressure.

This design has been studied and optimized using various theoretical models based on a semi-analytical approach: the partial domain method [20], the multiple-scattering theories [21] or numerical approaches based on the finite element method [22, 23].

Such a panel presents a low transmission or masking coefficient around resonant frequencies associated with the tubes’ cross-section (Fig. 2). Then, bandwidth associated with low transmission coefficient can be enlarged by using successive layers with different cross sections for the tubes [22, 24]. For integration purposes as well as to improve the insertion loss, tube gratings can be embedded in a viscoelastic matrix, leading to the panels described in the next section. It can be noted that, due to the resonances of the tube, this technology refers clearly to the
<figure><img src="image_4.png" /><figcaption>**Figure 3.** Left: sample picture of a typical design of an acoustic coating comprising soft rubber embedded with voided inclusions. Right: corresponding transmission coefficient (courtesy of the author, related to [23]).</figcaption></figure>

field of metamaterials but was initiated well before the terminology of metamaterials was introduced in the early 2000s.

## 4.2 Viscoelastic panels with periodic distributions of macro-inclusions

Anechoic and masking coatings have been first developed and used with the Alberich-type design. The name comes from the historical rubber coating put on German submarines during World War II [25]. It consists of lattices of resonant cavities in an elastomer or rubber matrix, as represented in the left panel of Figure 3.

The Alberich coating is a good candidate for underwater panels. Classically, the panel is made of a periodic grating of air inclusions, for which the cavities' diameters are tuned to maximize absorption at several specific frequencies, which in turn can lead to significant absorbing or masking properties. Specific methods have been applied to model these panels, in particular based on the finite element method [14]. Analytical [26–28] and semi-analytical [29, 30] models have also been developed to examine the acoustic performance of such periodically voided soft elastic media. By adjusting the wave velocities and mass density in the viscoelastic matrix, it is possible to tune the frequency ranges in which the panel shows good acoustic performance. Nevertheless, the main issue of the classical Alberich panel is that the air cavities are deformed under pressure, affecting the coating performance. To enlarge the frequency range of interest and improve resistance to hydrostatic pressure, it is possible to vary the size of the inclusions as well as their shape: cylinders, spheres, ellipsoids, gradual prisms, pyramids or disks, as well as their distribution [31–40]. The frequency resonance of each inclusion depends on its geometry and on its constituent material. Then combining different kind of inclusions may lead to different resonance frequencies. By carefully bringing these frequencies in the same range, one may enlarge the frequency band where the acoustic transmission is decreased and also reduce the level of transmission. For instance, it has been shown numerically that ellipsoidal inclusions of various sizes may improve the anechoic performance of the panel in comparison with a

panel where all the inclusions would be spherical with the same radius [32].

The steel backing corresponding to the hull of the submarine also affects the performance of the coating as constructive interference between scattered waves from the inclusions and reflected waves from the steel backing may occur [30, 41]. In addition, the mass of the steel support influences the low frequency absorption. An increase in the mass can decrease the frequency of the absorption peak [42].

A metamaterial comprising hard inclusions embedded in a viscoelastic matrix can also be a good candidate as an anechoic coating on the hull of an underwater vehicle, due to impedance matching of the viscoelastic medium with water and robustness of the hard scatterers under hydrostatic pressure [43–47]. Moreover, parametric studies have been performed on panels with rigid inclusions that present a low transmission coefficient in a wide frequency range, thanks to the arrangement of inclusions and interface effects [46]. In this later paper, a combination of different periodic arrays of inclusions induces resonances at distinct frequencies which allow the frequency range where panel transmission remains low to be widened.

## 4.3 Viscoelastic panels with random distribution of macro-inclusions

As mentioned above, metamaterials acoustic properties depend on the resonance frequency of the scatterers and not primarily on the periodicity of their distribution. Then strong acoustic attenuation was also achieved for random distributions of soft or hard inclusions embedded in a viscoelastic matrix. In the case of soft inclusions, the acoustic behavior of the effective material is driven by a cavity resonance, as shown by some early analytical models [48]. For frequencies close to this resonance, the effective speed of sound becomes very small and/or with a high imaginary part. Consequently, there is a very low transmission or masking coefficient. In the case of hard inclusions, the resonance is of dipole type [49]. For the same concentration of inclusions, the acoustical effect is smaller for the soft inclusions.

In both cases, the effective acoustic properties (dynamic density, wavenumber or sound speed) depend on the characteristics of the matrix, on the diameter or size of the inclusions and their concentration in the matrix, and on frequency [50].

Regarding numerical prediction, contrary to the case of periodic arrangements, finite element techniques are not suitable and semi-analytical techniques based on multiple scattering theory [51] have been developed by different authors. Recently, Leroy et al. developed a predictive analytical model for a periodic arrangement of spherical voids in a matrix that was shown to work also in the case of random configurations [26, 52]. The model is a simple predictive model that can be used for an arrangement of several different layers.
## 4.4 Other designs based on metamaterials

For more design versatility, other types of inclusions may be considered. Examples are very soft porous materials based on a silicon matrix [19] and core-shell inclusions (i.e. inclusions formed with a rigid kernel surrounded by a soft polymer layer) [53]. Initially developed for airborne applications, the concept of core-shell inclusions has been adapted to underwater applications and has been shown to improve the acoustic performance of an underwater anechoic coating [54–56].

Multiple layers of scatterers with different resonant frequencies can also lead to broadband performance [57–59], which can also be achieved by the simultaneous use of voided and hard inclusions [60, 61]. In particular, in the latter paper, it has been numerically shown that sound absorption in the low frequency band can be enhanced by a proper distribution of absorption layers and sound insulation layers on both sides of a steel plate.

A panel relying upon a tungsten-polyurethane composite has been recently proposed, with an impedance matched to water exhibiting high absorption in the [4–20] kHz frequency range. The panel is constituted of slender solid rods of finite lengths made of tungsten-polyurethane backed by a hard reflecting boundary. These rods behave as resonators whose length matches with one-quarter of the relevant wavelength. The broadband functionality is achieved by optimally engineering the distribution of the resonances of the rods, i.e. by optimizing the lengths of the rods [62].

The requirement of resistance to high hydrostatic pressure has led to the exploration of new configurations. In fact, rubber and polyurethane are the most commonly used base materials for underwater applications due to their versatility, with the complex dynamic moduli of the matrix being adjusted through chemical formulation, while being consistent with resistance to seawater environment. However the elastic moduli of such materials increase with pressure. Dealing with this constraint, Jiang and Wang [63] created the “phononic glass” for underwater applications. It can be seen as a “reversed core-shell” structure, composed of a metal skeleton and polyurethane infillings with an interpenetrating network structure. The physical connection among locally resonant structure units is helpful to excite more acoustic absorbing modes. In addition, the metal skeleton filled with polyurethane provides high mechanical strength and hence a good resistance to hydrostatic pressure. However, with a metal skeleton, the total weight might be a limitation of the phononic glass design for coating applications.

Finally, if several designs are proposed in the latter papers for underwater applications, only few of them present experimental results allowing for a definitive validation. Table 1 presents the characteristics of the devices described above, when experiments have been presented in the paper. They are sorted as a function of the *kh* product, where *k* is the wavenumber in water and *h* is the thickness of the panel. The *kh* product can be easily related to the fraction of wavelength, as a link with the expected acoustic performances (Sect. 2.2, i.e. $h = \lambda/10$

corresponds to $kh = 0.62$). The search has been mainly carried out on devices that are designed to perform at low $kh$ values.

In addition to the *kh* factors, Table 1 gives the advantages and the limitations of each device. Today, due to specific requirements for underwater acoustics (low frequency, large frequency range, small thickness, deep immersion, etc.), no device satisfies with all these criteria. Nevertheless macro-inclusions provide for a better efficiency.

# 5 Metamaterials approach: new trends

In this section, new trends for improved acoustic performance are presented based on new concepts, or on new available tools, either for the modeling or the manufacturing of panels. Moreover, based on analogies with electromagnetic stealth concepts, new design approaches are emerging: acoustic invisibility cloaks, phononic networks, tunable materials, etc. They gave very promising preliminary theoretical results, and studies are under progress for their technological feasibility and applicability to the underwater environment. Nevertheless, these new designs, based on a redirection of the incident energy, are often narrow band or use active materials, and are beyond the scope of this paper.

## 5.1 Jamming effect

If classically stealth or discretion are performed using a panel that dissipates the energy, Yu et al. [64] consider a structure made of a steel metasurface with various holes, in order to create destructive interferences between waves diffracted by the holes. The concept has been used with success in the [14–40] kHz frequency range, with a 38 mm-thick metasurface (see Tab. 1).

## 5.2 Hierarchical and bio-inspired designs

If periodic or random structures are commonly used for the design of acoustic panels, other types of arrangements are today under study, such as semi-chaotic distribution [65] and hierarchical and non-hierarchical structures [66] with advanced properties coming from the architecture. Moreover, new studies based on bioinspired metamaterials are today arising. For instance, Ref. [67] presents nacre-inspired mechanical metamaterials for elastic wave attenuation. All these structures can now be manufactured, thanks to the availability of new 3D printing facilities.

## 5.3 Advanced design methods

Recently, optimization tools have been used for the design of metamaterial coatings in order to get low-frequency underwater sound absorption with several
<table><caption>**Table 1.** Characteristics and performance of the devices investigated in literature when experiments have been presented in the paper. The devices are sorted as a function of the *kh* product, and the *λ/h* and natural frequencies are added for reference.</caption><thead><tr><th>Ref.</th><th>kh</th><th>λ/h</th><th>Target freq. or freq. range</th><th>Description</th><th>Performance</th><th>Exp. values (when available)</th></tr></thead><tbody><tr><td>[58]</td><td>0.15</td><td>43</td><td>700 Hz</td><td>Local resonance slab with steel plate backing.</td><td>Absorption coefficients (α) of the sample with the steel plate of different thickness.</td><td>α ≈ 0.98 at 700 Hz.</td></tr><tr><td>[36]</td><td>0.17</td><td>37.5</td><td>1 kHz</td><td>Viscoelastic rubber matrix, conical cavity, cylindrical oscillator and steel backing.</td><td>Acoustic absorption.</td><td>α ≈ 0.67 around 800 Hz.</td></tr><tr><td>[45]</td><td>0.2</td><td>31</td><td>800 Hz</td><td>Array of multi-resonant steel scatterers in a silicone rubber cylinder, inside a viscoelastic polymer matrix with steel backing.</td><td>Significant acoustic absorption on a large bandwidth (300–2000 Hz).</td><td>α ≈ 0.9 under low hydrostatic pressure.</td></tr><tr><td>[13]</td><td>0.21</td><td>30</td><td>5 kHz</td><td>Viscoelastic materials with micro-spheres (fluid-filled or elastic cavities).</td><td>Transmission loss (TL) increases with frequency in a wide band (up to 100 kHz).</td><td>TL around 3 and 13 dB at 5 and 100 kHz, respectively.</td></tr><tr><td>[59]</td><td>0.23</td><td>27.3</td><td>1 kHz</td><td>Two types of local resonance units in the metamaterial slab. Steel spheres embedded in a viscoelastic polymer matrix.</td><td>Design deduced from optimization. Acoustic absorption.</td><td>α ≈ 1 at 1 kHz.</td></tr><tr><td>[23]</td><td>0.29</td><td>21.4</td><td>1.75 kHz</td><td>Periodic array of air cylindrical cavities in silicone.</td><td>Transmission (T) measurement.</td><td>T ≈ −31 dB at 2 kHz.</td></tr><tr><td>[62]</td><td>0.32–1.58</td><td>20–4</td><td>4–20 kHz</td><td>Composite rods placed on a stepped stainless-steel base.</td><td>Measured transmittance, reflectance and absorption. Broad band performance.</td><td>α around 0.9 in the band.</td></tr><tr><td>[37]</td><td>0.6–2.51</td><td>10.4–2.5</td><td>2.4–10 kHz</td><td>Gradient cavity shaped polyurethane composite array supported by carbon fiber honeycomb with steel backing.</td><td>Acoustic absorption on a large bandwidth under hydrostatic pressure (3 MPa).</td><td>α > 0.9 in the band.</td></tr><tr><td>[19]</td><td>0.71</td><td>8.8</td><td>170 kHz</td><td>Macro-porous silicone rubber microbeads embedded in a water-based gel matrix.</td><td>Layer with negative index (n).</td><td>n ≈ −0.8.</td></tr><tr><td>[63]</td><td>1–2.51</td><td>6.2–2.5</td><td>12–30 kHz</td><td>Phononic glass: interpenetrating network structure is introduced into a locally resonant phononic crystal.</td><td>Impedance matching with water. Acoustic absorption.</td><td>α > 0.9 in the band.</td></tr><tr><td>[26]</td><td>1.35–2.79</td><td>4.7–2.2</td><td>1.4–2.9 MHz</td><td>Air inclusions in PDMS. Several layers.</td><td>Acoustic absorption.</td><td>α > 0.95 in the band.</td></tr><tr><td>[64]</td><td>2.28–6.45</td><td>2.8–1</td><td>14.3–40.5 kHz</td><td>Square holes drilled into a steel plate.</td><td>Scattering cross section reduction.</td><td>Below −10 dB in the band.</td></tr></tbody></table>

layers of acoustic metamaterial slabs [57] or to get a low anechoism coefficient over a broadband frequency range [68]. In the latter case, the genetic algorithm gives solutions with greatly improved broadband acoustic performance. Moreover, this type of optimization process could also be performed either for the choice of the materials or for the structuration of the panel, or for other objective functions (anechoic coefficient, masking coefficient, etc.), as well as for oblique incidence cases. For a reasonable calculation time of the optimization tools, it is necessary to use homogenized properties for the unit cell or for each layer through the use of dedicated homogenized models that can describe properly the structure (fluid model [69] versus elastic model) and take into account oblique incidence [70].

Moreover, in order to find the optimal distribution of layers or cavities or resonators, inverse design method based on geometrical optimization could be used [71] in relation to new hybrid cavities or resonators structuration.

Nevertheless, if complex and improved numerical methods can give interesting and new designs, common sense, based on simple models, actual observations and pragmatic experiences must remain tools used for first design approaches or further verifications of the obtained results. As an example, an optimization tool has been used for the design of such metamaterial coatings, in order to get a low anechoism coefficient over a broad frequency range. The optimized panel presents a specific arrangement of homogeneous layers with a gradual variation of the layer thickness. However, this result could probably be found without resorting to a metaheuristic approach [68].

## 6 Perspectives: to other domains and new challenges

If the panels presented in the previous sections have to comply with constraints related to underwater vehicles
(see Sect. 2), some designs could be transposed to other applications in sea water. In particular, human activities in the marine environment, such as the installation of offshore wind turbines, gas compressor stations at great depth, etc. emit very high noise levels into the environment at low or even very low frequencies (from 50 Hz to 1 kHz), which are highly harmful to marine ecosystems: see for example the European project AQUO [72] followed by PIAQUO (http://lifepiaquo-urn.eu/). Moreover, these waves propagate over very long distances and can also disturb wildlife since many animal species use sound waves to locate themselves, feed, communicate, reproduce, and so on.

Today, if several solutions exist to reduce these noises at relatively low depth (elastomer type with air micro-inclusions or air macro-inclusions), their performance can be significantly deteriorated under the effect of high hydrostatic pressure when immersed in deep sea (typically 1000 m and further) or when immersed during a very long time (degradation of the materials of the panels due to the marine environment, biofouling, etc.).

Moreover, complementary to defense applications, solutions are expected for industrial facilities that are static. For example, for offshore wind turbines, solutions can be a bubble screen in order to reduce the noise level during pile driving. It consists of injecting compressed air into the water through a ring of perforated pipes surrounding the pile to release air bubbles [73, 74]. Another solution consists in a net equipped with balloons filled with air ("Hydro sound damper" [75]) in order to reduce continuous noise and impulsive noise. Work is under progress to make these solutions more mature and independent of weather conditions, tide and water current.

Taking into account these scales in depth and time, breakthrough solutions have to be found based on acoustic metamaterials, following the new trends presented in this paper.

New challenges in the field of defense are also emerging with the multiplication of actors underwater, above water and in airspace, and their ability to communicate with each other, enabling collaborative combat. In practice the sonar emitter and receiver are no longer co-localized, as shown on Figure 4. This means hull coatings must ensure acoustic performance for all incident and scattered angles (bi-static configuration). As such, acoustic coatings are to be studied and developed by considering different angles of incidence. It could also be interesting to study new types of coatings aimed at redirecting acoustic energy towards given directions where no threat is apparent.

Underwater drones (UUVs) will also become a major part of these new actors in collaborative combat. As such, they must also be stealthy and discreet. As with submarines, these acoustic performances can be improved by the use of anechoic and hull decoupling coatings. Furthermore, requirements specific to UVVs may also appear. For example, a coating for a drone may require different technology than that used on submarines, in order to keep the latter secret in case an UUV is lost. Stealth and discretion

<figure><img src="image_5.png" /><figcaption>**Figure 4.** Illustration of a submarine under a cooperative bi-static threat, where one surface ship emits and another surface ship receives a bi-static echo, both surface ships being able to communicate with each other.</figcaption></figure>

are also important for docking stations, where UVVs are required to recharge and/or exchange information.

New concepts are still emerging, closely related to the development of metamaterials, as well as the evolution of marine warfare. As pointed out before, many concepts can be translated to civil applications related to the limitation of anthropogenic noise at sea.

**Conflicts of interest**

The authors declare no conflict of interest.

**Data availability statement**

No new data were created or analysed in this study.

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Cite this article as: Croënne C. Vasseur J.O. Roux L. Audoly C. & Hladky A.-C. 2025. A review of acoustic metamaterials for naval and underwater defense applications: from historical concepts to new trends. Acta Acustica, **9**, 24. https://doi.org/10.1051/aacus/2024086.