Electromagnetic Inspired Acoustic Metamaterials

Acoustic metamaterials and metasurfaces have been explored in the past few years to realize a wide range of extreme responses for sound waves. As one remarkable phenomenon, extreme anisotropy and hyperbolic sound propagation are particularly challenging to realize compared to electromagnetic waves because of the scalar nature of airborne acoustics. In parallel, moiré superlattices and the rapidly expanding domain of twistronics have shown that large anisotropy combined with tailored geometrical rotations can enable tantalizing emerging phenomena, such as tailored phase transitions in metamaterials. Connecting these areas of research, here, we explore the realization of acoustic hyperbolic metasurfaces and their combination to drive topological phase transitions from hyperbolic to elliptic sound propagation. The transition point occurring at a specific rotation angle between two acoustic metasurfaces supports highly directional canalization of sound, opening exciting opportunities for twisted acoustics metasurfaces for robust surface wave guiding and steering.

Recently, a significant attention has been directed toward so called ‘acoustic metamaterials’ which have large similarity with already-known ‘electromagnetic metamaterials’ which are applied for elimination of the electromagnetic waves. The stop of electromagnetic waves is realized with the negative refractive index, negative permittivity and negative permeability. Motivated by the mathematical analogy between acoustic and electromagnetic waves, the acoustic metamaterials are introduced. It was asked the material to have negative effective mass. To obtain the negative effective mass, the artificial material, usually composite, has to be designed. The basic unit is a vibration absorber which consists of a lumped mass attached with a spring to the basic mechanical system. The purpose of the unit is to give a band gap where some frequencies of acoustic wave are stopped. We investigated the nonlinear mass-in-mass unit excited with any periodic force. Mathematical model of the motion is a system of two coupled strongly nonlinear and nonhomogeneous second-order differential equations. The solution of equations is assumed in the form of the Ateb (inverse beta) periodic function. The frequency of vibration is obtained as the function of the parameters of the excitation force. The effective mass of the system is also determined. Regions of negative effective mass are calculated. For these values the motion of the forced mass stops. It is concluded that the stop frequency gaps are much wider for the nonlinear than for the linear system. Based on the obtained parameter values, the acoustic metamaterial could be designed.

This comprehensive review explores the design and applications of machine learning (ML) techniques to acoustic metamaterials (AMs) and phononic crystals (PnCs), with a particular focus on deep learning (DL). AMs and PnCs, characterized by artificially designed microstructures and geometries, offer unique acoustic properties for precise control and manipulation of sound waves. ML, including DL, in combination with traditional artificial design have promoted the design process, enabling data-driven approaches for feature identification, design optimization, and intelligent parameter search. ML algorithms process extensive AM data to discover novel structures and properties, enhancing overall acoustic performance. This review presents an in-depth exploration of applications associated with ML techniques in AMs and PnCs, highlighting specific advantages, challenges and potential solutions of applying of using ML algorithms associated with ML techniques. By bridging acoustic engineering and ML, this review paves the way for future breakthroughs in acoustic research and engineering.

Acoustic metamaterials (AMs) have attracted a substantial amount of attention in recent decades where the parameter design plays an important role. However, conventional design methods generally rely on analytical physical models and require a very large number of evaluations of acoustic performance. Here, we propose and experimentally demonstrate an inverse-design method for AMs based on machine learning using a Gauss–Bayesian model. As a result of the cycle of training and prediction and the use of adaptive acquisition functions, this method allows the parameters of AMs to be efficiently designed for specific functionalities without the need for physical models. Considering the significance of low-frequency ventilated sound absorption, we present a design for a typical acoustic metamaterial absorber with multiple structural parameters that facilitate high sound absorption at low frequencies. In the design process, the parameters were adaptively adjusted to improve the sound absorption performance at low frequencies using only 37 evaluations, and this high absorption performance was verified by the agreement of numerical and experimental results. Because of its low cost, high flexibility, and independence from physical models, this method paves the way for tremendous opportunities in the design of various AMs for particular desired functionalities.

A multiple scattering formulation of two-dimensional (2D) acoustic metamaterials is presented. This approach is comprehensive and can lead to frequency-dependent effective parameters (scalar bulk modulus and tensorial mass density), as it is possible to have not only positive or negative ellipsoidal refractive index, but also positive or negative hyperbolic refractive index. The correction due to multiple scattering interactions is included in the theory and it is demonstrated that its contribution is important only for lattices with high filling fractions. Since the surface fields on the scatterers are mainly responsible for the anomalous behavior of the resulting effective medium, complex scatterers can be used to engineer the frequency response. Anisotropic effects are also discussed within this formulation and some numerical examples are reported. A homogenization theory is also extended to electromagnetic wave propagation in 2D lattices of dielectric structures, where Mie resonances are found to be responsible for the metamaterial behavior.

The word “meta”, in Greek language, means beyond. It implies that the electromagnetic response of metamaterials (MTMs) is unachievable or unavailable in conventional materials. Many efforts have been done to search for an adequate definition for MTMs. In 2002, J.B. Pendry wrote in a conference paper: “meta-materials, materials whose permeability and permittivity derive from their structure”. Later, in 2006, C. Caloz and T. Itoh wrote: “Electromagnetic metamaterials are broadly defined as artificial effectively homogeneous electromagnetic structures with unusual properties not readily available in nature” [1]. Perhaps, a serious obstacle on the road to a universal definition for the term MTMs is the fact that researchers working with these objects do not commonly agree on their most essential characteristics. In [2] and [3], some of the problematic aspects of the non-naturality definition were raised, like the difficulty in separating classical composites from the new class of metamaterials. Another argument against the “not found in nature” property is that it unnecessary excludes impressive examples of natural media that could be called metamaterials par excellence, such as structural colors [4].

Stealth and Radar Absorbing materials play important role in several applications including Defense. Such applications require a certain type of coating or paint or film to absorb the incoming electromagnetic (EM) radiation. To achieve stealth at certain band of frequencies, reflection coefficient has to be minimized which essentially means there has to be perfect impedance matching between the incoming wave and material used. Therefore, both complex permittivity $(\epsilon_{r}) (\epsilon_{r}= \epsilon^{\prime} + \mathrm{i}\epsilon$”) and complex permeability $(\mu_{r}\,= \mu^{\prime} + \quad i \mu$”) of the material plays important role in stealth applications. Electromagnetic Metamaterials (MMs) are artificial materials which are, effectively homogeneous, periodic structures with unusual electromagnetic and material properties not readily available in nature. The constitutive electromagnetic parameters (electric permittivity $\varepsilon$ and magnetic permeability $\mu$) of such materials depend on the nature of the unit cell and are essentially uniform along the direction of propagation [1]. Recently, Metamaterial Absorbers (MMAs) have attracted wide interest among researchers due to their exotic properties and possibilities. Since the first prefect MMA was proposed in 2008, many researchers have proposed different topologies and methodologies to produce high absorption of electromagnetic energy. This has been possible by eliminating the reflection and transmission of electromagnetic radiation and by realizing the absorption due to the electrical and magnetic resonances engineered to coincide at the same frequency and the absorption in the intervening dielectric substrate [2]. These MMAs have been engineered to operate at specific frequency spectrum ranging from microwave to ultraviolet. They can be single band, multiband, broadband, polarization insensitive and wide angle [3].

The review focuses on architected acoustic metamaterials to manipulate airborne sound waves, with only limited discussions on elastic metamaterials related to solid media. We review the design of acoustic metamaterials and the physical mechanisms underpinning their performance and related manufacturing methodologies, while also examining potential issues and challenges affecting the use of metamaterials in acoustics. The complexities of several metamaterial architectures are discussed. A new classification system is proposed to distinguish metamaterial configurations based on the typology of the channels inside the acoustic meta-atom. Several types of acoustic metamaterials architectures, such as perforated and micro-perforated panels, acoustic foams, resonators, various geometrical paths, and piezoelectric patches, are also discussed. The fundamental acoustic mechanisms of these classes of metamaterials are identified and commented on. The paper also describes the main measurement techniques used for acoustic metamaterials and the physical quantities evaluated, providing a guide to characterize and assess their performance. The fundamental challenges of the current metamaterials designs are discussed, with a focus on the complex synergy between architectural patterns of acoustic metamaterials and their thickness. We clarify the distinction between acoustic and elastic metamaterials, emphasizing the design and applications of materials that manipulate sound waves in fluid media. The paper also offers further comments about the need for practical design tools to allow the use of acoustic metamaterials in real-world applications.

Method of measuring the amounts of electromagnetic radiation absorbed and controlled by metamaterials in anechoic chamber

An acoustic metamaterial consisting of a homogeneous damped plate with parallel attached resonators is presented. Theoretical analysis shows that the metamaterial plate can generate multiple resonant-type band gaps and the lower-bound frequency of each band gap coincides with the resonance frequencies of the resonators. The parallel arrangement of resonators, compared with the metamaterial plate with resonators attached in series reported by Peng et al. (2015), results in a wider second band gap with a lower edge, while the first band gap is almost the same, creating therefore an easier combination of the multiple band gaps into a wider one. It is noted that damping has a significant influence on the band gaps and the effective mass density (especially for the damping of resonators). Specifically, it can be concluded that damping cannot be neglected in practical engineering applications, damping in the material of the host plate can smooth and lower the responses in the whole frequency range, especially in the higher frequency range, and a high level of damping of resonators deactivates the effect of band gaps. Such weak/damped resonators actualise the metamaterial damping poorly, and rather tend only to contribute to the overall damping such as the damping of the host plate.

Acoustic metasurfaces are ultrathin (subwavelength thickness) structures that can demonstrate extreme acoustic properties, such as negative or near-zero values, similar to those seen in acoustic metamaterials. The negligibly small thickness of acoustic metasurfaces make them a more practical alternative to metamaterials for certain applications. In this work, we experimentally demonstrate an aqueous acoustic metamaterial that employs subwavelength, flexural elements that acoustically act in parallel to achieve enhanced acoustic transmission and broadband negative effective density. The metasurface was constructed from a brass plate, which was machined to have a parallel arrangement of circular, flexural elements on the surface, and experimentally tested in water over the nominal range of 50–100 kHz. The reflected and transmitted acoustic data were compared between a brass plate with and without the circular flexural elements. It was observed that the aqueous acoustic metasurface made from a brass plate with circular flexural elements showed improved broadband transmission. A detailed description of the experimental testing and analysis will be discussed. [Work supported by the Office of Naval Research]

Acoustic metamaterial consisting of an array Helmholtz resonators has been revealed to have the band gap phenomenon which implies a great potential for noise reduction. However, the application of the conventional acoustic metamaterial is often limited by the narrow band gap. In this paper, an acoustic metamaterial containing a series of membrane-coupled Helmholtz resonators is proposed to produce mult iple band gaps in the low-frequency regime for achieving broadband noise reduction. First, a theoretical model is developed to describe the dynamic of the membrane-coupled Helmholtz resonator system. The membrane is assumed to be loaded with a small mass at the centre for tuning its natural frequencies, thus the resonances of the coupled system and the band gaps of the proposed acoustic metamaterial. Subsequently, based on the theory of acoustic wave propagation together with the derived theoretical model for the membrane-coupled Helmholtz resonator system, a theoretical analysis of the proposed acoustic metamaterial is performed. Using the Bloch’s theorem, the dispersion relation of the proposed acoustic metamaterial is derived. Multiple band gaps are observed in the band structure. A corresponding finite element model of the proposed metamaterial is built to confirm the predictions from the theoretical analysis.

Design of low-frequency and broadband acoustic metamaterials with I-shaped antichiral units

Acoustic metamaterials are structures with exotic acoustic properties, with promising applications in acoustic beam steering, focusing, impedance matching, absorption and isolation. Recent work has shown that the efficiency of many acoustic metamaterials can be enhanced by controlling an additional parameter known as Willis coupling, which is analogous to bianisotropy in electromagnetic metamaterials. The magnitude of Willis coupling in a passive acoustic meta-atom has been shown theoretically to have an upper limit, however the feasibility of reaching this limit has not been experimentally investigated. Here we introduce a meta-atom with Willis coupling which closely approaches this theoretical limit, that is much simpler and less prone to thermo-viscous losses than previously reported structures. We perform two-dimensional experiments to measure the strong Willis coupling, supported by numerical calculations. Our meta-atom geometry is readily modeled analytically, enabling the strength of Willis coupling and its peak frequency to be easily controlled.

We present a type of sonic crystal composed with an array of two-dimensional Helmholtz resonators, which in the long-wave regime have both a high relative acoustic refractive index n and at the same time, a small acoustic impedance Z mismatch with air for airborne sound. We analyze the n and Z of such sonic crystals by finite-difference time-domain simulations, and by mapping our results to a corresponding electromagnetic (EM) model, and we find that our Helmholtz resonant sonic crystal has a bigger effective magnetic permeability mu than the conventional rigid-cylinder sonic crystal in its EM counterpart. As a result, a thin convergent lens with very good focusing effect is demonstrated based on our crystal.