The pursuit of artificial structures exhibiting unusual acoustic properties is a major scientific endeavor, in which anti-parity-time ($\mathcal{PT}$) symmetry has been coming into view recent years. At the same time, with the emergence of new acoustic metamaterials, the classical Fabry–Perot resonance mode also exhibits fascinating scattering features similar to those of the anti-$\mathcal{PT}$-symmetric system. We derive the generalized relation for the scattering parameters of an acoustic anti-$\mathcal{PT}$-symmetric system with a transfer matrix, including conjugate bidirectional reflection coefficients and pure real feature of transmission coefficient. In the absence of the real or the imaginary (representing gain/loss) part of the refractive index, the anti-$\mathcal{PT}$-symmetric system degrades into a pair of complementary media, resulting in the bidirectional total transmission. Moreover, a Fabry–Perot resonance mode exhibiting conjugate bidirectional reflection coefficients and a pure imaginary transmission coefficient has been demonstrated. Our results are meaningful for guiding the experimental test of an acoustic anti-$\mathcal{PT}$-symmetric system and the design of associated bidirectional response prototype devices.

Impurities usually affect the transmission of acoustic signals, and how to effectively suppress their adverse effects is an important content in the research of acoustic materials. In a recent theoretical proposal, it was pointed out that perfect transmission through impurities can be achieved by adding a gain-loss distribution respecting parity-time ($\mathcal{PT}$) symmetry. In this paper, we demonstrate a similar but not identical way to realize the extraordinary physical property of impurity-shielding, which leads to perfect transmission at the so-called exceptional points. By systematically probing into the system composed of an equivalent medium slab sandwiched by a pair of $\mathcal{PT}$-symmetric metasurfaces, we obtain the two complementary solutions of exceptional points corresponding to perfect transmission. Interestingly, the two solutions of exceptional points coalesce into one when the mass density of the slab approaches zero. At such a critical point, we find that the impurity-shielding effect can be perfectly demonstrated, irrespective of embedded impurities of almost any shape and materials, whether they are Hermitian or non-Hermitian. In addition, the proposed system is frequency independent, indicating that the prototype can work well even in the subwavelength range. Our paper shows that exceptional points can be used to eliminate scattering of impurities in a density-near-zero medium, revealing their potential applications in acoustic sensing, directional imaging, and other related wave disciplines.

Acoustic metasurfaces have shown great promise for applications in many acoustic wave modulation fields, while the use of intelligent optimization algorithms has facilitated the design of acoustic metasurfaces. In this paper, we utilize the stop band properties of phononic crystals to design a metasurface that can achieve both transmission focusing and reflection focusing, as well as a metasurface that utilizes acoustic focusing to filter the incident acoustic wave. In order to achieve the best effect, this paper uses the taboo genetic algorithm to optimize the arrangement order of the structural units controlling different focuses in the acoustic metasurface, and the optimization achieves a good focusing effect, which expands the design of acoustic metasurfaces as well as the application scenarios of acoustic focusing.

In this paper, a simple curled G-type structure is used as the basic unit, which is coded according to its different opening directions, and a composite structure model with special acoustic functions is constructed by different types of assembly methods. The curled G-structure as the basic unit has the characteristics of a Helmholtz resonator, which can resonate at a specific frequency and effectively attenuate the acoustic energy. In the 2 × 2 matrix assembly, there exists an optimal model with an ultra-wide forbidden bandwidth of 510 – 2120 Hz, which also has a high degree of symmetry and the bandgap characteristics of phononic crystals. In the 1 × N matrix assembly, the optimization is performed by genetic algorithm, and N is taken as 4 to achieve tunable acoustic focusing. The simplicity of the curled G-type structure and the simple assembly method make the resulting composite structure have a wide range of potential applications in areas such as noise reduction and imaging.

The special structural design of acoustic metamaterials further extends acoustic properties of the materials. We design a tunable acoustic passive phased array based on double-opening resonant rings, which modulates the acoustic waves only by the rotational angle, making up for the defect of the fixed structure of ordinary metamaterials. The rotation angle is selected based on the generalized Snell’s law, which not only enables focusing in a large frequency band range but also meets the focusing demand of acoustic waves incident at different angles and controls the position of the focal point.