Parity metamaterials and dynamic acoustic mimicry

Background：

Parity transformation, expressed as P:(x, y, z)→(−x, −y, −z), is a fundamental symmetry operation in physics. In the field of metamaterials, parity transformation has previously been studied in combination with time reversal, leading to PT symmetry and revealing non-Hermitian phenomena such as real eigenvalues and exceptional points. Similar to the relationship between an object and its mirror image, parity transformation establishes a one-to-one correspondence between a structure and its parity-inverted counterpart. However, unlike a mirror operation M:(x, y, z)→(x, y, −z), parity involves an additional 180° rotation, making it fundamentally distinct. To date, parity transformation alone has rarely been applied in metamaterial or meta-atom design. Meanwhile, sonar domes—widely used in underwater environments to protect sonar devices—are typically made of homogeneous materials to ensure broadband, distortion-free transmission. Yet this homogeneity inevitably preserves the sonar’s reflection signature, making acoustic invisibility unattainable. Conventional digital coding metasurfaces can alter reflection characteristics, but usually at the cost of disrupting transmission, thereby undermining sonar functionality. Achieving broadband, undistorted transmission together with tunable reflective camouflage within a single material system has remained a longstanding challenge.

Research Progress：

In this study, we introduced parity transformation alone into metamaterial design. By pairing arbitrary asymmetric meta-atoms with their unique parity-inverted counterparts, they can be utilized to construct parity metamaterials. Under the joint protection of parity transformation and reciprocity, these metamaterials maintain undistorted transmitted wavefronts across ultrabroad frequency ranges. Simultaneously, they allow flexible control of reflected wavefronts, enabling acoustic mimicry of flat, rugged, or periodic terrains—just as an octopus altering its appearance for camouflage and perceiving its environment at the same time (Fig. 1).

The underlying physical principle can be explained through the scattering properties of the paired metastructures (P₁ and P₂). As illustrated in Fig. 1(f), the transmission and reflection coefficients of P₁ are denoted as t and r, respectively. When the system is reciprocal, exchanging the incidence and transmission channels leaves the transmission coefficient unchanged (t′ = t), as shown in Fig. 1(g). In contrast, the reflection coefficient changes significantly (r′ ≠ r). Applying a parity operation, P₁ is transformed into its counterpart P₂, which preserves the same transmission coefficient (t″ = t′ = t) across frequencies and incident angles, while the reflection coefficient differs (r″ = r′ ≠ r). This phase difference between r′ and r over a broad spectrum allows reflection to be tuned without affecting transmission. Consequently, the metamaterial functions as an effectively homogeneous medium in transmission but as an inhomogeneous medium in reflection. By rotating the internal rotors of both P₁ and P₂—while maintaining their parity relation—the reflected acoustic signatures can be dynamically reconfigured while transmitted wavefronts remain intact.

The simulated 3D far-field radiation power patterns after rotor rotation confirm this principle. For instance, when a plane wave at 5680 Hz impinges normally on the parity metamaterial, the transmitted wave consistently aligns with the incident wave, while the reflected wave can be switched from “two-beam reflection” to “specular reflection” (Figs. 2(a) and 2(b)). Near-field results further validate this behavior (Figs. 2(c) and 2(d)). The experimental results are in good agreement with the simulations (Figs. 2(e) to 2(h)). Importantly, when integrated into sonar systems, such materials significantly suppress specular reflection signals, enhancing stealth and achieving “acoustic invisibility” akin to biological camouflage.

Future Prospects：

The introduction of parity metamaterials fills a long-standing gap in applying parity transformation to meta-atom and metamaterial design. By symmetry protection, they achieve ultrabroadband undistorted transmission with tunable reflection control, offering a fundamentally new strategy for acoustic stealth and wave manipulation. Unlike PT-symmetric metamaterials, this approach does not rely on global symmetry or balanced gain–loss conditions, making it robust and broadly applicable. Looking ahead, the concept can be extended to underwater acoustics, elastic waves, and beyond, enabling next-generation applications in sonar camouflage, broadband communication, and adaptive metasurfaces.

Sources: https://spj.science.org/doi/10.34133/research.0826