Underwater acoustic Luneburg lens based on a square-lattice isotropic truss structure

The Luneburg lens plays a vital role in areas such as antennas, radar, and imaging systems owing to its unique omnidirectionality. This focusing behavior is intrinsically related to the isotropy of the materials used to construct the lens. However, achieving the desired refractive index profile and isotropy simultaneously is challenging for underwater acoustic metamaterials, especially for solid-based materials due to their strong multiple scattering effects. Here, we design a two-dimensional (2D) compound lattice truss structure based on square lattice and realize an acoustic Luneburg lens with excellent omnidirectional performance. The effective stiffness matrix is derived using the strain energy equivalence principle. The derivation indicates that as the slenderness ratios of all beams are identical, the proposed structure can achieve isotropy. The refractive index of the structure can be adjusted by changing the beam thickness. Based on this structure, an underwater acoustic Luneburg lens is designed and demonstrated by numerical simulations. The results indicate that the designed Luneburg lens exhibits excellent focusing performance and omnidirectionality. Furthermore, the designed 2D structure lends itself to a direct extension into a three-dimensional configuration without compromising its isotropic properties. This work paves the way for future potential applications in acoustic localization and imaging systems.