Abstract
Hyperbolic metamaterials, the highly anisotropic subwavelength media, immensely widen the engineering feasibilities for wave manipulation. However, limited by the empirical structural topologies, the reported hyperbolic elastic metamaterials (HEMMs) suffer from the limitations of the relatively narrow frequency width, inflexible adjustable operating subwavelength scale and difficulty to further improve the imaging resolution. Here, we show an inverse-design strategy for HEMMs by topology optimization. We design broadband single-phase HEMMs supporting multipolar resonances at different prescribed deep-subwavelength scales, and demonstrate the super-resolution imaging for longitudinal waves. Benefiting from the extreme enhancement of the evanescent waves, an optimized HEMM at an ultra-low frequency can yield an imaging resolution of ~λ/64, representing the record in the field of elastic metamaterials. The present research provides a novel and general design methodology for exploring the HEMMs with unrevealed mechanisms and guides the ultrasonography and general biomedical applications.
Highlights
Metamaterials are artificial subwavelength composite materials or structures, which provide many encouraging opportunities to modulate and control the wave propagation with the extraordinary physical properties
Since our present study only focuses on the longitudinal wave propagation, the evident hyperbolic dispersions shown in Fig. 3(a,b) validate that our proposed topology optimization strategy is robust for the longitudinal waves, no matter whether the transverse waves exist or not
Since the hyperbolic dispersion is responsible for the above hyperlensing effect, we present the longitudinal waves propagating in the optimized hyperbolic elastic metamaterials (HEMMs) H1 and H3 at 13 kHz and 2.3 kHz, respectively, to verify the strongly anisotropic wave motions, see Fig. 4
Summary
Metamaterials are artificial subwavelength composite materials or structures, which provide many encouraging opportunities to modulate and control the wave propagation with the extraordinary physical properties. The concept of HMMs has been applied to engineering materials for better controlling the electromagnetic waves[2,5,6,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27] and acoustic waves[3,4,7,9] Unlike their electromagnetic[5] and acoustic[28] counterparts, elastic metamaterials (EMMs)[29,30,31,32,33,34] involve more material parameters and support both longitudinal and transverse wave modes. We demonstrate that a single-phase metamaterial with suitable constraints can exhibit the hyperbolic dispersion in the ultra-low frequency range, implying the comparable capacity of manipulating elastic waves as in the multi-phase local resonance metamaterials. We obtain a super-high, or almost ultimate, imaging resolution (~λ/64) which represents the record in the field of EMMs for longitudinal waves
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