Topology optimization of broadband hyperbolic elastic metamaterials with super-resolution imaging

TL;DR

This paper introduces a topology optimization method for broadband hyperbolic elastic metamaterials that achieve super-resolution imaging, overcoming previous limitations in frequency bandwidth and imaging resolution.

Contribution

It develops an inverse-design approach based on effective medium theory to create 2D broadband HEMMs supporting multipolar resonances with record super-resolution imaging capabilities.

Findings

Designed broadband HEMMs support multipolar resonances

Achieved super-high imaging resolution (~λ/64)

Demonstrated deep-subwavelength imaging for longitudinal waves

Abstract

Hyperbolic metamaterials are strongly anisotropic artificial composite materials at a subwavelength scale and can greatly widen the engineering feasibilities for manipulation of wave propagation. However, limited by the empirical structure topologies, the previously reported hyperbolic elastic metamaterials (HEMMs) suffer from the limitations of relatively narrow frequency width, inflexible adjusting operating subwavelength scale and being difficult to further ameliorate imaging resolution. Here, we develop an inverse-design approach for HEMMs by topology optimization based on the effective medium theory. We successfully design two-dimensional broadband HEMMs supporting multipolar resonances, and theoretically demonstrate their deep-subwavelength imagings for longitudinal waves. Under different prescribed subwavelength scales, the optimized HEMMs exhibit broadband negative effective mass densities. Moreover, benefiting from the extreme enhancement of evanescent waves, an optimized HEMM at the ultra-low frequency can yield a super-high imaging resolution (~{\lambda}/64), representing the record in the field of elastic metamaterials. The proposed computational approach can be easily extended to design hyperbolic metamaterials for other wave counterparts. The present research may provide a novel design methodology for exploring the HEMMs based on unrevealed resonances and serve as a useful guide for the ultrasonography and general biomedical applications.