Hyperbolic metamaterials are strongly anisotropic artificial compositematerials at a subwavelength scale and can greatly widen the engineeringfeasibilities for manipulation of wave propagation. However, limited by theempirical structure topologies, the previously reported hyperbolic elasticmetamaterials (HEMMs) suffer from the limitations of relatively narrowfrequency width, inflexible adjusting operating subwavelength scale and beingdifficult to further ameliorate imaging resolution. Here, we develop aninverse-design approach for HEMMs by topology optimization based on theeffective medium theory. We successfully design two-dimensional broadband HEMMssupporting multipolar resonances, and theoretically demonstrate theirdeep-subwavelength imagings for longitudinal waves. Under different prescribedsubwavelength scales, the optimized HEMMs exhibit broadband negative effectivemass densities. Moreover, benefiting from the extreme enhancement of evanescentwaves, an optimized HEMM at the ultra-low frequency can yield a super-highimaging resolution (~{lambda}/64), representing the record in the field ofelastic metamaterials. The proposed computational approach can be easilyextended to design hyperbolic metamaterials for other wave counterparts. Thepresent research may provide a novel design methodology for exploring the HEMMsbased on unrevealed resonances and serve as a useful guide for theultrasonography and general biomedical applications.
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