Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions

Abstract

We investigate non-Hermitian elastic lattices characterized by non-local feedback interactions. In one-dimensional lattices, proportional feedback produces non-reciprocity associated with complex dispersion relations characterized by gain and loss in opposite propagation directions. For non-local controls, such non-reciprocity occurs over multiple frequency bands characterized by opposite non-reciprocal behavior. The dispersion topology is investigated with focus on winding numbers and non-Hermitian skin effect, which manifests itself through bulk modes localized at the boundaries of finite lattices. In two-dimensional lattices, non-reciprocity is associated with directional wave amplification. Moreover, the combination of skin effect in two directions produces modes that are localized at the corners of finite two-dimensional lattices. Our results describe fundamental properties of non-Hermitian elastic lattices, and suggest new possibilities for the design of meta materials with novel functionalities related to selective wave filtering, amplification and localization. The considered non-local lattices also provide a platform for the investigation of topological phases of non-Hermitian systems.

Acoustic non-Hermitian skin effect from twisted winding topology

“…Though our experiments are carried out in 1D, it is feasible to extend the current design to two or three dimensions, greatly enriching the unique topology in non-Hermitian systems and enabling novel physical phenomena such as high-order NHSE 27 . Furthermore, the feedback mechanism 28,29 is universal and can be applied to design arbitrary lattices with non-Hermitian, time-dependent, and even nonlinear coupling, in acoustics and electromagnetics. In terms of applications, the demonstrated acoustic NHSE paves a way towards highly sensitive acoustic sensors, robust compact one-way waveguides, and novel amplifiers.…”

Non-Hermitian topological coupler for elastic waves

“…Very recently, by combining the above two concepts of topology and non-Hermiticity with metamaterials and photonic/phononic crystals, many special types of topological boundary and corner states have been proposed with optical [42], acoustic [43,44], mechanical [45], and elastic systems [46]. From a fundamental perspective, topological systems with non-Hermiticity can be used to generate new kinds of topological entities such as bulk Fermi arcs [47], bulk-edge correspondence in the non-Hermitian version [48], and non-Hermitian skin effect [49].…”

Realization of active metamaterials with odd micropolar elasticity

“…While Maxwell-Betti reciprocity and momentum conservation are distinct, one can certainly design and build mechanical systems that harness linear or angular momentum sources to achieve violations of Maxwell-Betti reciprocity 7,20,29 . Such approaches, however, inherently involve mechanical coupling to an external medium.…”

“…Recent advances in metamaterial design and prototyping have utilized active components to achieve functionalities such as sensing, lasing, and cloaking [10][11][12]15 , frequency dependent reflectivity 33 , unidirectional wave amplification 7,34,35 , energy harvesting 16 , and analog computation 17 . Nonetheless, all the active non-reciprocal metamaterials so-far realized exhibit either of the following fundamental limitations: the active nonreciprocal effects either vanish from the linear response in the quasistatic limit 33 or they require the presence of background sources of linear or angular momentum 7,29,36 . As a result, their functionalities are largely restricted to finite-frequency control or fundamentally require the sample to be in contact with an additional medium that acts as a momentum sink or source.…”