Nonreciprocal Wave Propagation in a Continuum-Based Metamaterial with Space-Time Modulated Resonators

Abstract

Breaking reciprocity with spatiotemporal modulation provides an opportunity to design unprecedented optical, acoustic, and mechanical waveguides. A main challenge is to physically realize continuum-based metamaterials whose properties can be rapidly tuned in both space and time at the length and time scales of the propagated waves. We design a tunable elastic metamaterial by embedding in a beam a set of permanent magnets, and placing oscillating electrical coils coaxially adjacent to each magnet. By programming in space and time the ac input of the coils, the magnet-coil effective coupling stiffness is modulated along with the resonance frequency. Distinctly nonreciprocal flexural wave propagation is then experimentally observed. In addition, robust tunability of unidirectional band gaps and wave energy bias are quantitatively analyzed by applying different modulation current amplitudes, material damping coefficients, and modulation frequencies. Both simplified analytical and finite-element-method-based numerical models of the modulated metamaterial are suggested and analyzed in support of the experimental work. Specifically, unidirectional frequency conversions and band gaps due to the second-order mode interactions are discussed for the first time when the large modulation amplitude is implemented. The suggested prototype sheds light on nonreciprocal waveguiding, which could be applied in advanced wave diodes, phononic logic, energy localization, trapping, and harvesting.

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

“…Among the key results, we demonstrate non-reciprocity associated with attenuation and amplification for waves propagating in different directions in 1D and 2D lattices, along with their topological properties associated with winding number of the complex dispersion bands, and localization of bulk modes at edges and corners. While idealized spring-mass lattices where used herein to elucidate the fundamental properties of elastic media with feedback interactions, we highlight that already existing platforms used to experimentally realize active materials with time-modulated properties [32][33][34][35][36] may potentially be modified to support feedback interactions of the type introduced here. The presented results open new possibilities for the design of active meta materials with novel functionalities such as those related to selective wave filtering, splitting, amplification and localization, both in one and two dimensions.…”

“…Topological states have been successfully observed in several platforms [13][14][15][16][17][18][19][20][21], and have been pursued to achieve robust, diffraction-free wave motion. Additional functionalities have been explored in the context of topological pumping [22][23][24][25][26], quasi-periodicity [27][28][29], and non-reciprocal wave propagation in active [30][31][32][33][34][35][36] or passive non-linear [37][38][39][40] systems. These works and the references therein illustrate a wealth of strategies for the manipulation of elastic and acoustic waves, and suggest intriguing possibilities for technological applications in acoustic devices, sensing, energy harvesting, among others.…”

Broadband Asymmetric Propagation in Pillared Meta-Plates

“…A ring resonator with air circulation-flow has been proposed to show nonreciprocal sound transmission among three ports [27]. Instead of fluid motion, spatiotemporal modulation was introduced in phononic crystals or metamaterials to achieve a nonreciprocal acoustic transmission [28][29][30][31][32][33]. Nonlinearity opens another route with frequency conversion in a nonlinear material associated with a band gap material as a filter [34][35][36][37].…”

Nonreciprocal wave propagation and parametric amplification of bulk elastic waves in nonlinear anisotropic materials

“…Their results showed scattering effects such as frequency conversion and generation of harmonics. Several recent works have also reported experimental realization of reciprocity breaking in a time modulated system [5,10].…”