Non-reciprocity in nonlinear chirality-induced autoparametric periodic structures

Abstract

Periodic structure with spatiotemporally modulated properties has become a rising concern due to its unusual behavior to manipulate non-reciprocal wave propagation. In this paper, by taking advantage of the asymmetric architecture of nonlinear chiral microstructures, we propose a novel autoparametric modulated periodic structure and investigate its global dynamics, non-reciprocal and topological effect. An analytical formulation for deriving the evolution equations and solving the dispersion relations of the autoparametric system is presented by combining the multiple-time scales perturbation method and Floquet-Bloch theorem. Non-reciprocal wave behavior and band topology of the autoparametric modulated periodic structure are analyzed and demonstrated by numerical calculations. We envision that the autoparametric modulated configuration realized by nonlinear chirality may serve as a building block for realizing one-way propagation and mechanical logic gate in passive or active ways.