Broadband non-reciprocity with robust signal integrity in a triangle-shaped nonlinear 1D metamaterial

In this paper, we propose and numerically study a nonlinear, asymmetric, passive metamaterial that achieves giant non-reciprocity with (i) broadband frequency operation and (ii) robust signal integrity. Previous studies have shown that nonlinearity and geometric asymmetry are necessary to break reciprocity passively. Herein, we employ strongly nonlinear coupling, triangle-shaped asymmetric cell topology, and spatial periodicity to break reciprocity with minimal frequency distortion. To investigate the nonlinear band structure of this system, we propose a new representation, namely a wavenumber-frequency-amplitude band structure, where amplitude-dependent dispersion is quantitatively computed and analyzed. Additionally, we observe and document the new nonlinear phenomenon of time-delayed wave transmission, whereby wave propagation in one direction is initially impeded and resumes only after a duration delay. Based on numerical evidence, we construct a nonlinear reduced-order model (ROM) to further study this phenomenon and show that it is caused by energy accumulation, instability, and a transition between distinct branches of certain nonlinear normal modes of the ROM. The implications and possible practical applications of our findings are discussed.