Nonreciprocal energy transmission in short discrete systems with strong spatiotemporal modulations

Abstract

Introducing spatiotemporally varying properties in a phononic lattice can enable nonreciprocal transmission of energy. The hallmark of this phenomenon is the unidirectional energy transmission in infinitely long systems. In short lattices, however, identifying nonreciprocity through differences in transmitted energies (norm bias) becomes challenging because the primary contributor to nonreciprocity is the transmitted phases. Although stronger modulation can achieve a higher norm bias, it can also result in parametric instabilities and trigger large-amplitude oscillations that lead to device failure. To better understand the tradeoff between stability and norm bias in strongly modulated systems, we investigate the parametric stability of a finite one-dimensional lattice with spatiotemporally modulated elasticity. We use Floquet theory to compute the stability charts for strongly modulated systems. Thus, we can identify operating conditions that allow for a relatively large norm bias while maintaining a stable, bounded response.