Parametric Instability in Discrete Models of Spatiotemporally Modulated Materials

TL;DR

This paper analyzes parametric instability in discrete models of spatiotemporally modulated materials, revealing how modulation parameters influence stability and highlighting the importance of spatial modulation effects.

Contribution

It provides a detailed computational and analytical investigation of parametric instability, emphasizing the role of spatial modulation often overlooked in previous studies.

Findings

Spatial modulation significantly affects parametric instability.

Analytical expressions for instability frequencies are derived.

Stability depends on modulation parameters, units, and damping.

Abstract

We investigate the phenomenon of parametric instability in discrete models of spatiotemporally modulated materials. These materials are celebrated in part because they exhibit nonreciprocal transmission characteristics. However, parametric instability may occur for strong modulations, or occasionally even at very small modulation amplitudes, and prevent the safe operation of spatiotemporally modulated devices due to an exponential growth in the response amplitude. We use Floquet theory to conduct a detailed computational investigation of parametric instability. We explore the roles of modulation parameters (frequency, amplitude, wavenumber), the number of modulated units, and damping on the stability of the system. We highlight the pivotal role of spatial modulation in parametric instability, a feature that is predominantly overlooked in this context. We use the perturbation method to obtain analytical expressions for modulation frequencies at which the response becomes unstable. We hope that our findings enable and inspire new applications of spatiotemporally modulated materials that operate at higher amplitudes.