Symmetry breaking and nonreciprocity in nonlinear phononic crystals: Inspiration from atomic interactions

Abstract

Symmetry breaking is an emerging trend in metamaterial research. To date, studies have primarily focused on breaking spatial or temporal symmetries through active interactions, leading to promising applications in waveguiding and manipulation. In this paper, we explore symmetry-breaking mechanisms by implementing the Morse-type potential function, resulting in asymmetric stiffness with different behaviors in tension and compression. We further answer whether this type of asymmetric stiffness leads to nonreciprocal behavior. Hence, our research focuses on wave propagation in nonlinear one- and two-dimensional phononic crystals using the Morse potential function. Our methodology then involves extracting dispersion curves using the semi-analytic method of multiple scales and numerical Spectro-spatial analysis. Our findings reveal interesting characteristics, including the formation of a bandgap at lower wave numbers (low-frequency waves), asymmetric wave propagation, and wave amplification. These results hold substantial potential for the design of advanced waveguides and wave filters.