Band degeneration and evolution in nonlinear triatomic chain superlattices

Abstract Nonlinear superlattices exhibit unique features allowing for wave manipulations. Despite the increasing attention received, the underlying physical mechanisms and the evolution process of the band structures and bandgaps in strongly nonlinear superlattices remain unclear. Here we establish and examine strongly nonlinear superlattice models (three triatomic models) to show the evolution process of typical nonlinear band structures based on analytical and numerical approaches. We find that the strongly nonlinear superlattices present particular band degeneration and bifurcation, accompanied with the vibration mode transfer in their unit cells. The evolution processes and the physical mechanisms of the band degeneration in different models are clarified with the consideration of the mode transfer. The observed degeneration may occur as the shifting, bifurcating, shortening, merging or disappearing of dispersion curves, all depending on the arrangement of the coupled nonlinear elements. Meanwhile, the dimension of the unit cell reduces, alongside changes in the frequency range and mechanisms (Bragg and local resonance) of the bandgaps. These findings answer some foundamental questions peritinent to the study of nonlinear periodic structures, nonlinear crystals and nonlinear metamaterials, which are of interest to the broad community of physics.