Dispersive higher harmonic generation and enhancement in mechanical metamaterials

Abstract

Higher harmonic generation (HHG) of elastic waves is beneficial for various applications, including engineering nondestructive testing, imaging, therapy, etc. Due to the ubiquity of dispersion in most materials and structures, however, it is usually difficult to simultaneously satisfy the conditions of phase-matching and non-zero energy flux that are needed for high-efficient HHG. Here we propose a mechanical metamaterial with coupled translation-rotation motion and explore its rich dispersion property for the enhancement of two HHGs in arbitrary regions of the acoustic band, i.e., the dispersive second harmonic generation (SHG) and the dispersive third harmonic generation (THG). Besides the phase-matching condition for enhancing SHG, we analytically obtain two phase-matching conditions for THG and reveal that THG is a complex process involving the interaction of multiple waves. By tailoring the dispersion of the metamaterial, the enhanced dispersive SHG and HHG are shown to be able to propagate at an arbitrarily slow group velocity, or even zero velocity, giving rise to localization. The analytical predictions are validated by numerical simulations and experimental tests. This work shows that by combining nonlinearity, mechanical metamaterials can be designed to have advanced capabilities of wave manipulation.