Description of bandgaps opening in chiral phononic crystals by analogy with Thomson scattering

Abstract

Chiral phononic crystals (PnCs) provide unique properties not offered by conventional metamaterial based on classic Bragg scattering and local resonance. However, it is insufficient to only consider the inertial amplification effect to describe its bandgap mechanism due to the absence of the bandgap caused by the chirality in some specific chiral structures. Here, we theoretically and experimentally introduce an analogy with Thomson scattering in electromagnetic waves to characterize the bandgap phenomena in chiral PnCs with translation–rotation coupling. Another phononic structures with translation–translation coupling are proposed to illustrate the universality of the analogy. We evidence that the coupling motion in chiral unit cells is similar to the result of Thomson scattering, which quantitatively formulizing as inertial amplification in theory and, twice elastic Thomson scattering allows the waves in the same polarization mode to superpose in antiphase, which is essence of the bandgap formation. This finding sheds a new light on the physics of the elastodynamic wave manipulation in chiral PnCs, thus opening a definite route for the pragmatic exploitation of chiral PnCs as well as other structures with motion coupling in achieving low-frequency and broad bandgaps.