Dispersion Engineering by Hybridizing the Back-Folded Soft Mode of Monomode Elastic Metamaterials with Stiff Acoustic Modes

Well-studied examples are phonon polaritons, plasmon polaritons, particle-plasmon polaritons, cavity polaritons, and magnetic resonances at optical frequencies. In all of these cases, the lowest propagating mode couples to a finite-frequency localized resonance.

Herein, the unusual metamaterial phonon dispersion relations arising from the hybridization of an ordinary acoustical phonon mode with a back-folded soft or easy phonon mode of a monomode elastic metamaterial are discussed. Conceptually, the single easy mode can have strictly zero wave velocity. In reality, its wave velocity is very much smaller than that of all other modes.