Active elastic metamaterials for zero-frequency and zero-wave-number band gaps

This paper is a contribution to the Physical Review Applied collection titled Phononics and Metamaterials. We create wave-matter stimuli-responsive metamaterials using optical trapping forces to manipulate mass-spring chains and create zero-frequency and zero-wave-number band gaps: the bosonic nature of phonons, and hence this elastodynamic setting, traditionally prohibits either zero-frequency or zero-wave-number band gaps. Here we generate zero-frequency band gaps using optomechanical interactions within a three-dimensional mass-spring chain by applying an optical trapping force to hold or manipulate a mass in a contactless manner independent of its elastodynamic excitations. Through careful modification of the geometrical parameters in the trapped monoatomic mass-spring chain, we demonstrate the existence of a zero-frequency band gap generated by the optical forces on the masses. The precise control we have over the system allows us to drive another set of masses and springs out of phase with its traveling wave, thereby creating a zero-wave-number band gap. This paper is a contribution to the Physical Review Applied collection titled Phononics and Metamaterials.