Negative group velocity from resonances in two-dimensional phononic crystals

We investigate two routes to obtain negative group velocity bands in two-dimensional phononic crystal structures. The negative dispersion originates from the resonances of sub-wavelength building blocks and as such, the system should be regarded as acoustic metamaterials. The first kind of acoustic metamaterial exhibits effectively negative bulk modulus and negative mass density simultaneously. Monopolar and dipolar Mie resonances are combined to achieve an effective medium with negative refractive index. In particular, we present a double negative metamaterial for airborne sonic waves. We then show that we can obtain negative group velocity from quadrupole resonances, and the result is explained using the quasi-static approximation. The negative dispersion in quadrupole bands cannot be described by standard effective medium theories even though the frequency can be very low