Phonon propagation dynamics in band-engineered one dimensional phononic crystal waveguides

The phonon propagation dynamics in a phononic crystal waveguide, realized via a suspended one-dimensional membrane array with periodic air holes, is investigated as function of its geometry. The bandstructure of the phononic crystal waveguide can be engineered by modifying the characteristics of the phonon waves by varying the waveguide width and the pitch of the air holes. This enables the phonon transmission bands, the bandgaps, the velocity and the nonlinear dispersion in the phononic crystal to be controlled. Indeed the engineered bandstructure can even be tuned to sustain multiple phonon modes in a given branch which while being spectrally degenerate can be temporally resolved via their differing group velocities. Furthermore, the ability to tune the bandstructure and thus the nonlinear dispersion can be harnessed to efficiently activate nonlinear phenomena such as mechanical four wave mixing. This systematic study reveals the key geometric parameters that enable the phonon transport in phononic crystal waveguides to be fully controlled.