Continuous Dirac Cone Evolution in Modulated Phononic Crystal

Dirac cones in the band structures of highly symmetric phononic crystal lattices have been extensively studied to produce unique acoustic phenomena. Traditionally, these interesting phenomena produced by Dirac cones occur at fixed frequencies, which cannot be adapted unless significant lattice material or geometric changes occur. To create tunable phononic structures, researchers have successfully utilized Miura-origami to modulate phononic inclusions between discrete high symmetry Bravais lattice configurations. However, the origami transformation between Bravais lattices is a continuous process, meaning that between the high symmetry Bravais lattices, the structure will transform into low symmetry lattices, which are largely unexplored. In this work, we study the perturbation of a hexagonal phononic lattice away from high symmetry. Interestingly, we see the Dirac cone at the K point of the Brillouin zone for the hexagonal lattice persist through the lattice modulation, despite loss of symmetry. Using this insight, we propose an origami phononic structure capable of continuous adjustment and refinement of Dirac cone frequency. Ultimately, we demonstrate continuous Dirac cone modulation for beam forming with the proposed origami phononic structure.