Dirac-like point at the high symmetric M point in a square phononic crystal

• We realized a Dirac-like point that is located at the high symmetric M point in square phononic crystal.
• The spatial phase experiences no change when waves transmitting through the phononic crystal.
• Acoustic cloaking and wave front shaping effect are demonstrated.

Using the accidental degeneracy of a doubly degenerate state and a single state, a new Dirac-like point was constructed at the high symmetric M point in a two-dimensional phononic crystal (PnC) that consists of a square array of square rods in water. When a plane wave at a frequency near the Dirac-like point impinges on the PnC slab from the left, the spatial phase experiences a minor change in the regions located near the incident interface, but this phase remains uniform in the far field. We also demonstrate two important properties that are correlated to these special field patterns: acoustic cloaking and wavefront reshaping.