Polarization state and level repulsion in two-dimensional phononic crystals and waveguides in the presence of material anisotropy

We investigate the polarization of Bloch waves in two-dimensional piezoelectric phononic crystals and phononic crystal waveguides managed therein. It is found that in addition to the strong coupling induced for waves polarized in the plane of the periodic structuration, a weaker but non-negligible coupling of polarization components originates from material anisotropy. Numerical illustrations are given for an array of air holes in lithium niobate arranged according to a square lattice. It is observed that when a band mostly polarized in-plane gets close to a band mostly polarized out-of-plane, a phenomenon of repelling can occur, that in some instances introduces a local band gap. This interaction is accompanied by a transfer of the polarization state from one band to the other.