Complete tunneling of acoustic waves between piezoelectric crystals

The coupling of mechanical displacements with electric fields in piezoelectric materials enables tunneling of acoustic waves across vacuum, but the conditions to achieve complete tunneling are still unexplored. This work demonstrates complete tunneling of acoustic waves occurring when leaky surface waves are excited, for arbitrary orientations of the anisotropic crystals. The mechanical displacements in piezoelectric materials carry along macroscopic electric fields, allowing tunneling of acoustic waves across a vacuum gap beyond the charge-charge interaction distance. However, no rigorous proof of complete acoustic wave tunneling has been presented, and the conditions to achieve complete tunneling have not been identified. Here, we demonstrate analytically the condition for such phenomenon for arbitrary anisotropic crystal symmetries and orientations, and that complete transmission of the incoming wave occurs at the excitation frequency of leaky surface waves. We also show that the complete transmission condition can be related to the surface electric impedance and the effective surface permittivity of the piezoelectric material, relevant to realize the complete tunneling experimentally. We support our findings with numerical results for the maximum power transmittance of a slow transverse wave tunneling between identical ZnO crystals. The results show that complete tunneling can be achieved for a large range of orientations.