Phononic crystal surface mode coupling and its use in acoustic Doppler velocimetry

It is numerically shown that surface modes of two-dimensional phononic crystals, which are Bloch modes bound to the interface between the phononic crystal and the surrounding host, can couple back and forth between the surfaces in a length scale determined by the separation of two surfaces and frequency. Supercell band structure computations through the finite-element method reveal that the surface band of an isolated surface splits into two bands which support either symmetric or antisymmetric hybrid modes. When the surface separation is 3.5 times the lattice constant, a coupling length varying between 30 and 48 periods can be obtained which first increases linearly with frequency and, then, decreases rapidly. In the linear regime, variation of coupling length can be used as a means of measuring speeds of objects on the order of 0.1 m/s by incorporating the Doppler shift. Speed sensitivity can be improved by increasing surface separation at the cost of larger device sizes.