THE NATURE OF BACKWARD PROPAGATING GUIDED WAVES AND THEIR OCCURRENCE IN SUPPORTED LAYERS

It is well known that the dispersion relations for guided acoustic modes in free standing plates commonly display backward propagation regions, where the group velocity V = partial derivative omega / partial derivative k is opposite in direction to the phase velocity nu = omega / k. At the boundaries of such regions there occur zero group velocity (ZGV), V = 0, modes. Accurate depiction of wave packet propagation and spread in this situation requires that account be taken also of the curvature alpha = partial derivative(2)omega /partial derivative k(2) of the dispersion relation. The generic types of wave packet behavior, dependent on the signs of V, nu and alpha are illustrated in the first part of this paper. In the second part, the existence of backward propagation in supported solid layers is explored. It is shown that for a single layer on an elastic substrate, backward propagation is a rare phenomenon, because it requires that the transverse velocity of the layer be very small compared to that of the substrate. On the other hand, in certain bi-layer structures of importance in the microelectronics industry, the fundamental branch can display backward propagation. This attribute can be exploited in the metrology of these films.