Real-space field of surface sources and the problem of fast leaky wave generation in a piezoelectric half-space

The total solution of the boundary problem for a piezoelectric half-space in the case of oscillating electric and mechanical surface sources is presented as a function of coordinates in terms of a Fourier integral over the real axis of acoustic wave slowness along the surface. In order to investigate the possible leaky wave contributions to the total field, the surface impedance matrix and the Fourier transform of the Green function are uniquely defined for complex values of slowness, using the procedure of analytic continuation from the real axis of slowness and appropriate energy relations. A simple expression for the calculation of plane partial wave group velocities is also proposed. This approach allows the problem to be automatically confined to leaky waves that can be generated by surface sources. The main calculations refer to the new fast leaky waves, which have high phase velocities not far from the velocities of the fastest bulk wave in piezoelectric crystals, and are thus potentially attractive for high frequency surface acoustic wave devices. In the case of lithium tetraborate with Euler angles (0°, 47.3°, 90°), having assumed a simple distribution of surface sources, the total field is exactly calculated in the vicinity of the sources both at the surface and in the bulk region. The asymptotic field far from the sources is also estimated: it is shown that fast leaky waves, ordinary surface acoustic waves, and so-called limiting bulk waves are present, and all contributions in relation to the distance from the sources are compared. It is shown that the fast leaky waves may have different ratios between the magnitudes of components, when propagating in opposite directions. Both free and metallized crystal surfaces are considered. In contrast to the free surface case, it is found that in the case of a metallized surface the new leaky waves give a good approximation of the total field near the sources. This different behavior should be taken into account in practical applications. A comparison with the well-known case of lithium niobate (0°, −49°, 0°), in which the slow leaky waves can be generated, is made. Previously published numerical and experimental results are discussed. Some experimental results are reinterpreted and explained by applying the present approach to a model of the experimental situation considered.