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-sp ace in the case of oscillating electric and mechanical surface sources is presented as a function of coordinates in terms of a Fourier integ ral over the real axis of acoustic wave slowness along the surface. In order to investigate the possible leaky wave contributions to the tot al field, the surface impedance matrix and the Fourier transform of th e Green function are uniquely defined for complex values of slowness, using the procedure of analytic continuation from the real axis of slo wness and appropriate energy relations. A simple expression for the ca lculation of plane partial wave group velocities is also proposed. Thi s approach allows the problem to be automatically confined to leaky wa ves that can be generated by surface sources. The main calculations re fer to the new fast leaky waves, which have high phase velocities not far from the velocities of the fastest bulk wave in piezoelectric crys tals, and are thus potentially attractive for high frequency surface a coustic wave devices. In the case of lithium tetraborate with Euler an gles (0 degrees, 47.3 degrees, 90 degrees), having assumed a simple di stribution of surface sources, the total field is exactly calculated i n the vicinity of the sources both at the surface and in the bulk regi on. 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 relat ion to the distance from the sources are compared. It is shown that th e fast leaky waves may have different ratios between the magnitudes of components, when propagating in opposite directions. Both free and me tallized crystal surfaces are considered. In contrast to the free surf ace 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 sou rces. This different behavior should be taken into account in practica l applications. A comparison with the well-known case of lithium nioba te (0 degrees, -49 degrees, 0 degrees), in which the slow leaky waves can be generated, is made. Previously published numerical and experime ntal results are discussed. Some experimental results are reinterprete d and explained by applying the present approach to a model of the exp erimental situation considered. (C) 1998 American Institute of Physics .