Abstract

Waves propagating along a perfectly conducting plane embedded in a piezoelectric medium are investigated. The theory of such waves is given, and numerical calculations are described. The numerical analysis of trigonal lithium niobate, langasite, and cubic dilithium tetraborate shows that the waves exists for many orientations of the conducting plane with respect to the crystallographic axes, and for many directions of propagation. The wave velocity is close to that of the slowest bulk wave for the same direction, and the piezoelectric coupling coefficient can be as high as 3.60% for lithium niobate, 0.25% for langasite, and 1.60% for dilithium tetraborate. The conditions of existence, and the properties of the piezoelectric interfacial wave (PIW) are presented in the form of tables and a symbolic map (for lithium niobate).

In terms of amplitudes, the ratio of the x component of the electric field and the z component of the electric displacement at the interface (see Fig. 1) is equal to a complex-valued function Z(r), where r is the x component of the slowness (the z component of the slowness is s). The function Z(r) is characteristic of the medium, and not of a particular solution of the field equations.

The x component of the electric field must be equal to zero at the perfectly conducting interface. Therefore, PIW exists if the function Z(r) is equal to zero for a particular r, say r with the subscript p (see Fig. 2), which is the slowness of PIW. This slowness is greater than the cutoff slowness of bulk waves (in Fig.2 denoted by r with the subscript c).

Figures

Fig. 1. The system of coordinates.

Fig. 2. An example of the function Z(r) and the slowness curve for bismuth germanium oxide (Euler angles: 30, 88, 164 degrees).

Fig. 3. Maps of PIW properties for lithium niobate.