Pure shear backward waves in the X-cut and Y-cut piezoelectric plates of potassium niobate

Abstract

The problem of the existence of pure shear backward waves and waves with zero group velocity is investigated for X-cut and Y-cut plates of orthorhombic crystal of potassium niobate, which distinguishes from the other crystals by exceptionally strong piezoelectric effect. The secular equations of the problem are derived in an explicit analytical form and they are studied numerically in the case of crystal-vacuum interface. Two factors contributing to the appearance of backward waves are identified: the negative displacement of the rays of bulk shear waves at oblique reflection from the surface in piezoelectric crystals and the concavity in cross section of the slowness surface for bulk shear waves near the X axis of the potassium niobate plate. The wide frequency ranges of the existence of symmetric and antisymmetric backward waves of the first and second orders are numerically found in the X-cut plate, for which both of these factors affect. To study the dispersion spreading of backward shear wave pulses, it is suggested to apply the parabolic equation corresponding to the second approximation in the dispersion theory. It is demonstrated that the “diffusion” coefficient in this equation vanishes at certain frequencies, leading to significant suppression of the dispersion distortions in the pulses of the waves under study.