Application of exceptional wave theory to materials used in surface acoustic wave devices

Abstract

The exceptional wave theory developed in the last two decades is applied to trigonal crystals, widely used in surface acoustic wave devices: quartz, lithium niobate, and lithium tantalate. For quartz all crystallographic orientations where one of bulk acoustic waves satisfies the stress-free mechanical boundary conditions, have been found and plotted on the stereographic projection of a unit wave normal sphere as ‘‘exceptional wave lines.’’ The possibility of existence and the main features of pure shear, quasishear, and quasilongitudinal exceptional waves are examined in three cut families with Euler angles (0°,θ,0°), (90°,90°,ψ), and (0°,θ,90°). These orientations are analyzed both without and with piezoelectric effect by means of analytical and numerical techniques. The obligatory existence of undamped surface skimming bulk waves or leaky waves is proved for selected cuts of trigonal crystals, such as a well-known 41°-rotated Y cut of lithium niobate. The behavior of these waves is compared in three crystals. A simple relation between elastic moduli of trigonal crystals with point symmetry of 32 or 3m has been derived, which allows the existence of a longitudinal type of exceptional waves. Such waves have been discovered in quartz. They are similar to those found earlier in lithium tetraborate and in both crystals they give rise to piezoelectrically coupled high velocity leaky waves with small attenuation.

Multilayered Structure as a Novel Material for Surface Acoustic Wave Devices: Physical Insight

“…Usually a high velocity LSAW is not suitable for SAW device applications because of its fast attenuation. In some crystals with strong acoustic anisotropy, a high-velocity LSAW degenerates into the quasi-longitudinal LBAW in selected orientations, and low-attenuated LSAW can propagate around such orientations (Naumenko, 1996). For example, such waves exist in some orientations of quartz and LBO.…”

Surface-bulk hybrid mode in 36°-rotated YX cut of lithium tantalate with periodic metal grating

“…In the absence of the piezoelectric effect and mechanical load caused by the grating, the fast shear BAW, propagating in 37°-YX cut, is pure horizontally polarized and leaves the boundary surface free of traction, thus being an ''exceptional'' bulk wave. 1 Therefore, in orientations close to 37°YX cut, within a grating, the bulk wave interacts strongly with the LSAW. This interaction results in parasitic resonances, which degrade SAW filter performance.…”

Hybrid surface-bulk mode in periodic gratings

“…In 128°YX cut of LN, the SBH mode is a result of interaction between a pure SAW and slow shear bulk wave. Since the latter becomes exceptional in 131°YX cut [1], it is strongly radiated in 128°YX cut. In this case, SBH is pure surface mode, having zero propagation loss.…”

“…Propagation velocity of LSAW in the grating also depends on orientation and electrode thickness and its maximum value tends to that of the fast shear surface skimming bulk wave with reducing metal thickness and rotation angle approaching 37° for LT and 41° for LN. In mentioned orientations, fast shear bulk wave becomes SH-polarized and satisfies stress-free mechanical boundary conditions without a metal grating (In SAW theory such a bulk wave is called exceptional) [1]. As a result, the bulk wave is strongly generated by the grating and interacts with the leaky wave, thus giving parasitic response and degradation of SAW filter performance.…”