Modelling of a BAW to STW reciprocal coupler for combined bulk and surface modes resonators

This paper presents a theoretical analysis of the dispersion equation of a BAW to STW reciprocal coupler. The analysis is based on the coupling of Modes model. We consider horizontal shear modes travelling either along the thickness or along Z´ direction at the surface of a singly rotated cut of a class 32 crystal. Coupling between both kinds of modes are created by purely sinusoidal corrugations. We use Brekhovskikh´s well-known expansion to project the boundary conditions in the coupler´s region onto the average plane of the corrugations. We propose a simple method to select Bloch´s partial waves required for a given ratio of SSBW wavelength to corrugation period. A quasi-analytic solution of the dispersion equation is derived when this ratio remains close to unity and three partial waves are considered. Corresponding numerical results are given. They show that in the case of a STW incident wave, reflection phenomena are very significant in compare with bulk scattering itself