Transversal Mode Orthogonality in SAW waveguides with transversally varying slowness anisotropy within the scalar field approximation

Within the 2D P-matrix model the scalar feld is identified with a power wave. As has been demonstrated recently, orthogonality of the transversal modes implies power conservation in the 2D P-matrix model [1]. Assuming continuity of the transversal mode profile and its derivative, however, orthogonality is only obtained if the slowness anisotropy is parabolic and constant within the waveguide. Orthogonality conditions for transversal modes within the parabolic approximation of slowness are derived for the case of transversally varying anisotropy constants. Thereto the transversal wave equations are identified with the elastic wave equations of a shear vertical bulk acoustic wave. Continuity of the displacement and the stress held at boundaries of transversal sections is required and therefrom orthogonality conditions of the modes are derived. Translating these conditions to the 2D P-matrix model implies discontinuity of the power waves at transversal section interfaces. For transversally varying anisotropy of the slowness an orthogonal mode description, fulfilling energy conservation within the 2D P-matrix model, was achieved. The new method was tested at a STW cut Quartz.