Theoretical analysis of the second stop-band of Rayleigh wave propagation on periodically corrugated anisotropic substrates

This paper presents a modeling of the dispersion curves for SAW propagation on periodically corrugated substrates in the second stop-band, which involves a strong coupling with BAW propagating both ways, towards- and from the depth of substrate. The proposed modeling uses series of Bloch functions to obey periodic boundary conditions which are integrated over one period of surface profile. The case of finite slope for trapezoidal profile is considered and the effect of anisotropy is taken into account. All equations are written in Lagrangian formalism, which will facilitate a further simulation of static thermal behavior of homogeneous crystalline structures with etched gratings. The paper presents results for energy reflection and conversion coefficients of a SAW-BAW transducer with a finite number of gratings on Y+θ cuts of quartz