Simulation of waveguiding in SAW devices on substrates with anisotropic slowness and excitation

The 2D P-matrix simulation method is extended to deal with SAW substrates exhibiting a strong anisotropy in slowness and excitation such as YZ-cut lithium niobate.In these substrates the parabolic approximation of the slowness curve is in general not valid. Instead, the exact form of the slowness as obtained from solutions of the basic wave equations of the piezoelectric half space needs to be employed. This has two major implications: Firstly, the imaginary branches cannot be simply determined as the complex roots of a parabolic equation. Secondly, the resulting transversal modes in general are not orthogonal as in the parabolic case. We determined the imaginary branches by analytical continuation of the exact slowness curve. The problem of non-orthonormal basis functions was dealt with by a projection technique including bounded as well as continuum modes. Besides the general anisotropy of the slowness also the anisotropy of excitation is taken into account. Thereto a convolution of the angle dependent excitation characteristic with the transversal charge distribution is determined. The method is verified at the example of very narrow resonators on YZ-cut lithium niobate, which exhibit strong diffraction effects. With respect to the parabolic approximation a significant improvement of simulation quality is observed.