We adapt the angular spectrum of plane waves (ASPW) decomposition to numerical simulations of the diffraction of surface-acoustic waves (SAWs) on anisotropic model substrate, such as YZ lithium niobate. We utilize the thin-element decomposition (TED) method, appropriately modified for an anisotropic substrate; we also introduce a novel "average-wavenumber" variation of this scheme; these are numerically found to be mutually consistent. We apply the TED method to simulate wave propagation both in infinite periodic structures of metallized gratings and also in finite gratings. We demonstrate that the ASPW provides a convenient and numerically fast tool for precise diffraction calculations in practical SAW devices which also display structural variations in the lateral direction, perpendicular to the principal direction of wave propagation. Additionally, we compare the present TED method to waveguide theory in an analysis of the role of SAW reflections from the electrodes.
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