Two- and three-dimensional elemental charge distributions in leaky acoustic wave devices

In this paper we construct elemental charge distributions for high precision modeling of interdigital transducers on leaky acoustic wave substrates such as the well known cuts of LiNbO₃ and LiTaO ₃. To this end we consider geometrically periodic and arbitrarily driven electrodes with infinite or finite aperture length. We define an elemental structure by considering one “hot” electrode neighbored by an infinite number of “grounded” electrodes. Due to the linearity assumption of the problem, the frequency-dependent elemental charge distribution (ECD) on this structure is sufficient to construct the charge distribution on the electrodes of any periodic IDT with the same pitch-to-mark ratio. To calculate the ECD we consider a certain number (say, ≈30) of appropriately defined multi-phase transducers and determine the corresponding charge distributions by employing our recently developed concept of multi-phase periodic Green´s functions in a method-of-moments application. The weighted superposition of the resulting auxiliary multi-phase field solutions leads to the ECDs which fully account for the leaky wave interaction with the electrodes. The analysis is then applied to several electrode geometries using 41°-cut, X-propagating lithium niobate. We then show how this method can be extended to 2D charge distributions