P-Matrix Analysis of Surface Acoustic Waves in Piezoelectric Phononic Crystals

Large time/memory costs have constituted a significant obstacle for accurately analyzing surface acoustic waves (SAWs) in large-sized two-dimensional (2-D) piezoelectric phononic crystals (PnCs). To overcome this obstacle, this study introduces the unit P-matrix and its associated cascading. To obtain an accurate unit P-matrix, the Y parameters of the SAW delay lines were derived using a three-dimensional (3-D) finite-element model (FEM) with and without 2-D piezoelectric PnCs, respectively, on the transmitting path. A time window function was adopted to extract the desired signals from the P-matrix analysis. Then, unit P-matrix cascading was used to obtain SAW propagation parameters for the large-sized piezoelectric PnCs. Using this method, the SAW in aluminum (Al) /128°-YXLiNbO
₃
PnCs was analyzed over 150 periods. Experiments were also conducted. To choose the appropriate size of the unit P-matrix, the variance between experimental results and theoretical results, and time/memory cost were compared for different periods. The results indicate that cascading by unit P-matrix of 25 PnCs periods can be appropriately adopted to accurately derive the SAW propagation parameters over 150 periods. This indicates the accuracy of the unit P-matrix derived by 3-D FEM and the effectiveness of P-matrix analysis.