Fig. 3: Schematic of superposition of piezoelectrically coupled acoustic waves propagating along x-crystal axis in bulk LN and definition of angular bisectors coordinate system.
From: Twist piezoelectricity: giant electromechanical coupling in magic-angle twisted bilayer LiNbO3
a Acoustic waves solved by Eqs. (1) and (2), arrows in green along ±x-axis in (i) represent the longitudinal acoustic displacement (\({u}_{x}\)), and the coupled transversal electric fields (\({E}_{y}\), \({E}_{z}\)) are shown in gray, noted that the magnetic field components in (i) quasi-longitudinal acoustic wave were not shown. The two piezoelectrical stiffened SH waves (\({u}_{y}\), \({u}_{z}\)) in (ii) and (iii) were in red and blue, respectively, while the coupled longitudinal electric field (\({E}_{x}\)) was marked as arrows along ±x-axis in gray. b Superposition of partial waves in upper and lower LN layers, the coordinate system consists of two angular bisectors between polarization directions of all partial waves were defined in the front view of interface at lower left quarter. c FEM-simulated admittance curves at 116 degrees and 297 degrees. d Distributions of components of stress fields which projected along the two angular bisectors, the black dashed line indicates symmetric and anti-symmetric.
