The potential application of Lithium Niobate (LiNbO3) crystal is immense, specifically in the domain of metasurfaces and nano-resonators. However, the practical application of LiNbO3 is impeded due to unreliable
experimental techniques and inaccurate inversion algorithms for material characterization. In the current
research, material characterization of anisotropic crystal is proposed by exploring the wavefield evolution in the
spatial and temporal domains. The presented framework has three major components: a physics-based mathematical model (Christoffel equation), a novel experimental technique, and an inversion algorithm based on
Bayesian filtering. An experimental technique based on Coulomb coupling is devised to visualize the propagation
of ultrasonic waves in an anisotropic crystal. The crystal is characterized by measuring the directional-dependent
acoustic wave velocity from the spatial–temporal information of the wave propagation. The anisotropic
constitutive properties of the crystal are estimated by exploring the wave velocity in the Bayesian filtering algorithm. The proposed algorithm is based on the probabilistic framework that integrates the experimental
measurement in a physics-based mathematical model for optimal state prediction of stiffness tensor through the
Bayesian filtering algorithm. In particular, we utilize the unscented Kalman filter (UKF) in conjunction with the
plane-wave Eigen solution to estimate the constitutive parameters. In the presence of measurement uncertainties,
the performance of the optimal prediction algorithm is illustrated by comparing the estimated parameter with
the corresponding theoretical value. The comparison demonstrates that the proposed inversion algorithm is
efficient and robust and performs satisfactorily even with significant measurement uncertainties
