Time reversal study of ultrasonic waves for anisotropic solids using a Gaussian beam model

Time reversal (TR) of ultrasonic bulk waves in fluids and isotropic solids has been used in many applications including ultrasonic NDE. However, the study of the TR method for anisotropic materials is not well established. In this paper, the full reconstruction of the input signal is investigated for anisotropic media using an analytical formulation, called a modular Gaussian beam (MGB) model. The time reversal operation of this model in the frequency domain is performed by taking the complex conjugate of the Gaussian amplitude and phase received at the TR mirror position. A narrowband reference signal having a particular frequency and number of cycles is then multiplied and the whole signal is inverse Fourier transformed to obtain the time domain signal. The original input signal is seen to be fully restored by the TR process of MGB model and this model can be more generalized to simulate the spatial and temporal focusing effects due to TR process in anisotropic materials.