Multi-Gaussian Ultrasonic Beam Modeling for Multiple Curved Interfaces—an ABCD Matrix Approach

A multi-Gaussian beam model uses a superposition of Gaussian beams to simulate the waves radiated from an ultrasonic transducer. We show that propagation and reflection/transmission laws for Gaussian beams in fluids and elastic solids can be written in the form of A , B , C , D matrices that are analogous to the A, B, C, D scalars used in Gaussian optics. This representation leads to simple expressions for a Gaussian beam even after that beam has been transmitted or reflected at multiple curved interfaces and produces a highly modular multi-Gaussian beam model that is also computationally very efficient. Some examples of the use of this model for both planar and curved interfaces are given.