To calculate the transmission coefficient of ultrasonic waves through a multi-layered medium, a new approach is proposed by expanding it into Debye’s series. Using this formalism, the transmission coefficient can be put in the form of resonance terms series. From this point of view, the relative amplitude of the transmitted wave can be considered as an infinite summation of terms taking into account all possible reflections and refractions on each interface. Our model is then used to investigate interaction between the ultrasonic plane wave and the N-plane-layer structure.
Obviously, the resulting infinite summation has to be reduced to a finite one, according to some level of accuracy. The numerical estimation of the transmission coefficient using the exact expression (Eq. (1)) is then compared to the one of our method in the case of two or three plane-layer structure. The effect of the order of the finite summation on the calculated value of the transmission coefficient is, as well, studied. Finally, our proposed method may be used, with the decomposition into Gaussian beams of a pressure field created by a circular source, to draw a 3D image of the pressure field transmitted through a multilayered structure.

This paper proposes an analytical model to describe the interaction of a bounded ultrasonic beam with an immersed plate. This model, based on the Gaussian beams decomposition, takes into account multiple reflections into the plate. It allows predicting three-dimensional spatial distributions of both transmitted and reflected fields. Thereby, it makes it easy to calculate the average pressure over the receiver’s area taking into account diffraction losses. So the acoustical parameters of the plate can be determined more accurately. A Green’s function for the interaction of an ultrasonic beam with the plate is derived. The obtained results are compared to those given by the angular spectrum approach. A good agreement is seen showing the validity of the proposed model.