Nonlinear wave propagation - a fast 3D simulation method based on quasi-linear approximation of the second harmonic field

A method for fast simulation of nonlinear wave propagation has been developed. It is based on quasi-linear approximation. By using the angular spectrum method, the contribution from an arbitrarily plane was found by back propagation of the wave field from the focal plane, squaring the field, and forward propagation of the result to the observation plane. In the spatial/time Fourier-domain, propagation is performed by a complex exponential factor, whereas the square operation corresponds to a 3D convolution. It turned out that the integration along the ultrasound beam could be solved analytically. The computation in the Fourier-domain was then reduced to a triple-integral. The resulting second harmonic wave in the observation plane was found by (3D) inverse FFT. A simulation program has been implemented in Matlab, using a laptop PC with 1.2 GHz Pentium III processor. Applied to a phased array transducer the simulation time was less than 5 minutes. The implementation of the algorithm was verified by measurements. We observed satisfactory accordance between simulations and measurements.